Supplementary Material
Reliability Generalization of the TTCT: Parameter-Based MASEM
03 October 2023
1 Data Preparation
1.1 Installing and
loading relevant R packages
library(pacman)
pacman::p_load(psych,
reshape2,
metaSEM,
metafor,
robumeta,
clubSandwich,
lavaan,
dplyr,
devtools)
# devtools::install_github("MathiasHarrer/dmetar")
library(dmetar)1.2 Data input
## Data
## Note: If variables are not included, then code them completely as NA,
## including the diagonals (i.e., not 1 but NA in the diagonal for
## completely missing variables)
Auth_mat <-
'
1,
0.54, 1,
0.11, 0.39, 1,
0.08, 0.18, 0.32, 1,
0.36, 0.25, 0.15, -0.07, 1
'
Barkul_mat_a <-
'
1,
0.95, 1,
0.47, 0.56, 1,
0.86, 0.84, 0.56, 1,
0.47, 0.49, 0.38, 0.6, 1
'
Barkul_mat_b <- '
1,
0.89, 1,
0.31, 0.47, 1,
0.64, 0.62, 0.38, 1,
0.28, 0.24, NA, 0.43, 1'
Berman_mat <-
'
1,
0.39, 1,
0.14, -0.23, 1,
-0.38, 0.14, 0.05, 1,
0.004, -0.29, 0.80, 0.25, 1
'
# Adjusted
Boynton_mat <-
'1
0.576, 1,
NA, NA, NA,
NA, NA, NA, NA,
NA, NA, NA, NA, NA
'
Callans_mat <-
'1
0.78, 1,
0.09, -0.01, 1,
0.26, 0.26, 0.27, 1,
0.51, 0.43, 0.42, 0.38, 1
'
#Carter Control Group Pre-Test
Carter_mat_a <-
'1
0.86, 1,
0.31, 0.28, 1,
0.05, 0.05, 0.54, 1,
0.81, 0.72, 0.49, 0.21, 1
'
#Carter Experimental Group Pre-Test
Carter_mat_b <-
'1,
0.82, 1,
0.62, 0.39, 1,
0.51, 0.40, 0.28, 1,
0.68, 0.60, 0.40, 0.33, 1
'
Chi_mat <-'
1,
0.433, 1,
-0.02, 0.42, 1,
0.18, 0.37, 0.42, 1,
-0.19, 0.4, 0.54, 0.45, 1,
'
Cho_mat_F <- '
1,
0.61, 1,
0.42, 0.43, 1,
0.32, 0.21, 0.58, 1,
0.69, 0.33, 0.63, 0.54, 1'
#Changed to Male correlation matrices from total
Cho_mat_M <- '
1,
0.59, 1,
0.26, 0.02, 1,
0.14, 0.31, 0.36, 1,
0.82, 0.69, 0.25, 0.24, 1,
'
Cockcroft_mat <- '
1,
0.29, 1,
0.42, 0.12, 1,
0.24, 0.65, 0.31, 1,
0.18, 0.31, 0.31, 0.46, 1 '
Conway_mat <-
'1,
0.82, 1,
0.45, 0.47, 1,
0.56, 0.56, 0.68, 1,
0.50, 0.43, 0.49, 0.65, 1
'
Crawford_mat <-
'1
0.94, 1,
0.38, 0.44, 1,
0.37, 0.48, 0.38, 1,
0.67, 0.72, 0.65, 0.40, 1
'
Digranes_mat <-
'1,
0.76, 1,
0.17, 0.45, 1,
0.80, 0.71, 0.09, 1,
0.81, 0.79, 0.37, 0.74, 1
'
## Adjusted
Dufner_mat <-
'1,
0.45, 1,
0.11, 0.09, 1,
-0.07, 0.42, 0.16, 1,
NA, NA, NA, NA, NA
'
Fishkin_mat <-
'1
0.60, 1,
0, -0.03, 1,
0.13, 0.11, 0.11, 1,
0.19, 0.26, 0.01, 0.09, 1
'
Forsyth_mat <-
'1,
0.91, 1,
0.56, 0.49, 1,
0.35, 0.40, 0.50, 1,
0.82, 0.77, 0.62, 0.33, 1'
#8th grade
Garcia_mat <-
'1,
0.626, 1,
0.392, 0.45, 1,
0.435, 0.387, 0.495, 1,
0.416, 0.525, 0.32, 0.567, 1'
Gollmar_mat <-
'1,
0.672, 1,
-0.26, 0.019, 1,
-0.13, 0.241, 0.377, 1,
0.188, 0.217, 0.22, 0.296, 1'
## Adjusted
Hamlen_mat <-'
1,
0.816, 1,
NA, NA, NA,
NA, NA, NA, NA,
0.319, 0.247, NA, NA, 1 '
Hokanson_mat <-
'1,
0.79, 1,
0.14, 0.28, 1,
0.32, 0.44, 0.48, 1,
0.48, 0.45, 0.36, 0.36, 1'
Houtz_mat <- '
1,
0.59, 1,
0.27, 0.16, 1,
0.49, 0.27, 0.22, 1,
0.5, 0.34, 0.46, 0.37, 1 '
Humble_mat <-
'1,
0.83, 1,
0.22, 0.28 1
0.44 0.38 0.06 1
0.34 0.25 0.07 0.37 1'
Ibrahim_mat_1 <- '
1,
0.611, 1,
0.524, 0.12, 1,
0.23, 0.246, 0.267, 1,
0.46, 0.485, 0.155, 0.484, 1 '
Kiehn_mat <-
'1,
0.8, 1,
NA, NA, NA,
NA, NA, NA, NA,
NA, NA, NA, NA, NA
'
#Kim (2006b)
Kim_mat_1 <- '
1,
0.844, 1,
0.351, 0.332, 1,
0.196, 0.209, 0.428, 1,
0.666, 0.563, 0.212, 0.443, 1
'
#Kim et al.(2006)
Kim_mat_2a <- '
1,
0.84, 1,
0.45, 0.49, 1,
0.39, 0.38, 0.49, 1,
0.65, 0.65, 0.34, 0.51, 1 '
Kim_mat_2b <- '
1,
0.79, 1,
0.08, 0.15, 1,
0.14, 0.15, 0.3, 1,
0.47, 0.48, 0.17, 0.25, 1 '
Kim_mat_2c <- '
1,
0.86, 1,
0.31, 0.32, 1,
0.22, 0.25, 0.41, 1,
0.66, 0.57, 0.2, 0.4, 1
'
#Kim et al. 2016
Kim_mat_3_a <- '
1,
0.46, 1,
-0.28, 0.24, 1,
0.1, 0.4, 0.51, 1,
-0.28, 0.12, 0.6, 0.66, 1'
Kim_mat_3_b <- '
1,
0.4, 1,
-0.27, 0.23, 1,
0.08, 0.34, 0.5, 1,
-0.22, 0.17, 0.64, 0.72, 1
'
Lew_mat <- '
1,
0.46, 1,
-0.15, 0.04, 1,
0.14, 0.36, 0.24, 1,
NA, NA, NA, NA, NA '
## Adjusted
Miranda_mat <-
'1,
0.49, 1,
0.02, 0.11, 1,
-0.25, -0.30, -0.31, 1,
0.41, 0.20, 0.14, -0.29, 1'
## Adjusted
#1st grade
Morrison_mat_a <-
'1,
0.36, 1,
NA, NA, NA,
NA, NA, NA, NA,
NA, NA, NA, NA, NA'
## Adjusted
#3rd grade
Morrison_mat_b <-
'1,
0.28, 1,
NA, NA, NA,
NA, NA, NA, NA,
NA, NA, NA, NA, NA'
## Adjusted
#5th grade
Morrison_mat_c <-
'1,
0.42, 1,
NA, NA, NA,
NA, NA, NA, NA,
NA, NA, NA, NA, NA'
Nguyen_mat <-
'1,
0.75, 1,
0.11, 0.09, 1,
0.17, 0.10, 0.15, 1,
0.38, 0.34, 0.13, 0.03, 1'
Zbarskaya_mat <-
'1,
0.614, 1,
0.008, 0.135, 1,
0.168, 0.327, 0.504, 1,
0.189, 0.153, 0.225, 0.442, 1'
#Children's house
Rose_mat_a <-
'1,
0.81, 1,
0.07, 0.27, 1,
0.66, 0.62, 0.57, 1,
-0.05, -0.06, -0.19, -0.12, 1'
#Montessori
Rose_mat_b <-
'1,
0.67, 1,
0.05, 0.13, 1,
0.56, 0.16, -0.30, 1,
0.34, 0.12, 0.43, 0.19, 1'
Roskos_mat_Y <-'
1,
0.26, 1,
0.15, 0.08, 1,
0.37, 0.47, 0.2, 1,
0.53, 0.31, 0.47, 0.37, 1 '
Roskos_mat_O <- '
1,
0.16, 1,
-0.06, -0.02, 1,
0.06, 0.25, 0.04, 1,
0.14, 0.29, 0.36, 0.47, 1
'
Samuels_mat <-
'1,
0.75, 1,
-0.11, 0.02, 1,
0.10, 0.24, 0.48, 1,
-0.16, -0.06, 0.07, 0.24, 1'
Shore_mat <-
'1,
0.26, 1,
-0.01, 0.33, 1,
-0.12, 0.70, 0.30, 1,
-0.29, 0.12, 0.54, 0.34, 1'
Stephens_mat <-
'1,
0.86, 1,
0.17, 0.16, 1,
0.33, 0.30, 0.12, 1,
0.65, 0.60, 0.30, 0.31, 1'
#Control Pre-Test
Storer_mat_a <-
'1,
0.77, 1,
0.11, 0.29, 1,
0.28, 0.19, 0.35, 1,
0.33, 0.49, -0.02, -0.14, 1'
#Treatment Pre-Test
Storer_mat_b <-
'1,
0.73, 1,
0.23, 0.20, 1,
0.43, 0.55, 0.29, 1,
0.57, 0.48, 0.40, 0.25, 1'
Tannehill_mat <-
'1,
0.84, 1,
0.35, 0.41, 1,
0.28, 0.36, 0.38, 1,
0.35, 0.33, 0.39, 0.41, 1'
Tisone_mat <-
'1,
0.68, 1,
-0.03, -0.12, 1,
0.15, 0.26, 0.30, 1,
0.13, 0.35, 0.11, 0.53, 1'
Trigani_mat <-
'1,
0.72, 1,
0.28, 0.24, 1,
0.17, 0.26, 0.37, 1,
0.69, 0.47, 0.52, 0.16, 1'
Voss_mat <-
'1,
0.71, 1,
0.43, 0.51, 1,
0.38, 0.44, 0.53, 1,
0.65, 0.79, 0.59, 0.42, 1'
Warne_mat <-
'1,
0.74, 1,
0.40, 0.37, 1,
0.35, 0.37, 0.43, 1,
0.63, 0.50, 0.50, 0.26, 1'
Watson_mat <-
'1,
0.64, 1,
NA, NA, NA,
0.41, 0.40, NA, 1,
NA, NA, NA, NA, NA'
Yoon_mat <-
'1,
0.73, 1,
-0.16, 0.08, 1,
0.08, 0.29, 0.47, 1,
0.09, 0.28, 0.53, 0.66, 1'
Zhang_mat <-
'1,
0.78, 1,
0.09, 0.15, 1,
0.25, 0.24, 0.33, 1,
0.83, 0.70, 0.06, 0.21, 1'
## New matrices after the update in 2023
Acar_mat <-
'1,
0.65, 1,
0.188, 0.274, 1,
0.338, 0.409, 0.363, 1,
0.529, 0.477, 0.413, 0.305, 1'
Gao_mat <-
'1,
0.31, 1,
0.28, 0.34, 1,
0.39, 0.41, 0.25, 1,
0.28, 0.17, 0.26, 0.31, 1'
Liu_mat <-
'1,
0.94, 1,
0.32, 0.32, 1,
0.49, 0.48, 0.66, 1,
0.41, 0.39, 0.62, .67, 1'
Wan_mat <-
'1,
0.27, 1,
0.24, 0.35, 1,
0.17, 0.19, 0.27, 1,
0.19, 0.14, 0.12, 0.35, 1'
Balcia_mat <-
'1,
0.292, 1,
0, 0.221, 1,
0.176, 0.148, 0.304, 1,
-0.117, 0.154, 0.035, 0.047, 1'
Balcib_mat <-
'1,
0.43, 1,
0.116, 0.166, 1,
0.267, 0.225, 0.363, 1,
-0.19, 0.016, -0.128, -0.107, 1'
Acaretal_mat <-
'1,
0.763, 1,
0.089, 0.21, 1,
0.294, 0.367, 0.469, 1,
0.567, 0.54, 0.277, 0.318, 1'
#This names columns and rows for correlation matrices
Auth_mat1 <-char2num(Auth_mat)
Auth <- getCov(Auth_mat1, diag=T)
colnames(Auth) <- c("Fl","Or", "El","Ab","Res")
rownames(Auth) <- c("Fl","Or", "El","Ab","Res")
#Barkul
Barkul_mat1 <-char2num(Barkul_mat_a)
Barkul <- getCov(Barkul_mat1, diag=T)
colnames(Barkul) <- c("Fl","Or", "El","Ab","Res")
rownames(Barkul) <- c("Fl","Or", "El","Ab","Res")
Barkul_mat2 <-char2num(Barkul_mat_b)
Barkul2 <- getCov(Barkul_mat2, diag=T)
colnames(Barkul2) <- c("Fl","Or", "El","Ab","Res")
rownames(Barkul2) <- c("Fl","Or", "El","Ab","Res")
Berman_mat1 <-char2num(Berman_mat)
Berman <- getCov(Berman_mat1, diag=T)
colnames(Berman) <- c("Fl","Or", "El","Ab","Res")
rownames(Berman) <- c("Fl","Or", "El","Ab","Res")
Boynton_mat1 <-char2num(Boynton_mat)
Boynton <- getCov(Boynton_mat1, diag=T)
colnames(Boynton) <- c("Fl","Or", "El","Ab","Res")
rownames(Boynton) <- c("Fl","Or", "El","Ab","Res")
Callans_mat1 <-char2num(Callans_mat)
Callans <- getCov(Callans_mat1, diag=T)
colnames(Callans) <- c("Fl","Or", "El","Ab","Res")
rownames(Callans) <- c("Fl","Or", "El","Ab","Res")
Carter_mat1 <-char2num(Carter_mat_a)
Carter_a <- getCov(Carter_mat1, diag=T)
colnames(Carter_a) <- c("Fl","Or", "El","Ab","Res")
rownames(Carter_a) <- c("Fl","Or", "El","Ab","Res")
Carter_mat2 <-char2num(Carter_mat_b)
Carter_b <- getCov(Carter_mat2, diag=T)
colnames(Carter_b) <- c("Fl","Or", "El","Ab","Res")
rownames(Carter_b) <- c("Fl","Or", "El","Ab","Res")
Chi_mat1 <-char2num(Chi_mat)
Chi <- getCov(Chi_mat1, diag=T)
colnames(Chi) <- c("Fl","Or", "Ab","El","Res")
rownames(Chi) <- c("Fl","Or", "Ab","El","Res")
Cho_mat1_F <-char2num(Cho_mat_F)
Cho_F <- getCov(Cho_mat1_F, diag=T)
colnames(Cho_F) <- c("Fl","Or", "Ab","El","Res")
rownames(Cho_F) <- c("Fl","Or", "Ab","El","Res")
Cho_mat1_M <-char2num(Cho_mat_M)
Cho_M <- getCov(Cho_mat1_M, diag=T)
colnames(Cho_M) <- c("Fl","Or", "Ab","El","Res")
rownames(Cho_M) <- c("Fl","Or", "Ab","El","Res")
Cockcroft_mat1 <-char2num(Cockcroft_mat)
Cockcroft <- getCov(Cockcroft_mat1, diag=T)
colnames(Cockcroft) <- c("Fl","Or", "Ab","El","Res")
rownames(Cockcroft) <- c("Fl","Or", "Ab","El","Res")
Conway_mat1 <-char2num(Conway_mat)
Conway <- getCov(Conway_mat1, diag=T)
colnames(Conway) <- c("Fl","Or", "El","Ab","Res")
rownames(Conway) <- c("Fl","Or", "El","Ab","Res")
Crawford_mat1 <-char2num(Crawford_mat)
Crawford <- getCov(Crawford_mat1, diag=T)
colnames(Crawford) <- c("Fl","Or", "El","Ab","Res")
rownames(Crawford) <- c("Fl","Or", "El","Ab","Res")
Digranes_mat1 <-char2num(Digranes_mat)
Digranes <- getCov(Digranes_mat1, diag=T)
colnames(Digranes) <- c("Fl","Or", "El","Ab","Res")
rownames(Digranes) <- c("Fl","Or", "El","Ab","Res")
Dufner_mat1 <-char2num(Dufner_mat)
Dufner <- getCov(Dufner_mat1, diag=T)
colnames(Dufner) <- c("Fl","Or", "El","Ab","Res")
rownames(Dufner) <- c("Fl","Or", "El","Ab","Res")
Fishkin_mat1 <-char2num(Fishkin_mat)
Fishkin <- getCov(Fishkin_mat1, diag=T)
colnames(Fishkin) <- c("Fl","Or", "El","Ab","Res")
rownames(Fishkin) <- c("Fl","Or", "El","Ab","Res")
Forsyth_mat1 <-char2num(Forsyth_mat)
Forsyth <- getCov(Forsyth_mat1, diag=T)
colnames(Forsyth) <- c("Fl","Or", "El","Ab","Res")
rownames(Forsyth) <- c("Fl","Or", "El","Ab","Res")
Garcia_mat1 <-char2num(Garcia_mat)
Garcia <- getCov(Garcia_mat1, diag=T)
colnames(Garcia) <- c("Fl","Or", "El","Ab","Res")
rownames(Garcia) <- c("Fl","Or", "El","Ab","Res")
Gollmar_mat1 <-char2num(Gollmar_mat)
Gollmar <- getCov(Gollmar_mat1, diag=T)
colnames(Gollmar) <- c("Fl","Or", "El","Ab","Res")
rownames(Gollmar) <- c("Fl","Or", "El","Ab","Res")
Hamlen_mat1 <-char2num(Hamlen_mat)
Hamlen<- getCov(Hamlen_mat1, diag=T)
colnames(Hamlen) <- c("Fl","Or", "Ab","El","Res")
rownames(Hamlen) <- c("Fl","Or", "Ab","El","Res")
Hokanson_mat1 <-char2num(Hokanson_mat)
Hokanson <- getCov(Hokanson_mat1, diag=T)
colnames(Hokanson) <- c("Fl","Or", "El","Ab","Res")
rownames(Hokanson) <- c("Fl","Or", "El","Ab","Res")
Houtz_mat1 <-char2num(Houtz_mat)
Houtz<- getCov(Houtz_mat1, diag=T)
colnames(Houtz) <- c("Fl","Or", "Ab","El","Res")
rownames(Houtz) <- c("Fl","Or", "Ab","El","Res")
Humble_mat1 <-char2num(Humble_mat)
Humble <- getCov(Humble_mat1, diag=T)
colnames(Humble) <- c("Fl","Or", "El","Ab","Res")
rownames(Humble) <- c("Fl","Or", "El","Ab","Res")
Ibrahim_mat1 <-char2num(Ibrahim_mat_1)
Ibrahim<- getCov(Ibrahim_mat1, diag=T)
colnames(Ibrahim) <- c("Fl","Or", "Ab","El","Res")
rownames(Ibrahim) <- c("Fl","Or", "Ab","El","Res")
Kiehn_mat1 <-char2num(Kiehn_mat)
Kiehn <- getCov(Kiehn_mat1, diag=T)
colnames(Kiehn) <- c("Fl","Or", "El","Ab","Res")
rownames(Kiehn) <- c("Fl","Or", "El","Ab","Res")
Kim_1_mat1 <-char2num(Kim_mat_1)
Kim_1<- getCov(Kim_1_mat1, diag=T)
colnames(Kim_1) <- c("Fl","Or", "Ab","El","Res")
rownames(Kim_1) <- c("Fl","Or", "Ab","El","Res")
Kim_2a_mat1 <-char2num(Kim_mat_2a)
Kim_2a<- getCov(Kim_2a_mat1, diag=T)
colnames(Kim_2a) <- c("Fl","Or", "Ab","El","Res")
rownames(Kim_2a) <- c("Fl","Or", "Ab","El","Res")
Kim_2b_mat1 <-char2num(Kim_mat_2b)
Kim_2b<- getCov(Kim_2b_mat1, diag=T)
colnames(Kim_2b) <- c("Fl","Or", "Ab","El","Res")
rownames(Kim_2b) <- c("Fl","Or", "Ab","El","Res")
Kim_2c_mat1 <-char2num(Kim_mat_2c)
Kim_2c<- getCov(Kim_2c_mat1, diag=T)
colnames(Kim_2c) <- c("Fl","Or", "Ab","El","Res")
rownames(Kim_2c) <- c("Fl","Or", "Ab","El","Res")
Kim_3_mat1 <-char2num(Kim_mat_3_a)
Kim_3a <- getCov(Kim_3_mat1, diag=T)
colnames(Kim_3a) <- c("Fl","Or", "Ab","El","Res")
rownames(Kim_3a) <- c("Fl","Or", "Ab","El","Res")
Kim_3_mat2 <-char2num(Kim_mat_3_b)
Kim_3b <- getCov(Kim_3_mat2, diag=T)
colnames(Kim_3b) <- c("Fl","Or", "Ab","El","Res")
rownames(Kim_3b) <- c("Fl","Or", "Ab","El","Res")
Lew_mat1 <-char2num(Lew_mat)
Lew<- getCov(Lew_mat1, diag=T)
colnames(Lew) <- c("Fl","Or", "Ab","El","Res")
rownames(Lew) <- c("Fl","Or", "Ab","El","Res")
Miranda_mat1 <-char2num(Miranda_mat)
Miranda <- getCov(Miranda_mat1, diag=T)
colnames(Miranda) <- c("Fl","Or", "El","Ab","Res")
rownames(Miranda) <- c("Fl","Or", "El","Ab","Res")
Morrison_mat1 <-char2num(Morrison_mat_a)
Morrison_a <- getCov(Morrison_mat1, diag=T)
colnames(Morrison_a) <- c("Fl","Or", "El","Ab","Res")
rownames(Morrison_a) <- c("Fl","Or", "El","Ab","Res")
Morrison_mat2 <-char2num(Morrison_mat_b)
Morrison_b <- getCov(Morrison_mat2, diag=T)
colnames(Morrison_b) <- c("Fl","Or", "El","Ab","Res")
rownames(Morrison_b) <- c("Fl","Or", "El","Ab","Res")
Morrison_mat3 <-char2num(Morrison_mat_c)
Morrison_c <- getCov(Morrison_mat3, diag=T)
colnames(Morrison_c) <- c("Fl","Or", "El","Ab","Res")
rownames(Morrison_c) <- c("Fl","Or", "El","Ab","Res")
Nguyen_mat1 <-char2num(Nguyen_mat)
Nguyen <- getCov(Nguyen_mat1, diag=T)
colnames(Nguyen) <- c("Fl","Or", "El","Ab","Res")
rownames(Nguyen) <- c("Fl","Or", "El","Ab","Res")
Zbarskaya_mat1 <-char2num(Zbarskaya_mat)
Zbarskaya <- getCov(Zbarskaya_mat1, diag=T)
colnames(Zbarskaya) <- c("Fl","Or", "El","Ab","Res")
rownames(Zbarskaya) <- c("Fl","Or", "El","Ab","Res")
#Children's Place
Rose_mat1 <- char2num(Rose_mat_a)
Rose <- getCov(Rose_mat1, diag=T)
colnames(Rose) <- c("Fl","Or", "El","Ab","Res")
rownames(Rose) <- c("Fl","Or", "El","Ab","Res")
#Montessori
Rose_mat2 <- char2num(Rose_mat_b)
Rose_b <- getCov(Rose_mat2, diag=T)
colnames(Rose_b) <- c("Fl","Or", "El","Ab","Res")
rownames(Rose_b) <- c("Fl","Or", "El","Ab","Res")
Roskos_mat1_Y <-char2num(Roskos_mat_Y)
Roskos_Y<- getCov(Roskos_mat1_Y, diag=T)
colnames(Roskos_Y) <- c("Fl","Or", "Ab","El","Res")
rownames(Roskos_Y) <- c("Fl","Or", "Ab","El","Res")
Roskos_mat1_O <-char2num(Roskos_mat_O)
Roskos_O<- getCov(Roskos_mat1_O, diag=T)
colnames(Roskos_O) <- c("Fl","Or", "Ab","El","Res")
rownames(Roskos_O) <- c("Fl","Or", "Ab","El","Res")
Samuels_mat1 <-char2num(Samuels_mat)
Samuels <- getCov(Samuels_mat1, diag=T)
colnames(Samuels) <- c("Fl","Or", "El","Ab","Res")
rownames(Samuels) <- c("Fl","Or", "El","Ab","Res")
Shore_mat1 <-char2num(Shore_mat)
Shore <- getCov(Shore_mat1, diag=T)
colnames(Shore) <- c("Fl","Or", "El","Ab","Res")
rownames(Shore) <- c("Fl","Or", "El","Ab","Res")
Stephens_mat1 <-char2num(Stephens_mat)
Stephens <- getCov(Stephens_mat1, diag=T)
colnames(Stephens) <- c("Fl","Or", "El","Ab","Res")
rownames(Stephens) <- c("Fl","Or", "El","Ab","Res")
Storer_mat1 <- char2num(Storer_mat_a)
Storer_a <- getCov(Rose_mat1, diag=T)
colnames(Storer_a) <- c("Fl","Or", "El","Ab","Res")
rownames(Storer_a) <- c("Fl","Or", "El","Ab","Res")
Storer_mat2 <- char2num(Storer_mat_b)
Storer_b <- getCov(Storer_mat2, diag=T)
colnames(Storer_b) <- c("Fl","Or", "El","Ab","Res")
rownames(Storer_b) <- c("Fl","Or", "El","Ab","Res")
Tannehill_mat1 <-char2num(Tannehill_mat)
Tannehill <- getCov(Tannehill_mat1, diag=T)
colnames(Tannehill) <- c("Fl","Or", "El","Ab","Res")
rownames(Tannehill) <- c("Fl","Or", "El","Ab","Res")
Tisone_mat1 <-char2num(Tisone_mat)
Tisone <- getCov(Tisone_mat1, diag=T)
colnames(Tisone) <- c("Fl","Or", "El","Ab","Res")
rownames(Tisone) <- c("Fl","Or", "El","Ab","Res")
Trigani_mat1 <-char2num(Trigani_mat)
Trigani <- getCov(Trigani_mat1, diag=T)
colnames(Trigani) <- c("Fl","Or", "El","Ab","Res")
rownames(Trigani) <- c("Fl","Or", "El","Ab","Res")
Voss_mat1 <-char2num(Voss_mat)
Voss <- getCov(Voss_mat1, diag=T)
colnames(Voss) <- c("Fl","Or", "El","Ab","Res")
rownames(Voss) <- c("Fl","Or", "El","Ab","Res")
Warne_mat1 <-char2num(Warne_mat)
Warne <- getCov(Warne_mat1, diag=T)
colnames(Warne) <- c("Fl","Or", "El","Ab","Res")
rownames(Warne) <- c("Fl","Or", "El","Ab","Res")
Watson_mat1 <-char2num(Watson_mat)
Watson <- getCov(Watson_mat1, diag=T)
colnames(Watson) <- c("Fl","Or", "El","Ab","Res")
rownames(Watson) <- c("Fl","Or", "El","Ab","Res")
Yoon_mat1 <-char2num(Yoon_mat)
Yoon <- getCov(Yoon_mat1, diag=T)
colnames(Yoon) <- c("Fl","Or", "El","Ab","Res")
rownames(Yoon) <- c("Fl","Or", "El","Ab","Res")
Zhang_mat1 <-char2num(Zhang_mat)
Zhang <- getCov(Zhang_mat1, diag=T)
colnames(Zhang) <- c("Fl","Or", "El","Ab","Res")
rownames(Zhang) <- c("Fl","Or", "El","Ab","Res")
## New studies after the update in 2023
Acar_mat1 <-char2num(Acar_mat)
Acar <- getCov(Acar_mat1, diag=T)
colnames(Acar) <- c("Fl","Or", "El","Ab","Res")
rownames(Acar) <- c("Fl","Or", "El","Ab","Res")
Acaretal_mat1 <-char2num(Acaretal_mat)
Acaretal <- getCov(Acaretal_mat1, diag=T)
colnames(Acaretal) <- c("Fl","Or", "El","Ab","Res")
rownames(Acaretal) <- c("Fl","Or", "El","Ab","Res")
Balcia_mat1 <-char2num(Balcia_mat)
Balcia <- getCov(Balcia_mat1, diag=T)
colnames(Balcia) <- c("Fl","Or", "El","Ab","Res")
rownames(Balcia) <- c("Fl","Or", "El","Ab","Res")
Balcib_mat1 <-char2num(Balcib_mat)
Balcib <- getCov(Balcib_mat1, diag=T)
colnames(Balcib) <- c("Fl","Or", "El","Ab","Res")
rownames(Balcib) <- c("Fl","Or", "El","Ab","Res")
Gao_mat1 <-char2num(Gao_mat)
Gao <- getCov(Gao_mat1, diag=T)
colnames(Gao) <- c("Fl","Or", "El","Ab","Res")
rownames(Gao) <- c("Fl","Or", "El","Ab","Res")
Liu_mat1 <-char2num(Liu_mat)
Liu <- getCov(Liu_mat1, diag=T)
colnames(Liu) <- c("Fl","Or", "El","Ab","Res")
rownames(Liu) <- c("Fl","Or", "El","Ab","Res")
Wan_mat1 <-char2num(Wan_mat)
Wan <- getCov(Wan_mat1, diag=T)
colnames(Wan) <- c("Fl","Or", "El","Ab","Res")
rownames(Wan) <- c("Fl","Or", "El","Ab","Res")
data <- list(Auth, Barkul, Barkul2, Berman, Boynton, Callans,
Carter_a, Carter_b, Chi, Cho_F, Cho_M, Cockcroft,
Conway, Crawford,
Digranes, Dufner, Fishkin, Forsyth, Garcia, Gollmar,
Hamlen, Hokanson, Houtz, Humble, Ibrahim,
Kiehn, Kim_1, Kim_2a, Kim_2b, Kim_2c, Kim_3a, Kim_3b,
Lew, Miranda, Morrison_a, Morrison_b, Morrison_c,
Nguyen,Zbarskaya, Rose, Rose_b,
Roskos_Y, Roskos_O, Samuels, Shore, Stephens,
Storer_a, Storer_b, Tannehill, Tisone, Trigani,
Voss, Warne, Watson, Yoon, Zhang,
Acar, Acaretal, Balcia, Balcib, Gao, Liu, Wan)
n <- c(30, 599, 147, 13, 62, 60, 24, 24, 203, 24, 35, 36, 25, 21, 17, 98, 116, 45, 95, 128, 118, 1758,
42, 125, 99, 89, 500, 1000, 1000, 1000, 125, 137, 135, 12, 184, 122, 121, 187, 125, 19, 12,
39, 31, 51, 18, 84, 43, 46, 199, 24, 107, 120, 432, 6, 163, 1067,
477, 319, 1047, 95, 264, 105, 375)
names <- c("Auth" , "Barkul" , "Barkul2" , "Berman" , "Boynton" , "Callans" ,
"Carter_a" , "Carter_b" , "Chi" , "Cho_F" , "Cho_M" , "Cockcroft" ,
"Conway" , "Crawford",
"Digranes" , "Dufner" , "Fishkin" , "Forsyth" , "Garcia" , "Gollmar" ,
"Hamlen" , "Hokanson" , "Houtz" , "Humble" , "Ibrahim",
"Kiehn" , "Kim_1" , "Kim_2a" , "Kim_2b" , "Kim_2c" , "Kim_3a" , "Kim_3b" ,
"Lew" , "Miranda" , "Morrison_a" , "Morrison_b" , "Morrison_c" ,
"Nguyen" , "Zbarskaya" , "Rose" , "Rose_b" ,
"Roskos_Y" , "Roskos_O" , "Samuels" , "Shore" , "Stephens" ,
"Storer_a" , "Storer_b" , "Tannehill" , "Tisone" , "Trigani" ,
"Voss" , "Warne" , "Watson" , "Yoon" , "Zhang",
"Acar", "Acaretal", "Balcia", "Balcib", "Gao", "Liu", "Wan")
study.names <- c("Auth" , "Barkul" , "Barkul2" , "Berman" , "Boynton" , "Callans" ,
"Carter" , "Carter" , "Chi" , "Cho" , "Cho" , "Cockcroft" ,
"Conway" , "Crawford",
"Digranes" , "Dufner" , "Fishkin" , "Forsyth" , "Garcia" , "Gollmar" ,
"Hamlen" , "Hokanson" , "Houtz" , "Humble" , "Ibrahim",
"Kiehn" , "Kim_1" , "Kim_2" , "Kim_2" , "Kim_2" , "Kim_3" , "Kim_3" ,
"Lew" , "Miranda" , "Morrison" , "Morrison" , "Morrison" ,
"Nguyen" , "Zbarskaya" , "Rose" , "Rose" ,
"Roskos" , "Roskos" , "Samuels" , "Shore" , "Stephens" ,
"Storer" , "Storer" , "Tannehill" , "Tisone" , "Trigani" ,
"Voss" , "Warne" , "Watson" , "Yoon" , "Zhang",
"Acar", "Acaretal", "Balcia", "Balcib", "Gao", "Liu", "Wan")
names(data) <- study.names
## Possible moderators
## Age group
## Code: 1 = Adults, 0 = Kindergarten up to High/Middle school
adults <- c(1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,
0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,
0,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0,
0,1,0,1,1,0,1,0,
1, 0, 0, 0, 1, 0, 1)
## Evidence against discriminant validity
## Coding: 1 = evidence present, 0 = evidence not present/reported
validity <- c(0,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,
0,0,
1, 1, 0, 1, 0, 0, 0)
## Test forms
## Subset the data
formsAB <- c(NA,"A","A","A","Both","A","A","A","A",
NA,NA,"B","A","A","A","B","A","Both",
"B","A","A","A","B","A","A","A","A","A",
"A","A","A","A",NA,"A","A","A","A","A","A",
"A","B","B","A","A","A","A","A","A","A","A",
"A","A","B","A","A","A",
"A", "A", "Both", "Both", NA, NA, NA)
forms <- as.vector(as.numeric(which(formsAB %in% c(NA, "Both")))) # which gives the positions of codes 1
## Standardized test scores
## Subset the data
scoring <- c(1,0,0,NA,0,1,0,0,0,0,0,0,1,1,0,0,0,
1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,NA,
NA,NA,1,0,0,1,1,1,0,1,1,1,1,0,1,1,0,
0,1,1,0,
0, 0, 0, 0, NA, NA, NA)
scores <- as.vector(as.numeric(which(scoring %in% NA))) # which gives the positions of codes 1
head(data, 5)## $Auth
## Fl Or El Ab Res
## Fl 1.00 0.54 0.11 0.08 0.36
## Or 0.54 1.00 0.39 0.18 0.25
## El 0.11 0.39 1.00 0.32 0.15
## Ab 0.08 0.18 0.32 1.00 -0.07
## Res 0.36 0.25 0.15 -0.07 1.00
##
## $Barkul
## Fl Or El Ab Res
## Fl 1.00 0.95 0.47 0.86 0.47
## Or 0.95 1.00 0.56 0.84 0.49
## El 0.47 0.56 1.00 0.56 0.38
## Ab 0.86 0.84 0.56 1.00 0.60
## Res 0.47 0.49 0.38 0.60 1.00
##
## $Barkul2
## Fl Or El Ab Res
## Fl 1.00 0.89 0.31 0.64 0.28
## Or 0.89 1.00 0.47 0.62 0.24
## El 0.31 0.47 1.00 0.38 NA
## Ab 0.64 0.62 0.38 1.00 0.43
## Res 0.28 0.24 NA 0.43 1.00
##
## $Berman
## Fl Or El Ab Res
## Fl 1.000 0.39 0.14 -0.38 0.004
## Or 0.390 1.00 -0.23 0.14 -0.290
## El 0.140 -0.23 1.00 0.05 0.800
## Ab -0.380 0.14 0.05 1.00 0.250
## Res 0.004 -0.29 0.80 0.25 1.000
##
## $Boynton
## Fl Or El Ab Res
## Fl 1.000 0.576 NA NA NA
## Or 0.576 1.000 NA NA NA
## El NA NA NA NA NA
## Ab NA NA NA NA NA
## Res NA NA NA NA NA1.3 Data checking and subsetting
## Check for positive definiteness
is.pd(data)## Auth Barkul Barkul2 Berman Boynton Callans Carter Carter
## TRUE TRUE NA TRUE TRUE TRUE TRUE TRUE
## Chi Cho Cho Cockcroft Conway Crawford Digranes Dufner
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## Fishkin Forsyth Garcia Gollmar Hamlen Hokanson Houtz Humble
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## Ibrahim Kiehn Kim_1 Kim_2 Kim_2 Kim_2 Kim_3 Kim_3
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## Lew Miranda Morrison Morrison Morrison Nguyen Zbarskaya Rose
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## Rose Roskos Roskos Samuels Shore Stephens Storer Storer
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## Tannehill Tisone Trigani Voss Warne Watson Yoon Zhang
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## Acar Acaretal Balcia Balcib Gao Liu Wan
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE## Simplify the data structure
TTCT <- data
TTCT.n <- n
# Overview of missing data
pattern.na(TTCT, show.na = TRUE)## Fl Or El Ab Res
## Fl 0 0 7 6 8
## Or 0 0 7 6 8
## El 7 7 7 7 10
## Ab 6 6 7 6 9
## Res 8 8 10 9 8# Overview of complete data
pattern.na(TTCT, show.na = FALSE)## Fl Or El Ab Res
## Fl 63 63 56 57 55
## Or 63 63 56 57 55
## El 56 56 56 56 53
## Ab 57 57 56 57 54
## Res 55 55 53 54 55# Which correlation matrices have missing values?
# Search in the pattern matrices for TRUE (i.e., NAs present)
# Create the relevant objects
x <- "TRUE"
y <- c(rep(NA, length(TTCT)))
for (i in 1:length(TTCT)) {
## Check missingness
y[i] <- x %in% as.matrix(is.na(TTCT[[i]]))
}
y## [1] FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
## [25] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
## [37] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSEtable(y)## y
## FALSE TRUE
## 53 10## Identify the correlation matrices with missing values
missexclude <- as.vector(which(y %in% x))
## Exclude the correlation matrices with missing values
TTCT <- TTCT[-missexclude]
TTCT.n <- TTCT.n[-missexclude]
names.studies <- names[-missexclude]
names.studid <- study.names[-missexclude]
mod.adults <- adults[-missexclude]
mod.validity <- validity[-missexclude]
mod.forms <- formsAB[-missexclude]
mod.scores <- scoring[-missexclude]
## Combine everything in an object
TTCT1 <- list(data = TTCT, n = TTCT.n)
TTCT1## $data
## $data$Auth
## Fl Or El Ab Res
## Fl 1.00 0.54 0.11 0.08 0.36
## Or 0.54 1.00 0.39 0.18 0.25
## El 0.11 0.39 1.00 0.32 0.15
## Ab 0.08 0.18 0.32 1.00 -0.07
## Res 0.36 0.25 0.15 -0.07 1.00
##
## $data$Barkul
## Fl Or El Ab Res
## Fl 1.00 0.95 0.47 0.86 0.47
## Or 0.95 1.00 0.56 0.84 0.49
## El 0.47 0.56 1.00 0.56 0.38
## Ab 0.86 0.84 0.56 1.00 0.60
## Res 0.47 0.49 0.38 0.60 1.00
##
## $data$Berman
## Fl Or El Ab Res
## Fl 1.000 0.39 0.14 -0.38 0.004
## Or 0.390 1.00 -0.23 0.14 -0.290
## El 0.140 -0.23 1.00 0.05 0.800
## Ab -0.380 0.14 0.05 1.00 0.250
## Res 0.004 -0.29 0.80 0.25 1.000
##
## $data$Callans
## Fl Or El Ab Res
## Fl 1.00 0.78 0.09 0.26 0.51
## Or 0.78 1.00 -0.01 0.26 0.43
## El 0.09 -0.01 1.00 0.27 0.42
## Ab 0.26 0.26 0.27 1.00 0.38
## Res 0.51 0.43 0.42 0.38 1.00
##
## $data$Carter
## Fl Or El Ab Res
## Fl 1.00 0.86 0.31 0.05 0.81
## Or 0.86 1.00 0.28 0.05 0.72
## El 0.31 0.28 1.00 0.54 0.49
## Ab 0.05 0.05 0.54 1.00 0.21
## Res 0.81 0.72 0.49 0.21 1.00
##
## $data$Carter
## Fl Or El Ab Res
## Fl 1.00 0.82 0.62 0.51 0.68
## Or 0.82 1.00 0.39 0.40 0.60
## El 0.62 0.39 1.00 0.28 0.40
## Ab 0.51 0.40 0.28 1.00 0.33
## Res 0.68 0.60 0.40 0.33 1.00
##
## $data$Chi
## Fl Or Ab El Res
## Fl 1.000 0.433 -0.02 0.18 -0.19
## Or 0.433 1.000 0.42 0.37 0.40
## Ab -0.020 0.420 1.00 0.42 0.54
## El 0.180 0.370 0.42 1.00 0.45
## Res -0.190 0.400 0.54 0.45 1.00
##
## $data$Cho
## Fl Or Ab El Res
## Fl 1.00 0.61 0.42 0.32 0.69
## Or 0.61 1.00 0.43 0.21 0.33
## Ab 0.42 0.43 1.00 0.58 0.63
## El 0.32 0.21 0.58 1.00 0.54
## Res 0.69 0.33 0.63 0.54 1.00
##
## $data$Cho
## Fl Or Ab El Res
## Fl 1.00 0.59 0.26 0.14 0.82
## Or 0.59 1.00 0.02 0.31 0.69
## Ab 0.26 0.02 1.00 0.36 0.25
## El 0.14 0.31 0.36 1.00 0.24
## Res 0.82 0.69 0.25 0.24 1.00
##
## $data$Cockcroft
## Fl Or Ab El Res
## Fl 1.00 0.29 0.42 0.24 0.18
## Or 0.29 1.00 0.12 0.65 0.31
## Ab 0.42 0.12 1.00 0.31 0.31
## El 0.24 0.65 0.31 1.00 0.46
## Res 0.18 0.31 0.31 0.46 1.00
##
## $data$Conway
## Fl Or El Ab Res
## Fl 1.00 0.82 0.45 0.56 0.50
## Or 0.82 1.00 0.47 0.56 0.43
## El 0.45 0.47 1.00 0.68 0.49
## Ab 0.56 0.56 0.68 1.00 0.65
## Res 0.50 0.43 0.49 0.65 1.00
##
## $data$Crawford
## Fl Or El Ab Res
## Fl 1.00 0.94 0.38 0.37 0.67
## Or 0.94 1.00 0.44 0.48 0.72
## El 0.38 0.44 1.00 0.38 0.65
## Ab 0.37 0.48 0.38 1.00 0.40
## Res 0.67 0.72 0.65 0.40 1.00
##
## $data$Digranes
## Fl Or El Ab Res
## Fl 1.00 0.76 0.17 0.80 0.81
## Or 0.76 1.00 0.45 0.71 0.79
## El 0.17 0.45 1.00 0.09 0.37
## Ab 0.80 0.71 0.09 1.00 0.74
## Res 0.81 0.79 0.37 0.74 1.00
##
## $data$Fishkin
## Fl Or El Ab Res
## Fl 1.00 0.60 0.00 0.13 0.19
## Or 0.60 1.00 -0.03 0.11 0.26
## El 0.00 -0.03 1.00 0.11 0.01
## Ab 0.13 0.11 0.11 1.00 0.09
## Res 0.19 0.26 0.01 0.09 1.00
##
## $data$Forsyth
## Fl Or El Ab Res
## Fl 1.00 0.91 0.56 0.35 0.82
## Or 0.91 1.00 0.49 0.40 0.77
## El 0.56 0.49 1.00 0.50 0.62
## Ab 0.35 0.40 0.50 1.00 0.33
## Res 0.82 0.77 0.62 0.33 1.00
##
## $data$Garcia
## Fl Or El Ab Res
## Fl 1.000 0.626 0.392 0.435 0.416
## Or 0.626 1.000 0.450 0.387 0.525
## El 0.392 0.450 1.000 0.495 0.320
## Ab 0.435 0.387 0.495 1.000 0.567
## Res 0.416 0.525 0.320 0.567 1.000
##
## $data$Gollmar
## Fl Or El Ab Res
## Fl 1.000 0.672 -0.260 -0.130 0.188
## Or 0.672 1.000 0.019 0.241 0.217
## El -0.260 0.019 1.000 0.377 0.220
## Ab -0.130 0.241 0.377 1.000 0.296
## Res 0.188 0.217 0.220 0.296 1.000
##
## $data$Hokanson
## Fl Or El Ab Res
## Fl 1.00 0.79 0.14 0.32 0.48
## Or 0.79 1.00 0.28 0.44 0.45
## El 0.14 0.28 1.00 0.48 0.36
## Ab 0.32 0.44 0.48 1.00 0.36
## Res 0.48 0.45 0.36 0.36 1.00
##
## $data$Houtz
## Fl Or Ab El Res
## Fl 1.00 0.59 0.27 0.49 0.50
## Or 0.59 1.00 0.16 0.27 0.34
## Ab 0.27 0.16 1.00 0.22 0.46
## El 0.49 0.27 0.22 1.00 0.37
## Res 0.50 0.34 0.46 0.37 1.00
##
## $data$Humble
## Fl Or El Ab Res
## Fl 1.00 0.83 0.22 0.44 0.34
## Or 0.83 1.00 0.28 0.38 0.25
## El 0.22 0.28 1.00 0.06 0.07
## Ab 0.44 0.38 0.06 1.00 0.37
## Res 0.34 0.25 0.07 0.37 1.00
##
## $data$Ibrahim
## Fl Or Ab El Res
## Fl 1.000 0.611 0.524 0.230 0.460
## Or 0.611 1.000 0.120 0.246 0.485
## Ab 0.524 0.120 1.000 0.267 0.155
## El 0.230 0.246 0.267 1.000 0.484
## Res 0.460 0.485 0.155 0.484 1.000
##
## $data$Kim_1
## Fl Or Ab El Res
## Fl 1.000 0.844 0.351 0.196 0.666
## Or 0.844 1.000 0.332 0.209 0.563
## Ab 0.351 0.332 1.000 0.428 0.212
## El 0.196 0.209 0.428 1.000 0.443
## Res 0.666 0.563 0.212 0.443 1.000
##
## $data$Kim_2
## Fl Or Ab El Res
## Fl 1.00 0.84 0.45 0.39 0.65
## Or 0.84 1.00 0.49 0.38 0.65
## Ab 0.45 0.49 1.00 0.49 0.34
## El 0.39 0.38 0.49 1.00 0.51
## Res 0.65 0.65 0.34 0.51 1.00
##
## $data$Kim_2
## Fl Or Ab El Res
## Fl 1.00 0.79 0.08 0.14 0.47
## Or 0.79 1.00 0.15 0.15 0.48
## Ab 0.08 0.15 1.00 0.30 0.17
## El 0.14 0.15 0.30 1.00 0.25
## Res 0.47 0.48 0.17 0.25 1.00
##
## $data$Kim_2
## Fl Or Ab El Res
## Fl 1.00 0.86 0.31 0.22 0.66
## Or 0.86 1.00 0.32 0.25 0.57
## Ab 0.31 0.32 1.00 0.41 0.20
## El 0.22 0.25 0.41 1.00 0.40
## Res 0.66 0.57 0.20 0.40 1.00
##
## $data$Kim_3
## Fl Or Ab El Res
## Fl 1.00 0.46 -0.28 0.10 -0.28
## Or 0.46 1.00 0.24 0.40 0.12
## Ab -0.28 0.24 1.00 0.51 0.60
## El 0.10 0.40 0.51 1.00 0.66
## Res -0.28 0.12 0.60 0.66 1.00
##
## $data$Kim_3
## Fl Or Ab El Res
## Fl 1.00 0.40 -0.27 0.08 -0.22
## Or 0.40 1.00 0.23 0.34 0.17
## Ab -0.27 0.23 1.00 0.50 0.64
## El 0.08 0.34 0.50 1.00 0.72
## Res -0.22 0.17 0.64 0.72 1.00
##
## $data$Miranda
## Fl Or El Ab Res
## Fl 1.00 0.49 0.02 -0.25 0.41
## Or 0.49 1.00 0.11 -0.30 0.20
## El 0.02 0.11 1.00 -0.31 0.14
## Ab -0.25 -0.30 -0.31 1.00 -0.29
## Res 0.41 0.20 0.14 -0.29 1.00
##
## $data$Nguyen
## Fl Or El Ab Res
## Fl 1.00 0.75 0.11 0.17 0.38
## Or 0.75 1.00 0.09 0.10 0.34
## El 0.11 0.09 1.00 0.15 0.13
## Ab 0.17 0.10 0.15 1.00 0.03
## Res 0.38 0.34 0.13 0.03 1.00
##
## $data$Zbarskaya
## Fl Or El Ab Res
## Fl 1.000 0.614 0.008 0.168 0.189
## Or 0.614 1.000 0.135 0.327 0.153
## El 0.008 0.135 1.000 0.504 0.225
## Ab 0.168 0.327 0.504 1.000 0.442
## Res 0.189 0.153 0.225 0.442 1.000
##
## $data$Rose
## Fl Or El Ab Res
## Fl 1.00 0.81 0.07 0.66 -0.05
## Or 0.81 1.00 0.27 0.62 -0.06
## El 0.07 0.27 1.00 0.57 -0.19
## Ab 0.66 0.62 0.57 1.00 -0.12
## Res -0.05 -0.06 -0.19 -0.12 1.00
##
## $data$Rose
## Fl Or El Ab Res
## Fl 1.00 0.67 0.05 0.56 0.34
## Or 0.67 1.00 0.13 0.16 0.12
## El 0.05 0.13 1.00 -0.30 0.43
## Ab 0.56 0.16 -0.30 1.00 0.19
## Res 0.34 0.12 0.43 0.19 1.00
##
## $data$Roskos
## Fl Or Ab El Res
## Fl 1.00 0.26 0.15 0.37 0.53
## Or 0.26 1.00 0.08 0.47 0.31
## Ab 0.15 0.08 1.00 0.20 0.47
## El 0.37 0.47 0.20 1.00 0.37
## Res 0.53 0.31 0.47 0.37 1.00
##
## $data$Roskos
## Fl Or Ab El Res
## Fl 1.00 0.16 -0.06 0.06 0.14
## Or 0.16 1.00 -0.02 0.25 0.29
## Ab -0.06 -0.02 1.00 0.04 0.36
## El 0.06 0.25 0.04 1.00 0.47
## Res 0.14 0.29 0.36 0.47 1.00
##
## $data$Samuels
## Fl Or El Ab Res
## Fl 1.00 0.75 -0.11 0.10 -0.16
## Or 0.75 1.00 0.02 0.24 -0.06
## El -0.11 0.02 1.00 0.48 0.07
## Ab 0.10 0.24 0.48 1.00 0.24
## Res -0.16 -0.06 0.07 0.24 1.00
##
## $data$Shore
## Fl Or El Ab Res
## Fl 1.00 0.26 -0.01 -0.12 -0.29
## Or 0.26 1.00 0.33 0.70 0.12
## El -0.01 0.33 1.00 0.30 0.54
## Ab -0.12 0.70 0.30 1.00 0.34
## Res -0.29 0.12 0.54 0.34 1.00
##
## $data$Stephens
## Fl Or El Ab Res
## Fl 1.00 0.86 0.17 0.33 0.65
## Or 0.86 1.00 0.16 0.30 0.60
## El 0.17 0.16 1.00 0.12 0.30
## Ab 0.33 0.30 0.12 1.00 0.31
## Res 0.65 0.60 0.30 0.31 1.00
##
## $data$Storer
## Fl Or El Ab Res
## Fl 1.00 0.81 0.07 0.66 -0.05
## Or 0.81 1.00 0.27 0.62 -0.06
## El 0.07 0.27 1.00 0.57 -0.19
## Ab 0.66 0.62 0.57 1.00 -0.12
## Res -0.05 -0.06 -0.19 -0.12 1.00
##
## $data$Storer
## Fl Or El Ab Res
## Fl 1.00 0.73 0.23 0.43 0.57
## Or 0.73 1.00 0.20 0.55 0.48
## El 0.23 0.20 1.00 0.29 0.40
## Ab 0.43 0.55 0.29 1.00 0.25
## Res 0.57 0.48 0.40 0.25 1.00
##
## $data$Tannehill
## Fl Or El Ab Res
## Fl 1.00 0.84 0.35 0.28 0.35
## Or 0.84 1.00 0.41 0.36 0.33
## El 0.35 0.41 1.00 0.38 0.39
## Ab 0.28 0.36 0.38 1.00 0.41
## Res 0.35 0.33 0.39 0.41 1.00
##
## $data$Tisone
## Fl Or El Ab Res
## Fl 1.00 0.68 -0.03 0.15 0.13
## Or 0.68 1.00 -0.12 0.26 0.35
## El -0.03 -0.12 1.00 0.30 0.11
## Ab 0.15 0.26 0.30 1.00 0.53
## Res 0.13 0.35 0.11 0.53 1.00
##
## $data$Trigani
## Fl Or El Ab Res
## Fl 1.00 0.72 0.28 0.17 0.69
## Or 0.72 1.00 0.24 0.26 0.47
## El 0.28 0.24 1.00 0.37 0.52
## Ab 0.17 0.26 0.37 1.00 0.16
## Res 0.69 0.47 0.52 0.16 1.00
##
## $data$Voss
## Fl Or El Ab Res
## Fl 1.00 0.71 0.43 0.38 0.65
## Or 0.71 1.00 0.51 0.44 0.79
## El 0.43 0.51 1.00 0.53 0.59
## Ab 0.38 0.44 0.53 1.00 0.42
## Res 0.65 0.79 0.59 0.42 1.00
##
## $data$Warne
## Fl Or El Ab Res
## Fl 1.00 0.74 0.40 0.35 0.63
## Or 0.74 1.00 0.37 0.37 0.50
## El 0.40 0.37 1.00 0.43 0.50
## Ab 0.35 0.37 0.43 1.00 0.26
## Res 0.63 0.50 0.50 0.26 1.00
##
## $data$Yoon
## Fl Or El Ab Res
## Fl 1.00 0.73 -0.16 0.08 0.09
## Or 0.73 1.00 0.08 0.29 0.28
## El -0.16 0.08 1.00 0.47 0.53
## Ab 0.08 0.29 0.47 1.00 0.66
## Res 0.09 0.28 0.53 0.66 1.00
##
## $data$Zhang
## Fl Or El Ab Res
## Fl 1.00 0.78 0.09 0.25 0.83
## Or 0.78 1.00 0.15 0.24 0.70
## El 0.09 0.15 1.00 0.33 0.06
## Ab 0.25 0.24 0.33 1.00 0.21
## Res 0.83 0.70 0.06 0.21 1.00
##
## $data$Acar
## Fl Or El Ab Res
## Fl 1.000 0.650 0.188 0.338 0.529
## Or 0.650 1.000 0.274 0.409 0.477
## El 0.188 0.274 1.000 0.363 0.413
## Ab 0.338 0.409 0.363 1.000 0.305
## Res 0.529 0.477 0.413 0.305 1.000
##
## $data$Acaretal
## Fl Or El Ab Res
## Fl 1.000 0.763 0.089 0.294 0.567
## Or 0.763 1.000 0.210 0.367 0.540
## El 0.089 0.210 1.000 0.469 0.277
## Ab 0.294 0.367 0.469 1.000 0.318
## Res 0.567 0.540 0.277 0.318 1.000
##
## $data$Balcia
## Fl Or El Ab Res
## Fl 1.000 0.292 0.000 0.176 -0.117
## Or 0.292 1.000 0.221 0.148 0.154
## El 0.000 0.221 1.000 0.304 0.035
## Ab 0.176 0.148 0.304 1.000 0.047
## Res -0.117 0.154 0.035 0.047 1.000
##
## $data$Balcib
## Fl Or El Ab Res
## Fl 1.000 0.430 0.116 0.267 -0.190
## Or 0.430 1.000 0.166 0.225 0.016
## El 0.116 0.166 1.000 0.363 -0.128
## Ab 0.267 0.225 0.363 1.000 -0.107
## Res -0.190 0.016 -0.128 -0.107 1.000
##
## $data$Gao
## Fl Or El Ab Res
## Fl 1.00 0.31 0.28 0.39 0.28
## Or 0.31 1.00 0.34 0.41 0.17
## El 0.28 0.34 1.00 0.25 0.26
## Ab 0.39 0.41 0.25 1.00 0.31
## Res 0.28 0.17 0.26 0.31 1.00
##
## $data$Liu
## Fl Or El Ab Res
## Fl 1.00 0.94 0.32 0.49 0.41
## Or 0.94 1.00 0.32 0.48 0.39
## El 0.32 0.32 1.00 0.66 0.62
## Ab 0.49 0.48 0.66 1.00 0.67
## Res 0.41 0.39 0.62 0.67 1.00
##
## $data$Wan
## Fl Or El Ab Res
## Fl 1.00 0.27 0.24 0.17 0.19
## Or 0.27 1.00 0.35 0.19 0.14
## El 0.24 0.35 1.00 0.27 0.12
## Ab 0.17 0.19 0.27 1.00 0.35
## Res 0.19 0.14 0.12 0.35 1.00
##
##
## $n
## [1] 30 599 13 60 24 24 203 24 35 36 25 21 17 116 45
## [16] 95 128 1758 42 125 99 500 1000 1000 1000 125 137 12 187 125
## [31] 19 12 39 31 51 18 84 43 46 199 24 107 120 432 163
## [46] 1067 477 319 1047 95 264 105 3752 Parameter-Based Meta-Analytic Structural Equation Modeling (pbMASEM)
Parameter-based MASEM comprises two steps: (1) Model-based generation of the relevant effect sizes and their sampling (co-)variances; and (2) Meta-analysis of the effect sizes.
2.1 Stage-1 Analysis: Model-Based Generation of Effect Sizes
2.1.1 Model Specification
In this step, we specify the analytic models for reliability
estimation. The extant literature indicated that several models may
describe the structure of the TTCT: (a) single-factor model with a
general TTCT factor (gTTCT); (b) two-factor model with a
factor representing innovativeness (INNOV) and a factor
describing adaptability (ADAPT); and (c) the two-factor
model from (b) with a cross-loading of the indicator Res.
In the following section, we specify these models and define the
reliability estimates.
## Model 1
## Single-factor model
SingleFactorModel <- " # Measurement Model
gCT =~ L1*Fl + L2*Or + L3*El + L4*Ab + L5*Res
# Residual variances
Fl ~~ R1*Fl
Or ~~ R2*Or
El ~~ R3*El
Ab ~~ R4*Ab
Res ~~ R5*Res
# Factor variances fixed to 1
gCT ~~ 1*gCT
# Additional constraints
R1 > 0
R2 > 0
R3 > 0
R4 > 0
R5 > 0
"
## Model 4
## Two-factor model with correlated traits ADAPT and INNOV and Res assigned to ADAPT
TwoFactorModel <- " # Measurement Model
Innov =~ L1*Fl + L2*Or
Adapt =~ L3*El + L4*Ab + L5*Res
# Residual variances
Fl ~~ R1*Fl
Or ~~ R2*Or
El ~~ R3*El
Ab ~~ R4*Ab
Res ~~ R5*Res
# Factor variances fixed to 1
Adapt ~~ 1*Adapt
Innov ~~ 1*Innov
# Factor correlation
Adapt ~~ fcorr*Innov
# Reliability coefficients
SREL1 := ((L1+L2)^2)/((L1+L2)^2 +
R1+R2)
SREL2 := ((L3+L4+L5)^2)/((L3+L4+L5)^2 +
R3+R4+R5)
# Composite reliability by Fu et al. (2022)
SRELCR := ((L1+L2)^2+(L3+L4+L5)^2+2*fcorr*(L1+L2)*(L3+L4+L5))/
((L1+L2)^2+(L3+L4+L5)^2+2*fcorr*(L1+L2)*(L3+L4+L5) +
R1+R2+R3+R4+R5)
# Additional constraints
R1 > 0
R2 > 0
R3 > 0
R4 > 0
R5 > 0
"
## Model 2
## Two-factor model with correlated traits ADAPT and INNOV and Res assigned to Innov
TwoFactorModelB <- " # Measurement Model
Innov =~ L1*Fl + L2*Or + L5*Res
Adapt =~ L3*El + L4*Ab
# Residual variances
Fl ~~ R1*Fl
Or ~~ R2*Or
El ~~ R3*El
Ab ~~ R4*Ab
Res ~~ R5*Res
# Factor variances fixed to 1
Adapt ~~ 1*Adapt
Innov ~~ 1*Innov
# Factor correlation
Adapt ~~ fcorr*Innov
# Reliability coefficients
SREL1 := ((L1+L2+L5)^2)/((L1+L2+L5)^2 +
R1+R2+R5)
SREL2 := ((L3+L4)^2)/((L3+L4)^2 +
R3+R4)
# Composite reliability by Fu et al. (2022)
SRELCR := ((L1+L2+L5)^2+(L3+L4)^2+2*fcorr*(L1+L2+L5)*(L3+L4))/
((L1+L2+L5)^2+(L3+L4)^2+2*fcorr*(L1+L2+L5)*(L3+L4) +
R1+R2+R3+R4+R5)
# Additional constraints
R1 > 0
R2 > 0
R3 > 0
R4 > 0
R5 > 0
"
## Model 3
## Two-factor model with correlated traits ADAPT and INNOV and a cross-loading of RES
TwoFactorModelC <- " # Measurement Model
Innov =~ L1*Fl + L2*Or + CL*Res
Adapt =~ L3*El + L4*Ab + L5*Res
# Residual variances
Fl ~~ R1*Fl
Or ~~ R2*Or
El ~~ R3*El
Ab ~~ R4*Ab
Res ~~ R5*Res
# Factor variances fixed to 1
Adapt ~~ 1*Adapt
Innov ~~ 1*Innov
# Factor correlation
Adapt ~~ fcorr*Innov
# Reliability coefficients
SREL1C := ((L1+L2+CL)^2)/((L1+L2+CL)^2 +
R1+R2+R5)
SREL2C := ((L3+L4+L5)^2)/((L3+L4+L5)^2 +
R3+R4+R5)
# Composite reliability by Fu et al. (2022)
SRELCRC := ((L1+L2+CL)^2+(L3+L4+L5)^2 +
2*fcorr*(L1+L2+CL)*(L3+L4+L5))/
((L1+L2+CL)^2+(L3+L4+L5)^2 +
2*fcorr*(L1+L2+CL)*(L3+L4+L5) +
R1+R2+R3+R4+R5)
# Additional constraints
R1 > 0
R2 > 0
R3 > 0
R4 > 0
R5 > 0
"2.1.2 Model Estimation
## Define a function to run the SEM in laavan and extract the
## model parameters
tra_study_lavaan <- function(id, data, para_names=NULL, model, ...) {
cor_i <- data$data[[id]]
n_i <- data$n[[id]]
fit_i <- sem(model=model, std.lv = T, sample.cov=cor_i, sample.nobs=n_i, ...)
results <- list()
coefs <- standardizedSolution(fit_i)$est.std[1:5]
vcoefs <- vcov(fit_i)[1:5,1:5]
if (is.null(para_names)) para_names <- names(coefs)
names(coefs) <- para_names
colnames(vcoefs) <- rownames(vcoefs) <- para_names
results$coefs <- coefs
results$vcoefs <- vcoefs
results$fit <- fit_i
results
}
## Specify some more parameters
k <- length(TTCT1$data)
para_names <- c("L1", "L2", "L3", "L4", "L5")
var_names <- c("Fl", "Or", "El", "Ab", "Res")2.1.2.1 Model 1: Single-factor model
## Model 1
## Single-factor model
## Model estimation
sfm.fit.all <- lapply(1:k, FUN = tra_study_lavaan,
data = TTCT1,
para_names = para_names,
model = SingleFactorModel,
estimator = "ML",
fixed.x = FALSE)
head(sfm.fit.all, 5)## [[1]]
## [[1]]$coefs
## L1 L2 L3 L4 L5
## 0.5976890 0.8960524 0.4174755 0.2081323 0.3135450
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.042572394 -0.011264727 0.010409972 0.004974506 0.007613374
## L2 -0.011264727 0.054008776 -0.005773406 -0.002480583 -0.003957476
## L3 0.010409972 -0.005773406 0.039023005 0.003161825 0.004834038
## L4 0.004974506 -0.002480583 0.003161825 0.038628760 0.002318153
## L5 0.007613374 -0.003957476 0.004834038 0.002318153 0.038679852
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 30
##
## Model Test User Model:
##
## Test statistic 6.068
## Degrees of freedom 5
## P-value (Chi-square) 0.300
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.9730757 0.9742243 0.5408478 0.8774297 0.5112117
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0008893069 0.0007806354 0.0004381411 0.0007106858 0.0004141340
## L2 0.0007806354 0.0008874639 0.0004384418 0.0007111127 0.0004144189
## L3 0.0004381411 0.0004384418 0.0014525250 0.0003954058 0.0002303779
## L4 0.0007106858 0.0007111127 0.0003954058 0.0010363019 0.0003737394
## L5 0.0004141340 0.0004144189 0.0002303779 0.0003737394 0.0014797243
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 599
##
## Model Test User Model:
##
## Test statistic 241.901
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## -0.999999970 -0.390001184 -0.140000116 0.379999174 -0.004000719
##
## [[3]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0355029837 1.384620e-02 4.970452e-03 -1.349108e-02 1.420374e-04
## L2 0.0138462020 6.560591e-02 1.938482e-03 -5.261538e-03 5.539476e-05
## L3 0.0049704525 1.938482e-03 7.031099e-02 -1.888765e-03 1.988538e-05
## L4 -0.0134910830 -5.261538e-03 -1.888765e-03 6.587916e-02 -5.397403e-05
## L5 0.0001420374 5.539476e-05 1.988538e-05 -5.397403e-05 7.100539e-02
##
## [[3]]$fit
## lavaan 0.6.16 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 13
##
## Model Test User Model:
##
## Test statistic 19.730
## Degrees of freedom 5
## P-value (Chi-square) 0.001
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.9292358 0.8337253 0.1106548 0.3106395 0.5530644
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0132722984 0.0032240784 0.0006336542 0.0017664748 0.0030590838
## L2 0.0032240784 0.0138996953 0.0008978624 0.0025289566 0.0045609420
## L3 0.0006336542 0.0008978624 0.0180692306 0.0003088704 0.0005538184
## L4 0.0017664748 0.0025289566 0.0003088704 0.0173304083 0.0015578240
## L5 0.0030590838 0.0045609420 0.0005538184 0.0015578240 0.0155443239
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 60
##
## Model Test User Model:
##
## Test statistic 20.992
## Degrees of freedom 5
## P-value (Chi-square) 0.001
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.96896788 0.88317014 0.35068734 0.08396762 0.83684140
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.022635827 0.016067093 0.0065103169 0.0015596295 0.015363744
## L2 0.016067093 0.025577869 0.0063465707 0.0015191196 0.015246930
## L3 0.006510317 0.006346571 0.0391775607 0.0005982731 0.005991323
## L4 0.001559629 0.001519120 0.0005982731 0.0416466192 0.001434152
## L5 0.015363744 0.015246930 0.0059913227 0.0014341521 0.027062538
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 24
##
## Model Test User Model:
##
## Test statistic 13.218
## Degrees of freedom 5
## P-value (Chi-square) 0.021## Extract relevant model parameters
## FIT INDICES
## Chi-squares and p values of the parameter-based models
## Select CFI and SRMR
## SRMR performs well in small samples (see Pavlov et al., 2021, EPM)
sfm_model_fit <- t(sapply(sfm.fit.all, function(x) {
fitMeasures(x$fit, c("chisq", "pvalue", "ntotal",
"cfi", "srmr"))}))
row.names(sfm_model_fit) <- names(TTCT1$data)
options(scipen=50)
round(sfm_model_fit,4)## chisq pvalue ntotal cfi srmr
## Auth 6.0684 0.2996 30 0.9263 0.0915
## Barkul 241.9006 0.0000 599 0.9157 0.0556
## Berman 19.7296 0.0014 13 0.0000 0.2533
## Callans 20.9919 0.0008 60 0.8249 0.1265
## Carter 13.2179 0.0214 24 0.8721 0.1466
## Carter 2.1289 0.8310 24 1.0000 0.0348
## Chi 97.7060 0.0000 203 0.6591 0.1254
## Cho 13.9922 0.0157 24 0.8011 0.0947
## Cho 10.2306 0.0690 35 0.9212 0.0961
## Cockcroft 8.8922 0.1134 36 0.8845 0.0962
## Conway 14.1535 0.0147 25 0.8468 0.1038
## Crawford 9.7633 0.0822 21 0.9322 0.1001
## Digranes 7.0518 0.2168 17 0.9618 0.0756
## Fishkin 2.2949 0.8070 116 1.0000 0.0336
## Forsyth 15.3126 0.0091 45 0.9354 0.0807
## Garcia 22.4599 0.0004 95 0.8848 0.0630
## Gollmar 68.0533 0.0000 128 0.5816 0.1725
## Hokanson 601.4395 0.0000 1758 0.8187 0.1122
## Houtz 6.7467 0.2402 42 0.9596 0.0725
## Humble 13.0713 0.0227 125 0.9593 0.0605
## Ibrahim 45.6004 0.0000 99 0.7167 0.1149
## Kim_1 212.7346 0.0000 500 0.8282 0.1158
## Kim_2 262.3095 0.0000 1000 0.9004 0.0802
## Kim_2 134.6176 0.0000 1000 0.9102 0.0849
## Kim_2 305.3774 0.0000 1000 0.8737 0.1028
## Kim_3 181.6475 0.0000 125 0.2080 0.3009
## Kim_3 69.7880 0.0000 137 0.7345 0.1431
## Miranda 1.9213 0.8599 12 1.0000 0.0801
## Nguyen 6.3830 0.2707 187 0.9927 0.0418
## Zbarskaya 60.8402 0.0000 125 0.5753 0.1558
## Rose 14.5966 0.0122 19 0.7449 0.1172
## Rose 7.1499 0.2097 12 0.7917 0.1517
## Roskos 8.9598 0.1107 39 0.8776 0.0875
## Roskos 2.6746 0.7500 31 1.0000 0.0691
## Samuels 21.1041 0.0008 51 0.7149 0.1485
## Shore 12.9287 0.0241 18 0.5875 0.1627
## Stephens 6.2337 0.2841 84 0.9927 0.0498
## Storer 33.0343 0.0000 43 0.7132 0.1172
## Storer 10.4611 0.0632 46 0.9234 0.0746
## Tannehill 50.4142 0.0000 199 0.8790 0.1066
## Tisone 10.3408 0.0661 24 0.7382 0.1507
## Trigani 44.2975 0.0000 107 0.7992 0.1077
## Voss 20.2329 0.0011 120 0.9486 0.0594
## Warne 89.9866 0.0000 432 0.8950 0.0731
## Yoon 161.6311 0.0000 163 0.4854 0.2409
## Zhang 131.0945 0.0000 1067 0.9490 0.0807
## Acar 83.3332 0.0000 477 0.8816 0.0710
## Acaretal 92.5820 0.0000 319 0.8430 0.1082
## Balcia 145.2432 0.0000 1047 0.5870 0.0766
## Balcib 13.0968 0.0225 95 0.7898 0.0752
## Gao 11.6331 0.0402 264 0.9628 0.0368
## Liu 102.8416 0.0000 105 0.7433 0.2090
## Wan 30.5925 0.0000 375 0.8500 0.0581## Write out these indices
write.csv(round(sfm_model_fit,4), "SingleFactorModel-Fit.csv")
write.table(round(sfm_model_fit,4), "SingleFactorModel-Fit.txt", sep='\t')
head(sfm_model_fit, 5)## chisq pvalue ntotal cfi srmr
## Auth 6.068386 0.2996214212 30 0.9263234 0.09146972
## Barkul 241.900625 0.0000000000 599 0.9156861 0.05555471
## Berman 19.729588 0.0014044654 13 0.0000000 0.25325626
## Callans 20.991851 0.0008129362 60 0.8249091 0.12650613
## Carter 13.217865 0.0214204692 24 0.8721300 0.146636832.1.2.2 Model 2:
Two-factor model with Res assigned to
Innov
## Two-factor model with two correlated traits and Res assigned to Innov
## Model estimation
tfm2.fit.all <- lapply(1:k, FUN = tra_study_lavaan,
data = TTCT1,
para_names = para_names,
model = TwoFactorModelB,
estimator = "ML",
fixed.x = FALSE)
head(tfm2.fit.all, 5)## [[1]]
## [[1]]$coefs
## L1 L2 L3 L4 L5
## 0.5895150 0.9156545 0.3050138 0.8405801 0.3806894
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0453756427 -0.016991967 0.0092965831 0.0018551323 0.0008401689
## L2 -0.0169919669 0.062985668 -0.0068274011 0.0028814532 0.0013049783
## L3 0.0092965831 -0.006827401 0.0385664551 0.0009598415 0.0004347016
## L4 0.0018551323 0.002881453 0.0009598415 0.1800957928 -0.0543381624
## L5 0.0008401689 0.001304978 0.0004347016 -0.0543381624 0.0625523360
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 24 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 30
##
## Model Test User Model:
##
## Test statistic 3.827
## Degrees of freedom 4
## P-value (Chi-square) 0.430
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.9788528 0.9694149 0.5060144 0.5773642 0.9699251
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0008809722 0.0007803088 0.0004113168 0.0003845587 0.0006460277
## L2 0.0007803088 0.0008960755 0.0004092506 0.0003808509 0.0006397988
## L3 0.0004113168 0.0004092506 0.0014832342 0.0001987962 0.0003339616
## L4 0.0003845587 0.0003808509 0.0001987962 0.0014797718 0.0003727326
## L5 0.0006460277 0.0006397988 0.0003339616 0.0003727326 0.0011392359
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 599
##
## Model Test User Model:
##
## Test statistic 209.518
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## -0.003999884 0.290000077 -0.999999919 0.400005817 0.125002325
##
## [[3]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.07100536071 -0.00004118225 0.0001420076 -0.000227209 -0.00007100308
## L2 -0.00004118225 0.06802013058 -0.0102958512 0.016473133 0.00514787415
## L3 0.00014200758 -0.01029585122 0.0355029029 -0.056803838 -0.01775126826
## L4 -0.00022720897 0.01647313328 -0.0568038377 0.859310580 0.34076063053
## L5 -0.00007100308 0.00514787415 -0.0177512683 0.340760631 0.14798934460
##
## [[3]]$fit
## lavaan 0.6.16 ended normally after 100 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 13
##
## Model Test User Model:
##
## Test statistic 8.000
## Degrees of freedom 4
## P-value (Chi-square) 0.092
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.9307451 0.8345907 0.5483165 0.2979739 0.9061197
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0133971910 0.0031000754 0.0029840845 0.0002603574 0.0007917301
## L2 0.0031000754 0.0140002467 0.0045808305 0.0002334600 0.0007099371
## L3 0.0029840845 0.0045808305 0.0155867000 0.0001533806 0.0004664207
## L4 0.0002603574 0.0002334600 0.0001533806 0.0495590200 -0.0959194740
## L5 0.0007917301 0.0007099371 0.0004664207 -0.0959194740 0.3231228568
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 60
##
## Model Test User Model:
##
## Test statistic 17.089
## Degrees of freedom 4
## P-value (Chi-square) 0.002
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.9713847 0.8820594 0.8347220 1.0000000 0.5399999
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.022556747 0.016059201 0.015329809 0.002324316 0.001255129
## L2 0.016059201 0.025618528 0.015237255 0.002110579 0.001139712
## L3 0.015329809 0.015237255 0.027130156 0.001997311 0.001078547
## L4 0.002324316 0.002110579 0.001997311 0.019965296 0.010781250
## L5 0.001255129 0.001139712 0.001078547 0.010781250 0.034108672
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 57 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 24
##
## Model Test User Model:
##
## Test statistic 5.102
## Degrees of freedom 4
## P-value (Chi-square) 0.277## Extract relevant model parameters
## FIT INDICES
## Chi-squares and p values of the parameter-based models
tfm2_model_fit <- t(sapply(tfm2.fit.all, function(x) {
fitMeasures(x$fit, c("chisq", "pvalue", "ntotal",
"cfi", "srmr"))}))
row.names(tfm2_model_fit) <- names(TTCT1$data)
options(scipen=50)
round(tfm2_model_fit,4)## chisq pvalue ntotal cfi srmr
## Auth 3.8267 0.4300 30 1.0000 0.0672
## Barkul 209.5178 0.0000 599 0.9269 0.0537
## Berman 7.9998 0.0916 13 0.7175 0.1554
## Callans 17.0886 0.0019 60 0.8567 0.1120
## Carter 5.1019 0.2770 24 0.9829 0.0709
## Carter 2.0598 0.7248 24 1.0000 0.0336
## Chi 114.0734 0.0000 203 0.5952 0.1638
## Cho 11.5357 0.0212 24 0.8333 0.0795
## Cho 6.5131 0.1640 35 0.9621 0.0579
## Cockcroft 8.8535 0.0649 36 0.8559 0.0942
## Conway 7.1166 0.1299 25 0.9478 0.0920
## Crawford 8.7763 0.0669 21 0.9320 0.0901
## Digranes 4.2876 0.3685 17 0.9946 0.0556
## Fishkin 2.7655 0.5978 116 1.0000 0.0510
## Forsyth 8.6404 0.0707 45 0.9709 0.0401
## Garcia 17.6336 0.0015 95 0.9101 0.0555
## Gollmar 50.4486 0.0000 128 0.6918 0.1480
## Hokanson 282.8336 0.0000 1758 0.9153 0.0723
## Houtz 6.6986 0.1527 42 0.9375 0.0732
## Humble 12.5814 0.0135 125 0.9567 0.0586
## Ibrahim 43.1922 0.0000 99 0.7265 0.1273
## Kim_1 133.7546 0.0000 500 0.8927 0.0786
## Kim_2 144.5767 0.0000 1000 0.9456 0.0508
## Kim_2 52.4440 0.0000 1000 0.9664 0.0483
## Kim_2 168.1729 0.0000 1000 0.9310 0.0628
## Kim_3 141.7916 0.0000 125 0.3822 0.2546
## Kim_3 60.1716 0.0000 137 0.7698 0.1375
## Miranda 0.9114 0.9229 12 1.0000 0.0521
## Nguyen 3.0839 0.5439 187 1.0000 0.0252
## Zbarskaya 27.6169 0.0000 125 0.8204 0.1117
## Rose 8.1898 0.0849 19 0.8886 0.0939
## Rose 6.0483 0.1956 12 0.8015 0.1636
## Roskos 8.8310 0.0655 39 0.8507 0.0857
## Roskos 1.9012 0.7539 31 1.0000 0.0603
## Samuels 9.0344 0.0602 51 0.9109 0.1071
## Shore 7.1004 0.1307 18 0.8387 0.1371
## Stephens 5.9531 0.2027 84 0.9885 0.0482
## Storer 18.5349 0.0010 43 0.8513 0.0939
## Storer 9.3526 0.0529 46 0.9249 0.0692
## Tannehill 36.5296 0.0000 199 0.9134 0.0929
## Tisone 9.7572 0.0447 24 0.7178 0.1732
## Trigani 32.3158 0.0000 107 0.8553 0.0814
## Voss 6.6525 0.1554 120 0.9910 0.0213
## Warne 52.9054 0.0000 432 0.9396 0.0496
## Yoon 121.9903 0.0000 163 0.6124 0.2126
## Zhang 19.0140 0.0008 1067 0.9939 0.0208
## Acar 57.6867 0.0000 477 0.9189 0.0565
## Acaretal 28.1507 0.0000 319 0.9567 0.0507
## Balcia 69.2343 0.0000 1047 0.8079 0.0569
## Balcib 4.5384 0.3380 95 0.9860 0.0468
## Gao 4.4435 0.3493 264 0.9975 0.0243
## Liu 55.8626 0.0000 105 0.8639 0.1704
## Wan 30.5920 0.0000 375 0.8442 0.0581## Write out these indices
write.csv(round(tfm2_model_fit,4), "TwoFactorModel2-Fit.csv")
write.table(round(tfm2_model_fit,4), "TwoFactorModel2-Fit.txt", sep='\t')
head(tfm2_model_fit, 5)## chisq pvalue ntotal cfi srmr
## Auth 3.826686 0.42996912 30 1.0000000 0.06722991
## Barkul 209.517841 0.00000000 599 0.9268554 0.05371925
## Berman 7.999803 0.09158543 13 0.7175163 0.15535802
## Callans 17.088567 0.00185784 60 0.8566965 0.11201201
## Carter 5.101863 0.27700454 24 0.9828550 0.07092265## Extract the scale reliability coefficients from the primary studies
## Point estimates
tfm2.srl1 <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[14,5]}))
tfm2.srl2 <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[15,5]}))
tfm2.srlcr <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[16,5]}))
## Standard errors
tfm2.srl1.se <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[14,6]}))
tfm2.srl2.se <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[15,6]}))
tfm2.srlcr.se <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[16,6]}))
## Lower 95% CI bound
tfm2.srl1.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[14,9]}))
tfm2.srl2.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[15,9]}))
tfm2.srlcr.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[16,9]}))
## Upper 95% CI bound
tfm2.srl1.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[14,10]}))
tfm2.srl2.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[15,10]}))
tfm2.srlcr.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[16,10]}))
## Factor correlation
tfm2.fcorr <- t(sapply(1:k, function(x) {parameterEstimates(tfm2.fit.all[[x]]$fit)[13,5]}))
## Save these statistics
tfm2.srl.summary <- data.frame(names.studies,
TTCT1$n,
t(tfm2.srl1 ),
t(tfm2.srl1.se),
t(tfm2.srl1.ci.low),
t(tfm2.srl1.ci.upp),
t(tfm2.srl2),
t(tfm2.srl2.se),
t(tfm2.srl2.ci.low),
t(tfm2.srl2.ci.upp),
t(tfm2.srlcr),
t(tfm2.srlcr.se),
t(tfm2.srlcr.ci.low),
t(tfm2.srlcr.ci.upp),
t(tfm2.fcorr))
colnames(tfm2.srl.summary) <- c("Study",
"N",
"Omega Factor 1",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Omega Factor 2",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Composite reliability",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Factor correlation")
tfm2.srl.summary## Study N Omega Factor 1 SE Lower 95% CI Upper 95% CI
## 1 Auth 30 0.65564386 0.104524431 0.45077974 0.8605080
## 2 Barkul 599 0.87684294 0.009058061 0.85908947 0.8945964
## 3 Berman 13 0.21016567 0.195514311 -0.17303533 0.5933667
## 4 Callans 60 0.82486789 0.038333729 0.74973516 0.9000006
## 5 Carter_a 24 0.92550812 0.026368277 0.87382725 0.9771890
## 6 Carter_b 24 0.87840114 0.041440901 0.79717846 0.9596238
## 7 Chi 203 0.67031672 0.034570247 0.60256028 0.7380732
## 8 Cho_F 24 0.78113939 0.075683560 0.63280234 0.9294764
## 9 Cho_M 35 0.88259986 0.033779342 0.81639357 0.9488062
## 10 Cockcroft 36 0.51583279 0.135877965 0.24951687 0.7821487
## 11 Conway 25 0.83865184 0.055255865 0.73035233 0.9469513
## 12 Crawford 21 0.92207022 0.030206796 0.86286599 0.9812745
## 13 Digranes 17 0.91767077 0.034578505 0.84989815 0.9854434
## 14 Fishkin 116 0.67544008 0.052009029 0.57350426 0.7773759
## 15 Forsyth 45 0.94055748 0.015555705 0.91006886 0.9710461
## 16 Garcia 95 0.77668460 0.039474752 0.69931551 0.8540537
## 17 Gollmar 128 0.69572184 0.041101217 0.61516494 0.7762787
## 18 Hokanson 1758 0.82110347 0.007243849 0.80690579 0.8353012
## 19 Houtz 42 0.75289536 0.063984429 0.62748818 0.8783025
## 20 Humble 125 0.79567253 0.030606303 0.73568528 0.8556598
## 21 Ibrahim 99 0.75192054 0.039023666 0.67543556 0.8284055
## 22 Kim_1 500 0.88283380 0.008954717 0.86528287 0.9003847
## 23 Kim_2a 1000 0.88851515 0.006118823 0.87652248 0.9005078
## 24 Kim_2b 1000 0.82563158 0.009412889 0.80718266 0.8440805
## 25 Kim_2c 1000 0.88656108 0.006190075 0.87442875 0.8986934
## 26 Kim_3a 125 0.58458079 0.052557496 0.48156999 0.6875916
## 27 Kim_3b 137 0.23957472 0.093681148 0.05596305 0.4231864
## 28 Miranda 12 0.66708273 0.162981604 0.34764466 0.9865208
## 29 Nguyen 187 0.77821059 0.026939478 0.72541019 0.8310110
## 30 Zbarskaya 125 0.65602250 0.050572601 0.55690203 0.7551430
## 31 Rose 19 0.68572571 0.114188180 0.46192099 0.9095304
## 32 Rose_b 12 0.73783670 0.118126130 0.50631374 0.9693597
## 33 Roskos_Y 39 0.66456878 0.089855121 0.48845598 0.8406816
## 34 Roskos_O 31 0.51431965 0.194303603 0.13349158 0.8951477
## 35 Samuels 51 0.64164977 0.074671111 0.49529708 0.7880025
## 36 Shore 18 0.04879865 0.194405933 -0.33222998 0.4298273
## 37 Stephens 84 0.88711473 0.021369179 0.84523191 0.9289976
## 38 Storer_a 43 0.68572584 0.075903808 0.53695711 0.8344946
## 39 Storer_b 46 0.82236445 0.044859980 0.73444050 0.9102884
## 40 Tannehill 199 0.80535849 0.023291147 0.75970868 0.8510083
## 41 Tisone 24 0.74438228 0.081760928 0.58413380 0.9046308
## 42 Trigani 107 0.85280675 0.023974059 0.80581846 0.8997950
## 43 Voss 120 0.88620094 0.017965305 0.85098959 0.9214123
## 44 Warne 432 0.84503235 0.012736174 0.82006991 0.8699948
## 45 Yoon 163 0.74419757 0.031567238 0.68232692 0.8060682
## 46 Zhang 1067 0.91182228 0.004665094 0.90267886 0.9209657
## 47 Acar 477 0.79342944 0.016278481 0.76152421 0.8253347
## 48 Acaretal 319 0.84145744 0.015254573 0.81155902 0.8713559
## 49 Balcia 1047 0.52510058 0.019826928 0.48624052 0.5639606
## 50 Balcib 95 0.38902701 0.104286830 0.18462858 0.5934254
## 51 Gao 264 0.50809527 0.052198613 0.40578787 0.6104027
## 52 Liu 105 0.85566248 0.025016074 0.80663188 0.9046931
## 53 Wan 375 0.43441826 0.050394311 0.33564723 0.5331893
## Omega Factor 2 SE Lower 95% CI Upper 95% CI Composite reliability
## 1 0.56496187 0.25729832 0.060666434 1.0692573 0.7062665
## 2 0.76734112 0.01859382 0.730897899 0.8037843 0.9067247
## 3 0.13125388 0.63906542 -1.121291339 1.3837991 0.3792193
## 4 0.57080369 0.37412291 -0.162463739 1.3040711 0.7960050
## 5 0.77000008 0.08239435 0.608510111 0.9314900 0.9062086
## 6 0.44168307 0.22914851 -0.007439755 0.8908059 0.8502797
## 7 0.59393298 0.05735172 0.481525674 0.7063403 0.7389661
## 8 0.74362049 0.10602301 0.535819218 0.9514218 0.8521182
## 9 0.52951075 0.15915172 0.217579111 0.8414424 0.8288963
## 10 0.57158106 0.16899674 0.240353530 0.9028086 0.7019128
## 11 0.81823414 0.07401261 0.673172080 0.9632962 0.8918299
## 12 0.55176587 0.19595122 0.167708530 0.9358232 0.8802762
## 13 0.19431940 0.44525652 -0.678367348 1.0670062 0.8539556
## 14 0.55499989 0.06156127 0.434342023 0.6756578 0.6332173
## 15 0.69824220 0.09756896 0.507010559 0.8894739 0.9148728
## 16 0.66395267 0.06913231 0.528455821 0.7994495 0.8312741
## 17 0.61601475 0.14217430 0.337358237 0.8946713 0.5904046
## 18 0.68896747 0.01872603 0.652265130 0.7256698 0.8376745
## 19 0.37844715 0.19970361 -0.012964733 0.7698590 0.7544145
## 20 0.12418332 0.17032751 -0.209652468 0.4580191 0.7245921
## 21 0.49703327 0.12591109 0.250252063 0.7438145 0.7632648
## 22 0.64133584 0.04348908 0.556098816 0.7265729 0.8553685
## 23 0.66067493 0.02159081 0.618357717 0.7029921 0.8796064
## 24 0.46688762 0.03601213 0.396305141 0.5374701 0.7621709
## 25 0.59277500 0.02756163 0.538755195 0.6467948 0.8475895
## 26 0.72052879 0.07125025 0.580880865 0.8601767 0.7188807
## 27 0.66982318 0.05641769 0.559246536 0.7803998 0.6533906
## 28 0.34500000 0.22212131 -0.090349758 0.7803498 0.5295116
## 29 0.26798772 0.11342589 0.045677058 0.4902984 0.6832934
## 30 0.75199998 0.03847119 0.676597836 0.8274021 0.7536246
## 31 0.78500003 0.08740302 0.613693262 0.9563068 0.8199745
## 32 0.34999851 0.22201730 -0.085147407 0.7851444 0.7224728
## 33 0.33423467 0.21365718 -0.084525713 0.7529950 0.7051059
## 34 0.07834996 0.33674747 -0.581662952 0.7383629 0.5443966
## 35 0.74000003 0.06263745 0.617232885 0.8627672 0.6581952
## 36 0.47991626 0.24917184 -0.008451579 0.9682841 0.5015645
## 37 0.23396191 0.18273740 -0.124196812 0.5921206 0.7925324
## 38 0.78499986 0.05809909 0.671127741 0.8988720 0.8199745
## 39 0.49852653 0.16718496 0.170850040 0.8262030 0.8118961
## 40 0.55369507 0.06374239 0.428762276 0.6786279 0.8048860
## 41 0.64999993 0.11519912 0.424213802 0.8757861 0.6900958
## 42 0.57668943 0.10559243 0.369732059 0.7836468 0.8213932
## 43 0.70101044 0.05527658 0.592670348 0.8093505 0.8902267
## 44 0.60592141 0.03833412 0.530787909 0.6810549 0.8427107
## 45 0.73500001 0.03558981 0.665245250 0.8047548 0.7849944
## 46 0.62011383 0.08280858 0.457811995 0.7824157 0.8619198
## 47 0.54442539 0.04311695 0.459917724 0.6289331 0.7995981
## 48 0.71460989 0.06454992 0.588094373 0.8411254 0.8473550
## 49 0.48524886 0.03780843 0.411145694 0.5593520 0.5777128
## 50 0.59196858 0.14094157 0.315728178 0.8682090 0.5673409
## 51 0.40557543 0.07389201 0.260749746 0.5504011 0.6626396
## 52 0.82925718 0.04431111 0.742409002 0.9161054 0.8909229
## 53 0.42685866 0.05944903 0.310340699 0.5433766 0.5986157
## SE Lower 95% CI Upper 95% CI Factor correlation
## 1 0.092312134 0.5253380 0.8871949 0.48204516
## 2 0.006367321 0.8942449 0.9192044 0.90362658
## 3 0.292905012 -0.1948640 0.9533026 -1.99997082
## 4 0.084711215 0.6299741 0.9620360 0.33847042
## 5 0.030774514 0.8458916 0.9665255 0.34618970
## 6 0.051826648 0.7487013 0.9518581 1.06267836
## 7 0.028113255 0.6838652 0.7940671 0.60827484
## 8 0.049000598 0.7560788 0.9481577 0.78415097
## 9 0.048676434 0.7334922 0.9243004 0.41362514
## 10 0.081491839 0.5421917 0.8616339 1.05894673
## 11 0.035242566 0.8227557 0.9609040 0.70916554
## 12 0.045274721 0.7915393 0.9690130 0.74551392
## 13 0.068403324 0.7198875 0.9880236 1.86818896
## 14 0.047527870 0.5400644 0.7263702 -0.02750486
## 15 0.022620103 0.8705382 0.9592074 0.65616223
## 16 0.028347792 0.7757135 0.8868348 0.80388201
## 17 0.084898049 0.4240075 0.7568017 -0.29942308
## 18 0.006533163 0.8248697 0.8504793 0.51334010
## 19 0.062922580 0.6310885 0.8777404 0.92952069
## 20 0.042791799 0.6407217 0.8084624 1.38626219
## 21 0.039552275 0.6857437 0.8407858 0.67185316
## 22 0.011844659 0.8321534 0.8785836 0.42054700
## 23 0.006389031 0.8670841 0.8921287 0.68298986
## 24 0.012648486 0.7373803 0.7869614 0.29332002
## 25 0.008232262 0.8314545 0.8637244 0.43867231
## 26 0.038151808 0.6441045 0.7936568 0.43386323
## 27 0.047508286 0.5602760 0.7465051 1.51035460
## 28 0.183120296 0.1706024 0.8884208 0.39013455
## 29 0.038323521 0.6081807 0.7584062 0.36799956
## 30 0.033105707 0.6887387 0.8185106 0.36486522
## 31 0.064210127 0.6941250 0.9458241 0.71164813
## 32 0.114449578 0.4981557 0.9467898 -0.55999978
## 33 0.077116973 0.5539595 0.8562524 1.11841425
## 34 0.133724762 0.2823009 0.8064923 2.07692958
## 35 0.060411229 0.5397913 0.7765990 -0.10999984
## 36 0.161694096 0.1846499 0.8184791 3.33168104
## 37 0.040502569 0.7131489 0.8719160 0.74456919
## 38 0.042682138 0.7363191 0.9036300 0.71164801
## 39 0.047358438 0.7190753 0.9047170 0.74711475
## 40 0.022718967 0.7603577 0.8494144 0.64817413
## 41 0.082728037 0.5279519 0.8522398 -0.11999973
## 42 0.030549877 0.7615165 0.8812698 0.41817045
## 43 0.016719483 0.8574572 0.9229963 0.74367211
## 44 0.012553997 0.8181054 0.8673161 0.66580678
## 45 0.024549758 0.7368778 0.8331111 0.29000067
## 46 0.017322974 0.8279674 0.8958722 0.28115578
## 47 0.015202535 0.7698017 0.8293946 0.67112035
## 48 0.017402647 0.8132464 0.8814636 0.40766667
## 49 0.019136542 0.5402059 0.6152198 0.32801365
## 50 0.074883057 0.4205728 0.7141090 0.42054211
## 51 0.034017154 0.5959672 0.7293120 1.30264434
## 52 0.018060142 0.8555256 0.9263201 0.50835576
## 53 0.033849719 0.5322715 0.6649599 0.99740458## Write out the results
write.table(tfm2.srl.summary, "TwoFactorModel2-Reliability.txt", sep='\t')
## Note: The standard errors of the derived parameters are identical
## to the asymptotic sampling errors.2.1.2.3 Model 3:
Two-factor model with a cross-loading of Res
## Model 3
## Two-factor model with a cross-loading of RES
## Model estimation
tfmc.fit.all <- lapply(1:k, FUN = tra_study_lavaan,
data = TTCT1,
para_names = para_names,
model = TwoFactorModelC,
estimator = "ML",
fixed.x = FALSE)
head(tfmc.fit.all, 5)## [[1]]
## [[1]]$coefs
## L1 L2 L3 L4 L5
## 0.5841981 0.9243441 0.2905938 0.8505294 0.3762364
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0472744385 -0.020955050 0.0149970190 0.001811084 0.0008011436
## L2 -0.0209550502 0.069905399 -0.0173292962 0.002865578 0.0012676049
## L3 0.0149970190 -0.017329296 0.0603273242 0.004479300 -0.0008967692
## L4 0.0018110844 0.002865578 0.0044793005 0.187477810 -0.0567234757
## L5 0.0008011436 0.001267605 -0.0008967692 -0.056723476 0.0626024237
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 30
##
## Model Test User Model:
##
## Test statistic 3.824
## Degrees of freedom 3
## P-value (Chi-square) 0.281
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.9846454 0.9648144 -0.3436892 0.5755731 0.9729435
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0008728441 0.0007796787 -0.0002618658 0.0003795444 0.0006415783
## L2 0.0007796787 0.0009044976 -0.0002901420 0.0003719003 0.0006286568
## L3 -0.0002618658 -0.0002901420 0.0217819949 -0.0006943377 0.0015061441
## L4 0.0003795444 0.0003719003 -0.0006943377 0.0014633668 0.0003967688
## L5 0.0006415783 0.0006286568 0.0015061441 0.0003967688 0.0010857613
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 599
##
## Model Test User Model:
##
## Test statistic 105.953
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## 0.3900001 1.0000000 -0.0369997 0.7995635 0.2577819
##
## [[3]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0656059229 0.0138461529 -0.00051230348 0.00072316879 0.00023315188
## L2 0.0138461529 0.0355029412 -0.00131359810 0.00185427814 0.00059782508
## L3 -0.0005123035 -0.0013135981 0.04042756743 -0.00006860764 -0.00002211932
## L4 0.0007231688 0.0018542781 -0.00006860764 0.04830886299 0.00731762625
## L5 0.0002331519 0.0005978251 -0.00002211932 0.00731762625 0.06864667893
##
## [[3]]$fit
## lavaan 0.6.16 ended normally after 84 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 13
##
## Model Test User Model:
##
## Test statistic 6.722
## Degrees of freedom 3
## P-value (Chi-square) 0.081
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.9543728 0.8172905 0.3321244 0.5717039 0.4722738
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0145420153 0.0018926695 0.0009926216 0.0004149356 0.0003427705
## L2 0.0018926695 0.0150344590 0.0034681932 0.0003553357 0.0002935362
## L3 0.0009926216 0.0034681932 0.0252735672 0.0086084156 0.0054244604
## L4 0.0004149356 0.0003553357 0.0086084156 0.0284483805 0.0059111611
## L5 0.0003427705 0.0002935362 0.0054244604 0.0059111611 0.0246184116
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 60
##
## Model Test User Model:
##
## Test statistic 4.379
## Degrees of freedom 3
## P-value (Chi-square) 0.223
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.9840361 0.8739518 0.7425230 1.0000000 0.5400000
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.022195703 0.0159245264 0.013379938 0.001956134 0.0010563119
## L2 0.015924526 0.0259417568 0.013868937 0.001737302 0.0009381423
## L3 0.013379938 0.0138689368 0.024062723 0.001476038 0.0007970600
## L4 0.001956134 0.0017373016 0.001476038 0.019965294 0.0107812522
## L5 0.001056312 0.0009381423 0.000797060 0.010781252 0.0341086691
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 24
##
## Model Test User Model:
##
## Test statistic 0.644
## Degrees of freedom 3
## P-value (Chi-square) 0.886## Extract relevant model parameters
## FIT INDICES
## Chi-squares and p values of the parameter-based models
tfmc_model_fit <- t(sapply(tfmc.fit.all, function(x) {
fitMeasures(x$fit, c("chisq", "pvalue", "ntotal",
"cfi", "srmr"))}))
row.names(tfmc_model_fit) <- names(TTCT1$data)
options(scipen=50)
round(tfmc_model_fit,4)## chisq pvalue ntotal cfi srmr
## Auth 3.8239 0.2811 30 0.9432 0.0678
## Barkul 105.9531 0.0000 599 0.9634 0.0207
## Berman 6.7223 0.0813 13 0.7371 0.1304
## Callans 4.3791 0.2233 60 0.9849 0.0658
## Carter 0.6436 0.8864 24 1.0000 0.0421
## Carter 2.0061 0.5711 24 1.0000 0.0328
## Chi 55.4909 0.0000 203 0.8070 0.1078
## Cho 4.5596 0.2070 24 0.9655 0.0536
## Cho 6.4872 0.0902 35 0.9475 0.0580
## Cockcroft 8.2605 0.0409 36 0.8439 0.0962
## Conway 0.7394 0.8639 25 1.0000 0.0151
## Crawford 3.8836 0.2743 21 0.9874 0.0518
## Digranes 4.1299 0.2478 17 0.9790 0.0554
## Fishkin 0.6283 0.8899 116 1.0000 0.0151
## Forsyth 4.2433 0.2364 45 0.9922 0.0310
## Garcia 11.5125 0.0093 95 0.9438 0.0469
## Gollmar 33.1378 0.0000 128 0.8000 0.1100
## Hokanson 196.2533 0.0000 1758 0.9413 0.0444
## Houtz 2.9690 0.3964 42 1.0000 0.0447
## Humble 6.2968 0.0980 125 0.9834 0.0406
## Ibrahim 40.7638 0.0000 99 0.7365 0.1105
## Kim_1 81.5590 0.0000 500 0.9350 0.0973
## Kim_2 117.9371 0.0000 1000 0.9555 0.0404
## Kim_2 12.0904 0.0071 1000 0.9937 0.0131
## Kim_2 107.9193 0.0000 1000 0.9559 0.0864
## Kim_3 43.2068 0.0000 125 0.8197 0.1415
## Kim_3 36.3656 0.0000 137 0.8633 0.1240
## Miranda 0.6569 0.8833 12 1.0000 0.0430
## Nguyen 3.0489 0.3841 187 0.9997 0.0239
## Zbarskaya 4.3840 0.2229 125 0.9895 0.0362
## Rose 7.9763 0.0465 19 0.8677 0.0878
## Rose 7.1287 0.0679 12 0.5999 0.1509
## Roskos 8.8309 0.0316 39 0.8198 0.0855
## Roskos 2.1785 0.5362 31 1.0000 0.0618
## Samuels 4.1263 0.2481 51 0.9801 0.0680
## Shore 7.5574 0.0561 18 0.7629 0.1392
## Stephens 1.8276 0.6090 84 1.0000 0.0280
## Storer 18.0516 0.0004 43 0.8460 0.0878
## Storer 9.1835 0.0269 46 0.9132 0.0768
## Tannehill 6.4306 0.0924 199 0.9909 0.0214
## Tisone 1.9791 0.5768 24 1.0000 0.0637
## Trigani 7.1323 0.0678 107 0.9789 0.0529
## Voss 2.8902 0.4089 120 1.0000 0.0183
## Warne 28.0935 0.0000 432 0.9690 0.0439
## Yoon 23.1185 0.0000 163 0.9339 0.0907
## Zhang 17.3737 0.0006 1067 0.9942 0.0187
## Acar 44.7849 0.0000 477 0.9369 0.0470
## Acaretal 23.1567 0.0000 319 0.9639 0.0372
## Balcia 69.1219 0.0000 1047 0.8053 0.0568
## Balcib 4.2004 0.2406 95 0.9688 0.0417
## Gao 4.2199 0.2387 264 0.9931 0.0240
## Liu 3.6774 0.2985 105 0.9982 0.0300
## Wan 27.6775 0.0000 375 0.8554 0.0551## Write out these indices
write.csv(round(tfmc_model_fit,4), "TwoFactorModel3-Fit.csv")
write.table(round(tfmc_model_fit,4), "TwoFactorModel3-Fit.txt", sep='\t')
head(tfmc_model_fit, 5)## chisq pvalue ntotal cfi srmr
## Auth 3.8238669 0.2811222 30 0.9431856 0.06779564
## Barkul 105.9531146 0.0000000 599 0.9633586 0.02069093
## Berman 6.7223298 0.0812949 13 0.7371126 0.13038098
## Callans 4.3791012 0.2233310 60 0.9849006 0.06584712
## Carter 0.6436149 0.8863791 24 1.0000000 0.04213503## Extract the scale reliability coefficients from the primary studies
## Point estimates
tfmc.srl1 <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[15,5]}))
tfmc.srl2 <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[16,5]}))
tfmc.srlcr <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[17,5]}))
## Standard errors
tfmc.srl1.se <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[15,6]}))
tfmc.srl2.se <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[16,6]}))
tfmc.srlcr.se <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[17,6]}))
## Lower 95% CI bound
tfmc.srl1.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[15,9]}))
tfmc.srl2.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[16,9]}))
tfmc.srlcr.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[17,9]}))
## Upper 95% CI bound
tfmc.srl1.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[15,10]}))
tfmc.srl2.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[16,10]}))
tfmc.srlcr.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[17,10]}))
## Factor correlation
tfmc.fcorr <- t(sapply(1:k, function(x) {parameterEstimates(tfmc.fit.all[[x]]$fit)[14,5]}))
## Save these statistics
tfmc.srl.summary <- data.frame(names.studies,
TTCT1$n,
t(tfmc.srl1 ),
t(tfmc.srl1.se),
t(tfmc.srl1.ci.low),
t(tfmc.srl1.ci.upp),
t(tfmc.srl2),
t(tfmc.srl2.se),
t(tfmc.srl2.ci.low),
t(tfmc.srl2.ci.upp),
t(tfmc.srlcr),
t(tfmc.srlcr.se),
t(tfmc.srlcr.ci.low),
t(tfmc.srlcr.ci.upp),
t(tfmc.fcorr))
colnames(tfmc.srl.summary) <- c("Study",
"N",
"Omega Factor 1",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Omega Factor 2",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Composite reliability",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Factor correlation")
tfmc.srl.summary## Study N Omega Factor 1 SE Lower 95% CI Upper 95% CI
## 1 Auth 30 0.653670574 0.107856677 0.4422754 0.8650658
## 2 Barkul 599 0.787772957 0.028512584 0.7318893 0.8436566
## 3 Berman 13 0.683443320 0.159833437 0.3701755 0.9967111
## 4 Callans 60 0.856329746 0.040851555 0.7762622 0.9363973
## 5 Carter_a 24 0.927154283 0.025691873 0.8767991 0.9775094
## 6 Carter_b 24 0.847019015 0.227871788 0.4003985 1.2936395
## 7 Chi 203 0.593002702 0.049954691 0.4950933 0.6909121
## 8 Cho_F 24 0.817798140 0.062998939 0.6943225 0.9412738
## 9 Cho_M 35 0.882090358 0.034132973 0.8151910 0.9489898
## 10 Cockcroft 36 0.343777202 0.472594250 -0.5824905 1.2700449
## 11 Conway 25 0.807463911 0.069678278 0.6708970 0.9440308
## 12 Crawford 21 0.933745960 0.031927839 0.8711685 0.9963234
## 13 Digranes 17 0.913968974 0.038167446 0.8391622 0.9887758
## 14 Fishkin 116 0.669786264 0.051302281 0.5692356 0.7703369
## 15 Forsyth 45 0.937871024 0.016425512 0.9056776 0.9700644
## 16 Garcia 95 0.735378067 0.051965699 0.6335272 0.8372290
## 17 Gollmar 128 0.766058096 0.038435615 0.6907257 0.8413905
## 18 Hokanson 1758 0.804897564 0.008142107 0.7889393 0.8208558
## 19 Houtz 42 0.458329744 1.281344374 -2.0530591 2.9697186
## 20 Humble 125 0.001128471 0.106290290 -0.2071967 0.2094536
## 21 Ibrahim 99 0.758951858 0.043049709 0.6745760 0.8433277
## 22 Kim_1 500 0.889613867 0.008285288 0.8733750 0.9058527
## 23 Kim_2a 1000 0.878281651 0.006987244 0.8645869 0.8919764
## 24 Kim_2b 1000 0.824550915 0.009605933 0.8057236 0.8433782
## 25 Kim_2c 1000 0.888960436 0.005933615 0.8773308 0.9005901
## 26 Kim_3a 125 0.564555188 0.065229490 0.4367077 0.6924026
## 27 Kim_3b 137 0.596009927 0.061019415 0.4764141 0.7156058
## 28 Miranda 12 0.664389696 0.166030810 0.3389753 0.9898041
## 29 Nguyen 187 0.776273251 0.028415615 0.7205797 0.8319668
## 30 Zbarskaya 125 0.648665206 0.047054876 0.5564393 0.7408911
## 31 Rose 19 0.716436267 0.119989951 0.4812603 0.9516122
## 32 Rose_b 12 0.993535779 0.080098040 0.8365465 1.1505251
## 33 Roskos_Y 39 0.658265502 0.504882906 -0.3312868 1.6478178
## 34 Roskos_O 31 0.314200161 0.418032551 -0.5051286 1.1335289
## 35 Samuels 51 0.659250852 0.072295634 0.5175540 0.8009477
## 36 Shore 18 0.105086770 0.441498475 -0.7602343 0.9704079
## 37 Stephens 84 0.871663728 0.051241046 0.7712331 0.9720943
## 38 Storer_a 43 0.716436134 0.079760447 0.5601085 0.8727637
## 39 Storer_b 46 0.835509219 0.049907087 0.7376931 0.9333253
## 40 Tannehill 199 0.772246618 0.031778095 0.7099627 0.8345305
## 41 Tisone 24 0.750704490 0.080076475 0.5937575 0.9076515
## 42 Trigani 107 0.857182140 0.022762679 0.8125681 0.9017962
## 43 Voss 120 0.877239537 0.020103505 0.8378374 0.9166417
## 44 Warne 432 0.832182178 0.014113254 0.8045207 0.8598436
## 45 Yoon 163 0.807233506 0.028921209 0.7505490 0.8639180
## 46 Zhang 1067 0.912546014 0.004657329 0.9034178 0.9216742
## 47 Acar 477 0.768526179 0.019834695 0.7296509 0.8074015
## 48 Acaretal 319 0.835859365 0.016044373 0.8044130 0.8673058
## 49 Balcia 1047 0.523362679 0.020534407 0.4831160 0.5636094
## 50 Balcib 95 0.410740294 0.111844169 0.1915298 0.6299508
## 51 Gao 264 0.544652556 0.094784192 0.3588790 0.7304262
## 52 Liu 105 0.881255287 0.022466718 0.8372213 0.9252892
## 53 Wan 375 0.149122509 0.293522612 -0.4261712 0.7244163
## Omega Factor 2 SE Lower 95% CI Upper 95% CI Composite reliability
## 1 0.4304457 0.22889696 -0.01818406 0.8790755 0.7080218
## 2 0.8229706 0.02047607 0.78283822 0.8631029 0.9178338
## 3 0.7640593 0.10566824 0.55695338 0.9711653 0.6825557
## 4 0.6209308 0.08270351 0.45883493 0.7830267 0.8126529
## 5 0.7684078 0.07699323 0.61750383 0.9193117 0.9125341
## 6 0.4775192 0.73579760 -0.96461763 1.9196559 0.8488549
## 7 0.7425099 0.03375371 0.67635385 0.8086659 0.8036901
## 8 0.7974172 0.07274661 0.65483647 0.9399979 0.8789835
## 9 0.5326083 0.16591194 0.20742687 0.8577897 0.8283102
## 10 0.6753116 0.19549267 0.29215303 1.0584702 0.7281700
## 11 0.8246381 0.06286488 0.70142522 0.9478510 0.9091115
## 12 0.7211523 0.10708496 0.51126967 0.9310350 0.9031175
## 13 0.1955976 0.45213661 -0.69057391 1.0817690 0.8537584
## 14 0.4145217 0.06674312 0.28370756 0.5453358 0.6674900
## 15 0.7290754 0.07478038 0.58250858 0.8756423 0.9219511
## 16 0.7041132 0.05642252 0.59352706 0.8146993 0.8415844
## 17 0.6126398 0.05983735 0.49536079 0.7299189 0.6615778
## 18 0.6345411 0.01541796 0.60432247 0.6647598 0.8430808
## 19 0.7879058 0.43981282 -0.07411152 1.6499230 0.8128315
## 20 0.8493046 0.07297606 0.70627414 0.9923350 0.8239503
## 21 0.5848694 0.07905407 0.42992630 0.7398126 0.7830406
## 22 0.7072821 0.02020063 0.66768961 0.7468746 0.8731967
## 23 0.6546655 0.02028131 0.61491491 0.6944162 0.8832819
## 24 0.4826084 0.02931695 0.42514820 0.5400685 0.7778928
## 25 0.6794377 0.01538088 0.64929172 0.7095837 0.8706154
## 26 0.8472008 0.02375504 0.80064182 0.8937598 0.8387767
## 27 0.8589660 0.02029488 0.81918874 0.8987432 0.8404802
## 28 0.1303795 0.93840119 -1.70885300 1.9696121 0.5333744
## 29 0.2079270 0.10271652 0.00660629 0.4092477 0.6841580
## 30 0.7088408 0.04021720 0.63001658 0.7876651 0.7958535
## 31 0.5457922 0.16855638 0.21542774 0.8761566 0.8180477
## 32 0.9882623 0.11155613 0.76961626 1.2069083 0.7823291
## 33 0.3066629 0.90301354 -1.46321117 2.0765369 0.7052351
## 34 0.6699684 0.11288397 0.44871988 0.8912169 0.6355349
## 35 0.6433924 0.07396237 0.49842882 0.7883560 0.7680445
## 36 0.9003439 0.05294429 0.79657497 1.0041128 0.8075012
## 37 0.5430463 0.39655382 -0.23418488 1.3202775 0.8198361
## 38 0.5457923 0.11204374 0.32619063 0.7653940 0.8180476
## 39 0.3700022 0.22709589 -0.07509756 0.8151020 0.8158777
## 40 0.6777027 0.04460754 0.59027352 0.7651319 0.8392724
## 41 0.6648445 0.10273171 0.46349403 0.8661949 0.8010826
## 42 0.7005870 0.04481718 0.61274692 0.7884270 0.8574797
## 43 0.7123495 0.04952693 0.61527846 0.8094205 0.8922357
## 44 0.6426562 0.03068659 0.58251154 0.7028008 0.8524045
## 45 0.7939201 0.02771560 0.73959848 0.8482416 0.8556028
## 46 0.5389738 0.06830205 0.40510422 0.6728433 0.8581444
## 47 0.5661430 0.03723139 0.49317081 0.6391152 0.8049032
## 48 0.6079822 0.04093878 0.52774369 0.6882208 0.8424831
## 49 0.3589216 0.03532058 0.28969453 0.4281487 0.5792981
## 50 0.3911986 0.12714698 0.14199514 0.6404021 0.5543793
## 51 0.2629380 0.11025555 0.04684107 0.4790349 0.6621669
## 52 0.8470109 0.02635796 0.79535023 0.8986715 0.9254371
## 53 0.6114610 0.17720180 0.26415188 0.9587702 0.6171623
## SE Lower 95% CI Upper 95% CI Factor correlation
## 1 0.093818456 0.52414099 0.8919026 0.4756440
## 2 0.005606417 0.90684544 0.9288222 0.8964628
## 3 0.116558945 0.45410435 0.9110070 -0.2555810
## 4 0.039229646 0.73576425 0.8895416 0.3046393
## 5 0.028867430 0.85595499 0.9691132 0.3155412
## 6 0.052077286 0.74678534 0.9509245 1.0626498
## 7 0.021633441 0.76128929 0.8460908 0.6051602
## 8 0.039679215 0.80121365 0.9567533 0.4926070
## 9 0.049017303 0.73223802 0.9243823 0.3944023
## 10 0.073562141 0.58399081 0.8723491 0.8396080
## 11 0.029530824 0.85123213 0.9669908 0.6654713
## 12 0.035981513 0.83259500 0.9736399 0.6492101
## 13 0.068628757 0.71924852 0.9882683 1.8872193
## 14 0.044358320 0.58054932 0.7544307 0.1409425
## 15 0.021161247 0.88047580 0.9634264 0.5991126
## 16 0.026490306 0.78966433 0.8935044 0.6792078
## 17 0.046748235 0.56995292 0.7532026 -0.3256691
## 18 0.006154373 0.83101841 0.8551431 0.5311592
## 19 0.092697734 0.63114733 0.9945158 0.8470350
## 20 0.024863841 0.77521808 0.8726825 0.9188289
## 21 0.037837034 0.70888135 0.8571998 0.4052477
## 22 0.008823746 0.85590243 0.8904909 0.1960032
## 23 0.006193187 0.87114352 0.8954204 0.6547173
## 24 0.011914261 0.75454131 0.8012444 0.2602787
## 25 0.006371702 0.85812707 0.8831037 0.2200001
## 26 0.022318890 0.79503245 0.8825209 0.4653317
## 27 0.020846923 0.79962097 0.8813394 0.4123712
## 28 0.311078740 -0.07632876 1.1430775 0.3290446
## 29 0.038487946 0.60872302 0.7595930 0.3713846
## 30 0.027128831 0.74268192 0.8490250 0.3269998
## 31 0.065195767 0.69026632 0.9458290 0.7106701
## 32 0.095298156 0.59554813 0.9691100 0.9965016
## 33 0.077288864 0.55375168 0.8567185 1.1226288
## 34 0.107921399 0.42401286 0.8470570 0.5035671
## 35 0.047824175 0.67431084 0.8617782 0.2400000
## 36 0.068962607 0.67233699 0.9426654 0.8649308
## 37 0.043676233 0.73423222 0.9054399 0.7635129
## 38 0.043337322 0.73310804 0.9029872 0.7106699
## 39 0.047857357 0.72207900 0.9096764 0.7013148
## 40 0.018905308 0.80221867 0.8763261 0.6336887
## 41 0.060289851 0.68291666 0.9192485 0.2600004
## 42 0.021163632 0.81599972 0.8989596 0.2800012
## 43 0.016376975 0.86013739 0.9243339 0.6807858
## 44 0.011747424 0.82937996 0.8754290 0.5602003
## 45 0.018001022 0.82032143 0.8908841 0.3064697
## 46 0.014981635 0.82878090 0.8875078 0.2958872
## 47 0.014734698 0.77602375 0.8337827 0.6221182
## 48 0.015013955 0.81305629 0.8719099 0.4256407
## 49 0.019721613 0.54064442 0.6179517 0.3286024
## 50 0.075349720 0.40669651 0.7020620 0.4286474
## 51 0.034014145 0.59550045 0.7288334 1.2698901
## 52 0.012212749 0.90150054 0.9493736 0.5317692
## 53 0.033075235 0.55233604 0.6819886 0.8782378## Write out the results
write.table(tfmc.srl.summary, "TwoFactorModel3-Reliability.txt", sep='\t')
## Note: The standard errors of the derived parameters are identical
## to the asymptotic sampling errors.2.1.2.4 Model 4:
Two-factor model with Res assigned to
Adapt
## Model 4
## Two-factor model with two correlated traits and Res assigned to Adapt
## Model estimation
tfm.fit.all <- lapply(1:k, FUN = tra_study_lavaan,
data = TTCT1,
para_names = para_names,
model = TwoFactorModel,
estimator = "ML",
fixed.x = FALSE)
head(tfm.fit.all, 5)## [[1]]
## [[1]]$coefs
## L1 L2 L3 L4 L5
## 0.5400006 1.0000000 0.7651308 0.3827568 0.2172019
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0275242359 0.0087000184 0.001834831 0.0009178736 0.0005208637
## L2 0.0087000184 0.0161111333 0.003397832 0.0016997646 0.0009645616
## L3 0.0018348309 0.0033978323 0.098934551 -0.0177614703 -0.0084516627
## L4 0.0009178736 0.0016997646 -0.017761470 0.0517805816 0.0040403316
## L5 0.0005208637 0.0009645616 -0.008451663 0.0040403316 0.0488336913
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 43 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 30
##
## Model Test User Model:
##
## Test statistic 4.964
## Degrees of freedom 4
## P-value (Chi-square) 0.291
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.9862142 0.9632796 0.5600021 1.0000000 0.6000011
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0008705508 0.0007793315 0.0003499718 0.0006249483 0.0003749692
## L2 0.0007793315 0.0009071488 0.0003418333 0.0006104153 0.0003662494
## L3 0.0003499718 0.0003418333 0.0014053266 0.0004666676 0.0002800007
## L4 0.0006249483 0.0006104153 0.0004666676 0.0008333332 0.0005000003
## L5 0.0003749692 0.0003662494 0.0002800007 0.0005000003 0.0013666619
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 70 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 599
##
## Model Test User Model:
##
## Test statistic 114.018
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## 0.3900009 1.0000000 0.8000005 0.2500011 1.0000000
##
## [[3]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0656059346 0.0138461869 0.0009315682 0.0002911170 0.001164458
## L2 0.0138461869 0.0355029321 0.0023886292 0.0007464516 0.002985780
## L3 0.0009315682 0.0023886292 0.0482838580 0.0071006269 0.028402263
## L4 0.0002911170 0.0007464516 0.0071006269 0.0687871724 0.008875766
## L5 0.0011644579 0.0029857805 0.0284022630 0.0088757656 0.035502755
##
## [[3]]$fit
## lavaan 0.6.16 ended normally after 97 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 13
##
## Model Test User Model:
##
## Test statistic 6.752
## Degrees of freedom 4
## P-value (Chi-square) 0.150
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.9618307 0.8109534 0.4200000 0.3800001 1.0000000
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0147972551 0.0016112889 0.0009307011 0.0008420632 0.002215956
## L2 0.0016112889 0.0152574253 0.0007847067 0.0007099730 0.001868350
## L3 0.0009307011 0.0007847067 0.0149433848 0.0013078335 0.003441668
## L4 0.0008420632 0.0007099730 0.0013078335 0.0152056072 0.003113891
## L5 0.0022159562 0.0018683503 0.0034416678 0.0031138911 0.008194451
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 54 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 60
##
## Model Test User Model:
##
## Test statistic 5.793
## Degrees of freedom 4
## P-value (Chi-square) 0.215
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.9836156 0.8743249 0.4899993 0.2100005 1.0000000
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.022280592 0.015866532 0.006525511 0.002796660 0.013317397
## L2 0.015866532 0.025984911 0.005800456 0.002485920 0.011837689
## L3 0.006525511 0.005800456 0.035136823 0.002054426 0.009782957
## L4 0.002796660 0.002485920 0.002054426 0.039050023 0.004192714
## L5 0.013317397 0.011837689 0.009782957 0.004192714 0.019965261
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 62 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 24
##
## Model Test User Model:
##
## Test statistic 8.537
## Degrees of freedom 4
## P-value (Chi-square) 0.074## Extract relevant model parameters
## FIT INDICES
## Chi-squares and p values of the parameter-based models
tfm_model_fit <- t(sapply(tfm.fit.all, function(x) {
fitMeasures(x$fit, c("chisq", "pvalue", "ntotal",
"cfi", "srmr"))}))
row.names(tfm_model_fit) <- names(TTCT1$data)
options(scipen=50)
round(tfm_model_fit,4)## chisq pvalue ntotal cfi srmr
## Auth 4.9636 0.2911 30 0.9336 0.0983
## Barkul 114.0180 0.0000 599 0.9608 0.0288
## Berman 6.7520 0.1496 13 0.8056 0.1312
## Callans 5.7929 0.2152 60 0.9804 0.0720
## Carter 8.5375 0.0738 24 0.9294 0.1234
## Carter 2.0228 0.7316 24 1.0000 0.0333
## Chi 56.2894 0.0000 203 0.8077 0.1096
## Cho 7.8447 0.0974 24 0.9149 0.0717
## Cho 10.2295 0.0367 35 0.9062 0.0962
## Cockcroft 8.3021 0.0811 36 0.8723 0.0992
## Conway 0.8890 0.9261 25 1.0000 0.0184
## Crawford 4.1617 0.3846 21 0.9977 0.0513
## Digranes 6.6504 0.1556 17 0.9507 0.0747
## Fishkin 2.0369 0.7290 116 1.0000 0.0310
## Forsyth 10.3382 0.0351 45 0.9603 0.0653
## Garcia 13.5111 0.0090 95 0.9373 0.0476
## Gollmar 43.1792 0.0000 128 0.7400 0.1268
## Hokanson 283.9768 0.0000 1758 0.9149 0.0735
## Houtz 3.4475 0.4859 42 1.0000 0.0473
## Humble 8.2194 0.0839 125 0.9787 0.0538
## Ibrahim 42.7677 0.0000 99 0.7295 0.0975
## Kim_1 167.2994 0.0000 500 0.8649 0.0992
## Kim_2 192.5836 0.0000 1000 0.9270 0.0605
## Kim_2 77.5064 0.0000 1000 0.9491 0.0616
## Kim_2 236.0753 0.0000 1000 0.9024 0.0848
## Kim_3 64.7562 0.0000 125 0.7276 0.1798
## Kim_3 51.0455 0.0000 137 0.8072 0.1601
## Miranda 1.3888 0.8461 12 1.0000 0.0638
## Nguyen 5.9355 0.2040 187 0.9898 0.0384
## Zbarskaya 4.3965 0.3550 125 0.9970 0.0372
## Rose 7.9987 0.0916 19 0.8937 0.0882
## Rose 8.8010 0.0663 12 0.5348 0.1686
## Roskos 8.9535 0.0623 39 0.8469 0.0889
## Roskos 2.1785 0.7030 31 1.0000 0.0618
## Samuels 4.9267 0.2949 51 0.9836 0.0861
## Shore 17.9608 0.0013 18 0.2736 0.2218
## Stephens 1.8280 0.7674 84 1.0000 0.0280
## Storer 18.1023 0.0012 43 0.8557 0.0882
## Storer 10.3482 0.0350 46 0.9109 0.0710
## Tannehill 7.1674 0.1273 199 0.9916 0.0201
## Tisone 3.5012 0.4777 24 1.0000 0.0752
## Trigani 21.8630 0.0002 107 0.9087 0.0915
## Voss 16.1637 0.0028 120 0.9589 0.0549
## Warne 56.1459 0.0000 432 0.9356 0.0552
## Yoon 23.1916 0.0001 163 0.9369 0.0918
## Zhang 129.4983 0.0000 1067 0.9493 0.0806
## Acar 58.2737 0.0000 477 0.9180 0.0561
## Acaretal 72.5066 0.0000 319 0.8772 0.0887
## Balcia 87.3886 0.0000 1047 0.7544 0.0587
## Balcib 4.8293 0.3053 95 0.9785 0.0421
## Gao 10.6000 0.0314 264 0.9629 0.0356
## Liu 3.6785 0.4513 105 1.0000 0.0299
## Wan 28.6877 0.0000 375 0.8553 0.0558## Write out these indices
write.csv(round(tfm_model_fit,4), "TwoFactorModel4-Fit.csv")
write.table(round(tfm_model_fit,4), "TwoFactorModel4-Fit.txt", sep='\t')
head(tfm_model_fit, 5)## chisq pvalue ntotal cfi srmr
## Auth 4.963578 0.29105512 30 0.9335511 0.09825559
## Barkul 114.017957 0.00000000 599 0.9608442 0.02876380
## Berman 6.752014 0.14958800 13 0.8056406 0.13120072
## Callans 5.792855 0.21516132 60 0.9803705 0.07195184
## Carter 8.537495 0.07375882 24 0.9293966 0.12344312## Extract the scale reliability coefficients from the primary studies
## Point estimates
tfm.srl1 <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[14,5]}))
tfm.srl2 <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[15,5]}))
tfm.srlcr <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[16,5]}))
## Standard errors
tfm.srl1.se <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[14,6]}))
tfm.srl2.se <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[15,6]}))
tfm.srlcr.se <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[16,6]}))
## Lower 95% CI bound
tfm.srl1.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[14,9]}))
tfm.srl2.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[15,9]}))
tfm.srlcr.ci.low <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[16,9]}))
## Upper 95% CI bound
tfm.srl1.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[14,10]}))
tfm.srl2.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[15,10]}))
tfm.srlcr.ci.upp <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[16,10]}))
## Factor correlation
tfm.fcorr <- t(sapply(1:k, function(x) {parameterEstimates(tfm.fit.all[[x]]$fit)[13,5]}))
## Save these statistics
tfm.srl.summary <- data.frame(names.studies,
TTCT1$n,
t(tfm.srl1 ),
t(tfm.srl1.se),
t(tfm.srl1.ci.low),
t(tfm.srl1.ci.upp),
t(tfm.srl2),
t(tfm.srl2.se),
t(tfm.srl2.ci.low),
t(tfm.srl2.ci.upp),
t(tfm.srlcr),
t(tfm.srlcr.se),
t(tfm.srlcr.ci.low),
t(tfm.srlcr.ci.upp),
t(tfm.fcorr))
colnames(tfm.srl.summary) <- c("Study",
"N",
"Omega Factor 1",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Omega Factor 2",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Composite reliability",
"SE",
"Lower 95% CI",
"Upper 95% CI",
"Factor correlation")
tfm.srl.summary## Study N Omega Factor 1 SE Lower 95% CI Upper 95% CI
## 1 Auth 30 0.7700003 0.073695681 0.62555945 0.9144412
## 2 Barkul 599 0.9744939 0.002080806 0.97041555 0.9785722
## 3 Berman 13 0.6950003 0.141042586 0.41856188 0.9714387
## 4 Callans 60 0.8827988 0.031949253 0.82017946 0.9454182
## 5 Carter_a 24 0.9279418 0.029174066 0.87076173 0.9851220
## 6 Carter_b 24 0.9099999 0.035050009 0.84130312 0.9786966
## 7 Chi 203 0.7165000 0.033685510 0.65047763 0.7825224
## 8 Cho_F 24 0.8050006 0.071425899 0.66500843 0.9449928
## 9 Cho_M 35 0.7476911 0.085012742 0.58106919 0.9143130
## 10 Cockcroft 36 0.5554435 0.188006684 0.18695714 0.9239298
## 11 Conway 25 0.9011436 0.039548341 0.82363032 0.9786570
## 12 Crawford 21 0.9700000 0.012895183 0.94472590 0.9952741
## 13 Digranes 17 0.8640321 0.065895715 0.73487891 0.9931854
## 14 Fishkin 116 0.7595687 0.052606411 0.65646200 0.8626753
## 15 Forsyth 45 0.9538664 0.013684640 0.92704499 0.9806878
## 16 Garcia 95 0.7710162 0.047072858 0.67875512 0.8632773
## 17 Gollmar 128 0.8359994 0.026507783 0.78404511 0.8879537
## 18 Hokanson 1758 0.8949419 0.005770018 0.88363288 0.9062509
## 19 Houtz 42 0.7823017 0.080033070 0.62543972 0.9391636
## 20 Humble 125 0.9132729 0.016844923 0.88025750 0.9462884
## 21 Ibrahim 99 0.7596899 0.048448655 0.66473228 0.8546475
## 22 Kim_1 500 0.9209904 0.007201180 0.90687639 0.9351045
## 23 Kim_2a 1000 0.9130688 0.005498046 0.90229281 0.9238448
## 24 Kim_2b 1000 0.8830057 0.007417871 0.86846695 0.8975445
## 25 Kim_2c 1000 0.9282173 0.004592202 0.91921677 0.9372179
## 26 Kim_3a 125 0.7300000 0.041266747 0.64911862 0.8108813
## 27 Kim_3b 137 0.7000003 0.042888383 0.61594059 0.7840600
## 28 Miranda 12 0.6674744 0.201382393 0.27277217 1.0621766
## 29 Nguyen 187 0.8623294 0.021582766 0.82002798 0.9046309
## 30 Zbarskaya 125 0.8070000 0.031014799 0.74621216 0.8677879
## 31 Rose 19 0.8959023 0.047807892 0.80220051 0.9896040
## 32 Rose_b 12 0.8350000 0.087049574 0.66438593 1.0056140
## 33 Roskos_Y 39 0.4299804 0.188549800 0.06042962 0.7995313
## 34 Roskos_O 31 0.3140816 0.300832780 -0.27553980 0.9037030
## 35 Samuels 51 0.8750002 0.032745994 0.81081927 0.9391812
## 36 Shore 18 0.6299999 0.138441342 0.35865989 0.9013400
## 37 Stephens 84 0.9262282 0.016156380 0.89456231 0.9578942
## 38 Storer_a 43 0.8959024 0.031779111 0.83361644 0.9581883
## 39 Storer_b 46 0.8439369 0.046020784 0.75373784 0.9341360
## 40 Tannehill 199 0.9161898 0.012441007 0.89180584 0.9405737
## 41 Tisone 24 0.8400000 0.059866512 0.72266381 0.9573362
## 42 Trigani 107 0.8600006 0.025102314 0.81080093 0.9092002
## 43 Voss 120 0.8378753 0.029424061 0.78020522 0.8955454
## 44 Warne 432 0.8564004 0.013961649 0.82903610 0.8837648
## 45 Yoon 163 0.8650001 0.019668799 0.82644992 0.9035502
## 46 Zhang 1067 0.8821890 0.007137126 0.86820044 0.8961775
## 47 Acar 477 0.7879230 0.019422465 0.74985562 0.8259903
## 48 Acaretal 319 0.8659268 0.015029260 0.83647000 0.8953836
## 49 Balcia 1047 0.6460001 0.017586365 0.61153148 0.6804688
## 50 Balcib 95 0.6047810 0.083199766 0.44171246 0.7678495
## 51 Gao 264 0.4732834 0.064834453 0.34621024 0.6003566
## 52 Liu 105 0.9692173 0.006039498 0.95738007 0.9810545
## 53 Wan 375 0.4282572 0.059613730 0.31141646 0.5450980
## Omega Factor 2 SE Lower 95% CI Upper 95% CI Composite reliability
## 1 0.45624463 0.17409530 0.11502411 0.7974652 0.6874343
## 2 0.77863942 0.01432646 0.75056007 0.8067188 0.9172739
## 3 0.76409048 0.10526202 0.55778071 0.9704002 0.6762777
## 4 0.65864387 0.06537841 0.53050455 0.7867832 0.8232824
## 5 0.62746975 0.11075333 0.41039721 0.8445423 0.8533497
## 6 0.60965463 0.13709507 0.34095323 0.8783560 0.8498451
## 7 0.73092237 0.03255818 0.66710951 0.7947352 0.8028454
## 8 0.78704960 0.07139832 0.64711146 0.9269877 0.8653867
## 9 0.53593998 0.12201920 0.29678675 0.7750932 0.7712868
## 10 0.64197605 0.09590072 0.45401408 0.8299380 0.7316390
## 11 0.83260782 0.05680361 0.72127479 0.9439409 0.9084899
## 12 0.75090462 0.08896888 0.57652882 0.9252804 0.9017108
## 13 0.74279966 0.10223453 0.54242367 0.9431757 0.8840397
## 14 0.13501415 0.13384830 -0.12732370 0.3973520 0.5451633
## 15 0.72290929 0.06714584 0.59130587 0.8545127 0.8942712
## 16 0.73147909 0.04742468 0.63852843 0.8244298 0.8370563
## 17 0.57767217 0.06370018 0.45282212 0.7025222 0.7373011
## 18 0.66848336 0.01363646 0.64175639 0.6952103 0.8356207
## 19 0.63128965 0.09716736 0.44084511 0.8217342 0.7921521
## 20 0.45739326 0.08042479 0.29976356 0.6150230 0.7720023
## 21 0.59575313 0.06800033 0.46247492 0.7290313 0.7734210
## 22 0.60299308 0.02887455 0.54640001 0.6595862 0.8330267
## 23 0.69120730 0.01660130 0.65866936 0.7237452 0.8681365
## 24 0.45982149 0.03034301 0.40035029 0.5192927 0.7583341
## 25 0.57274705 0.02227366 0.52909149 0.6164026 0.8274552
## 26 0.81414657 0.02790440 0.75945495 0.8688382 0.7397523
## 27 0.83913813 0.02259066 0.79486124 0.8834150 0.7616337
## 28 0.04610459 0.17784906 -0.30247317 0.3946823 0.4571518
## 29 0.22396085 0.10291225 0.02225656 0.4256651 0.6642839
## 30 0.70948779 0.03970823 0.63166108 0.7873145 0.7953206
## 31 0.55870035 0.14077852 0.28277951 0.8346212 0.8163590
## 32 0.59599430 0.16621832 0.27021238 0.9217762 0.7568527
## 33 0.64891319 0.09356723 0.46552478 0.8323016 0.7144250
## 34 0.66999465 0.08855887 0.49642245 0.8435668 0.6355428
## 35 0.63343611 0.07502833 0.48638329 0.7804889 0.7764478
## 36 0.68826146 0.12894239 0.43553903 0.9409839 0.5965216
## 37 0.55117737 0.08116852 0.39208999 0.7102647 0.8204643
## 38 0.55870048 0.09357911 0.37528880 0.7421122 0.8163591
## 39 0.53121564 0.11713183 0.30164147 0.7607898 0.7952131
## 40 0.65969490 0.04177264 0.57782203 0.7415678 0.8386434
## 41 0.62199784 0.12765061 0.37180724 0.8721884 0.7710646
## 42 0.62354154 0.05290719 0.51984535 0.7272377 0.8171664
## 43 0.74098227 0.03907849 0.66438983 0.8175747 0.8692816
## 44 0.65742730 0.02780843 0.60292377 0.7119308 0.8352745
## 45 0.79446255 0.02747778 0.74060709 0.8483180 0.8557819
## 46 0.38759036 0.03173293 0.32539496 0.4497858 0.7712278
## 47 0.61657373 0.02990038 0.55797007 0.6751774 0.7961029
## 48 0.56882185 0.04065881 0.48913204 0.6485117 0.8033695
## 49 0.38402612 0.03195386 0.32139770 0.4466545 0.5647673
## 50 0.32904399 0.10989756 0.11364873 0.5444392 0.5565458
## 51 0.52320575 0.05035568 0.42451043 0.6219011 0.6757915
## 52 0.84682712 0.02577615 0.79630679 0.8973475 0.9254409
## 53 0.49301651 0.04512961 0.40456410 0.5814689 0.6127853
## SE Lower 95% CI Upper 95% CI Factor correlation
## 1 0.089172197 0.51266000 0.8622086 0.5250131
## 2 0.005562633 0.90637138 0.9281765 0.8720216
## 3 0.114536395 0.45179054 0.9007650 -0.2899996
## 4 0.034783979 0.75510706 0.8914578 0.5302387
## 5 0.047287275 0.76066833 0.9460310 0.8234923
## 6 0.050779068 0.75031999 0.9493703 1.0336723
## 7 0.021735104 0.76024536 0.8454454 0.5716607
## 8 0.043172322 0.78077054 0.9500029 0.7090588
## 9 0.061062399 0.65160666 0.8909669 0.9957951
## 10 0.072698823 0.58915192 0.8741261 0.7845056
## 11 0.029817101 0.85004946 0.9669303 0.6827169
## 12 0.035560859 0.83201280 0.9714088 0.7643346
## 13 0.045706132 0.79445729 0.9736220 1.0398209
## 14 0.070251030 0.40747384 0.6828528 0.6704365
## 15 0.026008062 0.84329635 0.9452461 0.8915926
## 16 0.027244187 0.78365869 0.8904539 0.7791342
## 17 0.036354007 0.66604852 0.8085536 0.2946672
## 18 0.006418958 0.82303978 0.8482016 0.6169859
## 19 0.051780409 0.69066433 0.8936398 0.7257213
## 20 0.033500218 0.70634311 0.8376615 0.6891124
## 21 0.036703874 0.70148273 0.8453593 0.7498885
## 22 0.012075119 0.80935995 0.8566935 0.7292714
## 23 0.006883575 0.85464495 0.8816281 0.8568125
## 24 0.012683112 0.73347561 0.7831925 0.6521377
## 25 0.008944629 0.80992409 0.8449864 0.7642222
## 26 0.032991000 0.67509111 0.8044135 -0.2595952
## 27 0.028219152 0.70632520 0.8169422 -0.2178581
## 28 0.225939266 0.01431894 0.8999846 0.6841114
## 29 0.041725233 0.58250396 0.7460639 0.8047517
## 30 0.026779849 0.74283305 0.8478081 0.3269999
## 31 0.064886960 0.68918285 0.9435351 0.7107625
## 32 0.100135516 0.56059070 0.9531147 0.3400007
## 33 0.074331273 0.56873837 0.8601116 0.9707069
## 34 0.105000135 0.42974630 0.8413393 0.5037385
## 35 0.045035613 0.68817960 0.8647160 0.2399999
## 36 0.136849912 0.32830071 0.8647425 -0.2906585
## 37 0.032228515 0.75729762 0.8836311 0.7700793
## 38 0.043132015 0.73182188 0.9008963 0.7107627
## 39 0.049547402 0.69810200 0.8923242 0.9521721
## 40 0.018983592 0.80143623 0.8758505 0.6041018
## 41 0.072799427 0.62838038 0.9137489 0.3688393
## 42 0.026912805 0.76441824 0.8699145 0.6899985
## 43 0.019220322 0.83161048 0.9069528 0.9260633
## 44 0.012890119 0.81001034 0.8605387 0.8128623
## 45 0.017943182 0.82061395 0.8909499 0.3176184
## 46 0.012018395 0.74767218 0.7947834 1.0418061
## 47 0.015185967 0.76633894 0.8258668 0.8029838
## 48 0.017997045 0.76809598 0.8386431 0.7857492
## 49 0.019922710 0.52571955 0.6038151 0.3553703
## 50 0.070746154 0.41788587 0.6952057 0.4998183
## 51 0.032542279 0.61200981 0.7395732 1.0997318
## 52 0.012211446 0.90150695 0.9493749 0.5310279
## 53 0.032670096 0.54875314 0.6768176 0.8372851## Write out the results
write.table(tfm.srl.summary, "TwoFactorModel4-Reliability.txt", sep='\t')
## Note: The standard errors of the derived parameters are identical
## to the asymptotic sampling errors.2.2 Stage-2 Analysis: Meta-Analysis of the Reliability Coefficients
2.2.1 Data Preparation
## Create effect size and study identifiers
esid <- as.vector(seq(1:length(TTCT1$data)))
studid <- as.vector(as.numeric(as.factor(names.studid)))
## Create a meta-analytic data set with effect sizes,
## sampling variances, and moderators
srel.meta1 <- data.frame(esid, studid, names.studies,
TTCT1$n,
t(tfm.srl1), t(tfm.srl1.se),
t(tfm.srl2), t(tfm.srl2.se),
t(tfm.srlcr), t(tfm.srlcr.se),
t(tfmc.srl1), t(tfmc.srl1.se),
t(tfmc.srl2), t(tfmc.srl2.se),
t(tfmc.srlcr), t(tfmc.srlcr.se),
t(tfm.fcorr), t(tfmc.fcorr),
mod.adults, mod.forms,
mod.scores, mod.validity)
## Column names
colnames(srel.meta1) <- c("ESID", "STUDID", "Reference",
"N",
"SREL1", "SE.SREL1",
"SREL2", "SE.SREL2",
"SRELCR", "SE.SRELCR",
"SREL1C", "SE.SREL1C",
"SREL2C", "SE.SREL2C",
"SRELCRC", "SE.SRELCRC",
"Fcorr", "FcorrC",
"Adults", "Forms",
"Scores", "Validity")
## Create sampling variances
srel.meta1$SREL1.vg <- srel.meta1$SE.SREL1^2
srel.meta1$SREL2.vg <- srel.meta1$SE.SREL2^2
srel.meta1$SRELCR.vg <- srel.meta1$SE.SRELCR^2
srel.meta1$SREL1C.vg <- srel.meta1$SE.SREL1C^2
srel.meta1$SREL2C.vg <- srel.meta1$SE.SREL2C^2
srel.meta1$SRELCRC.vg <- srel.meta1$SE.SRELCRC^2
## Identify the studies with poor model fit
tfm_model_fit## chisq pvalue ntotal cfi srmr
## Auth 4.9635776 2.910551e-01 30 0.9335511 0.09825559
## Barkul 114.0179567 0.000000e+00 599 0.9608442 0.02876380
## Berman 6.7520142 1.495880e-01 13 0.8056406 0.13120072
## Callans 5.7928546 2.151613e-01 60 0.9803705 0.07195184
## Carter 8.5374948 7.375882e-02 24 0.9293966 0.12344312
## Carter 2.0227827 7.315683e-01 24 1.0000000 0.03325786
## Chi 56.2893634 1.743727e-11 203 0.8077218 0.10964189
## Cho 7.8447267 9.743453e-02 24 0.9149484 0.07170580
## Cho 10.2295462 3.673353e-02 35 0.9061654 0.09617379
## Cockcroft 8.3021446 8.111662e-02 36 0.8723006 0.09924377
## Conway 0.8889755 9.261371e-01 25 1.0000000 0.01843786
## Crawford 4.1616946 3.845649e-01 21 0.9976996 0.05125261
## Digranes 6.6504236 1.555558e-01 17 0.9506538 0.07473993
## Fishkin 2.0368505 7.289810e-01 116 1.0000000 0.03097716
## Forsyth 10.3381919 3.510037e-02 45 0.9602724 0.06526681
## Garcia 13.5111291 9.030442e-03 95 0.9372565 0.04764523
## Gollmar 43.1791907 9.498747e-09 128 0.7400054 0.12680085
## Hokanson 283.9767705 0.000000e+00 1758 0.9149149 0.07349493
## Houtz 3.4474977 4.859062e-01 42 1.0000000 0.04730142
## Humble 8.2194499 8.386228e-02 125 0.9787311 0.05375296
## Ibrahim 42.7677064 1.156233e-08 99 0.7294550 0.09754886
## Kim_1 167.2993976 0.000000e+00 500 0.8649442 0.09923085
## Kim_2 192.5835800 0.000000e+00 1000 0.9270304 0.06051507
## Kim_2 77.5063974 5.551115e-16 1000 0.9490579 0.06163331
## Kim_2 236.0752688 0.000000e+00 1000 0.9024048 0.08477319
## Kim_3 64.7562446 2.896572e-13 125 0.7275914 0.17983244
## Kim_3 51.0455158 2.183865e-10 137 0.8072334 0.16014229
## Miranda 1.3887585 8.461465e-01 12 1.0000000 0.06378383
## Nguyen 5.9355052 2.040168e-01 187 0.9897562 0.03840829
## Zbarskaya 4.3964860 3.549986e-01 125 0.9969846 0.03721615
## Rose 7.9986995 9.162585e-02 19 0.8936954 0.08815120
## Rose 8.8009741 6.627133e-02 12 0.5347775 0.16864982
## Roskos 8.9535133 6.227199e-02 39 0.8469183 0.08886656
## Roskos 2.1784895 7.029693e-01 31 1.0000000 0.06181563
## Samuels 4.9266837 2.949033e-01 51 0.9835969 0.08610035
## Shore 17.9607613 1.256080e-03 18 0.2735955 0.22179542
## Stephens 1.8279847 7.673586e-01 84 1.0000000 0.02798716
## Storer 18.1023205 1.178548e-03 43 0.8557475 0.08815127
## Storer 10.3481802 3.495378e-02 46 0.9109395 0.07096107
## Tannehill 7.1674124 1.273013e-01 199 0.9915642 0.02005184
## Tisone 3.5011952 4.776966e-01 24 1.0000000 0.07522753
## Trigani 21.8629651 2.134086e-04 107 0.9087319 0.09152566
## Voss 16.1637294 2.807151e-03 120 0.9589320 0.05493900
## Warne 56.1459071 1.868794e-11 432 0.9355730 0.05516412
## Yoon 23.1916233 1.159389e-04 163 0.9369490 0.09184230
## Zhang 129.4982963 0.000000e+00 1067 0.9492744 0.08064859
## Acar 58.2737384 6.685208e-12 477 0.9179879 0.05611845
## Acaretal 72.5065989 6.661338e-15 319 0.8771856 0.08868595
## Balcia 87.3885778 0.000000e+00 1047 0.7544349 0.05869789
## Balcib 4.8292585 3.052695e-01 95 0.9784702 0.04205625
## Gao 10.6000200 3.144678e-02 264 0.9629362 0.03563730
## Liu 3.6784591 4.512667e-01 105 1.0000000 0.02992893
## Wan 28.6876679 9.046612e-06 375 0.8553399 0.05579743### EXCLUSIONS DUE TO POOR MODEL FIT
## Exclude samples with at least two fails on the following three criteria:
## Significant chi-square value (p>.05), CFI >= .90, SRMR <= .10
fitexclude <- c(3,7,17,21,22,26,27,32,36,38, 49, 53)
## Data exclusions due to poor model fit
srel.meta <- srel.meta1[-fitexclude,]
## ADD NEW MODERATORS (see Table 1 in the manuscript)
srel.meta$LanguageEnglish <- c(1,0,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,0,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,0,1,0,
1,1,0,0,0)
srel.meta$Culture <- c("Western","Eastern","Western","Western",
"Western","Western","Western","African",
"Western","Western","Western","Western",
"Western","Western","Western","Western",
"African","Western","Western","Western",
"Western","Mixed","Western","Western",
"Western","Western","Western","Western",
"Western","Western","Western","Western",
"Western","Eastern","Western","Eastern",
"Mixed","Western","Eastern","Eastern",
"Eastern")
table(srel.meta$Culture)##
## African Eastern Mixed Western
## 2 6 2 31srel.meta$CultureWestern <- c(1,0,1,1,1,1,1,0,1,1,1,1,1,
1,1,1,0,1,1,1,1,0,1,1,1,1,
1,1,1,1,1,1,1,0,1,0,0,1,0,
0,0)
srel.meta$PropFemale <- c(53,62.1,75,54.17,79.17,100,0,
27.8,60,52,47.05,38.79,NA,NA,
50,69.05,54,51.27,51.27,51.27,
58.33,70.59,75,49,73,94.12,45,
50,50,50,100,46,75,39.9,100,
44.7,69.83,52.94,52,31.66,47.94)
head(srel.meta, 5)## ESID STUDID Reference N SREL1 SE.SREL1 SREL2 SE.SREL2
## 1 1 3 Auth 30 0.7700003 0.073695681 0.4562446 0.17409530
## 2 2 6 Barkul 599 0.9744939 0.002080806 0.7786394 0.01432646
## 4 4 8 Callans 60 0.8827988 0.031949253 0.6586439 0.06537841
## 5 5 9 Carter_a 24 0.9279418 0.029174066 0.6274697 0.11075333
## 6 6 9 Carter_b 24 0.9099999 0.035050009 0.6096546 0.13709507
## SRELCR SE.SRELCR SREL1C SE.SREL1C SREL2C SE.SREL2C SRELCRC
## 1 0.6874343 0.089172197 0.6536706 0.10785668 0.4304457 0.22889696 0.7080218
## 2 0.9172739 0.005562633 0.7877730 0.02851258 0.8229706 0.02047607 0.9178338
## 4 0.8232824 0.034783979 0.8563297 0.04085155 0.6209308 0.08270351 0.8126529
## 5 0.8533497 0.047287275 0.9271543 0.02569187 0.7684078 0.07699323 0.9125341
## 6 0.8498451 0.050779068 0.8470190 0.22787179 0.4775192 0.73579760 0.8488549
## SE.SRELCRC Fcorr FcorrC Adults Forms Scores Validity SREL1.vg
## 1 0.093818456 0.5250131 0.4756440 1 <NA> 1 0 5.431053e-03
## 2 0.005606417 0.8720216 0.8964628 1 A 0 0 4.329754e-06
## 4 0.039229646 0.5302387 0.3046393 1 A 1 0 1.020755e-03
## 5 0.028867430 0.8234923 0.3155412 0 A 0 1 8.511261e-04
## 6 0.052077286 1.0336723 1.0626498 0 A 0 1 1.228503e-03
## SREL2.vg SRELCR.vg SREL1C.vg SREL2C.vg SRELCRC.vg
## 1 0.0303091744 7.951681e-03 0.0116330628 0.0523938196 8.801903e-03
## 2 0.0002052475 3.094289e-05 0.0008129674 0.0004192693 3.143191e-05
## 4 0.0042743360 1.209925e-03 0.0016688495 0.0068398708 1.538965e-03
## 5 0.0122663005 2.236086e-03 0.0006600723 0.0059279576 8.333285e-04
## 6 0.0187950590 2.578514e-03 0.0519255515 0.5413981029 2.712044e-03
## LanguageEnglish Culture CultureWestern PropFemale
## 1 1 Western 1 53.00
## 2 0 Eastern 0 62.10
## 4 1 Western 1 75.00
## 5 1 Western 1 54.17
## 6 1 Western 1 79.172.2.2 Description of the Meta-Analytic Data
## Number of effect sizes
length(srel.meta$ESID)## [1] 41## Number of primary studies
length(unique(srel.meta$STUDID))## [1] 36## Proportion adult samples
prop.table(table(srel.meta$Adults))##
## 0 1
## 0.5609756 0.4390244## Proportion evidence against validity
prop.table(table(srel.meta$Validity))##
## 0 1
## 0.5853659 0.4146341## Distribution of test forms
prop.table(table(srel.meta$Forms))##
## A B Both
## 0.80555556 0.13888889 0.05555556## Distribution of test score types
prop.table(table(srel.meta$Scores))##
## 0 1
## 0.6153846 0.3846154## Distribution of the sample sizes
psych::describe(srel.meta$N)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 41 244.93 385.48 95 156 103.78 12 1758 1746 2.2 4.44
## se
## X1 60.2sum(unique(srel.meta$N))## [1] 7750## Distribution of English language
prop.table(table(srel.meta$LanguageEnglish))##
## 0 1
## 0.1707317 0.8292683## Distribution of cultures
prop.table(table(srel.meta$Culture))##
## African Eastern Mixed Western
## 0.04878049 0.14634146 0.04878049 0.75609756prop.table(table(srel.meta$CultureWestern))##
## 0 1
## 0.2439024 0.7560976## Distribution of the proportion of women in the samples
psych::describe(srel.meta$PropFemale)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 39 57.72 20.25 52 57.32 10.82 0 100 100 0.15 0.76 3.24The meta-analytic data are hierarchical with multiple effect sizes derived from independent samples that are nested in primary studies.
2.2.3 Meta-Analysis of the Two-Factor Model without Cross-Loadings
2.2.3.1 Meta-Analytic Baseline Models
## Reliability of factor 1
## Three-level REM
## Model specification and estimation
MLREMCSC.tfm.srel1 <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t")
## Summarize the results
summary(MLREMCSC.tfm.srel1, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 35.6884 -71.3768 -65.3768 -60.3102 -64.7101
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0057 0.0757 36 no STUDID
## sigma^2.2 0.0004 0.0203 41 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 40) = 861.2384, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.8570 0.0148 57.9085 40 <.0001 0.8271 0.8869 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## 95% confidence intervals
confint(MLREMCSC.tfm.srel1, digits=4)##
## estimate ci.lb ci.ub
## sigma^2.1 0.0057 0.0016 0.0123
## sigma.1 0.0757 0.0394 0.1109
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0004 0.0001 0.0039
## sigma.2 0.0203 0.0091 0.0628## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfm.srel1))## % of total variance I2
## Level 1 1.922637 ---
## Level 2 6.554086 6.55
## Level 3 91.523277 91.52
## Total I2: 98.08%plot(dmetar::var.comp(MLREMCSC.tfm.srel1))
## RVE standard errors
clubSandwich::conf_int(MLREMCSC.tfm.srel1, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.857 0.0148 31.8 0.827 0.887# Profile plots
profile.rma.mv(MLREMCSC.tfm.srel1, sigma2=1)
profile.rma.mv(MLREMCSC.tfm.srel1, sigma2=2)
## Reliability of factor 2
## Three-level REM
## Model specification and estimation
MLREMCSC.tfm.srel2 <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t")
## Summarize the results
summary(MLREMCSC.tfm.srel2, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 16.3594 -32.7188 -26.7188 -21.6521 -26.0521
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0167 0.1293 41 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 40) = 382.1116, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.6184 0.0234 26.4764 40 <.0001 0.5712 0.6656 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## 95% confidence intervals
confint(MLREMCSC.tfm.srel2, digits=4)##
## estimate ci.lb ci.ub
## sigma^2.1 0.0000 0.0000 0.0231
## sigma.1 0.0000 0.0000 0.1520
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0167 0.0029 0.0313
## sigma.2 0.1293 0.0543 0.1769## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfm.srel2))## % of total variance I2
## Level 1 8.1522935395056 ---
## Level 2 91.8477061651105 91.85
## Level 3 0.0000002953839 0
## Total I2: 91.85%plot(dmetar::var.comp(MLREMCSC.tfm.srel2))
## RVE standard errors
clubSandwich::conf_int(MLREMCSC.tfm.srel2, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.618 0.0228 28.2 0.572 0.665# Profile plots
profile.rma.mv(MLREMCSC.tfm.srel2, sigma2=1)
profile.rma.mv(MLREMCSC.tfm.srel2, sigma2=2)
## Composite reliability
## Three-level REM
## Model specification and estimation
MLREMCSC.tfm.srelcr <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t")
## Summarize the results
summary(MLREMCSC.tfm.srelcr, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 41.7088 -83.4175 -77.4175 -72.3509 -76.7509
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0012 0.0353 36 no STUDID
## sigma^2.2 0.0031 0.0555 41 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 40) = 451.2230, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.8098 0.0123 65.7916 40 <.0001 0.7849 0.8347 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## 95% confidence intervals
confint(MLREMCSC.tfm.srelcr, digits=4)##
## estimate ci.lb ci.ub
## sigma^2.1 0.0012 0.0000 0.0070
## sigma.1 0.0353 0.0000 0.0839
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0031 0.0006 0.0081
## sigma.2 0.0555 0.0237 0.0899## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfm.srelcr))## % of total variance I2
## Level 1 6.556074 ---
## Level 2 66.537875 66.54
## Level 3 26.906050 26.91
## Total I2: 93.44%plot(dmetar::var.comp(MLREMCSC.tfm.srelcr))
## RVE standard errors
clubSandwich::conf_int(MLREMCSC.tfm.srelcr, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.81 0.0123 30.8 0.785 0.835# Profile plots
profile.rma.mv(MLREMCSC.tfm.srel1, sigma2=1)
profile.rma.mv(MLREMCSC.tfm.srel1, sigma2=2)
2.2.3.2 Moderator Analyses for the Reliability of Factor 1
2.2.3.2.1 MODERATOR: Age groups
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel1.age <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Adults)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.age, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 35.2617 -70.5235 -62.5235 -55.8692 -61.3470
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0056 0.0751 36 no STUDID
## sigma^2.2 0.0004 0.0204 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 569.5950, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 2.0193, p-val = 0.1633
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8746 0.0192 45.6565 39 <.0001 0.8359 0.9134 ***
## Adults -0.0425 0.0299 -1.4210 39 0.1633 -0.1029 0.0180
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.age, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8746 0.0153 17.7 0.842 0.9068
## Adults -0.0425 0.0321 27.7 -0.108 0.0232## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8746 0.0192 0.8359 0.9134 0.7125 1.0367
## 2 0.8322 0.0229 0.7858 0.8785 0.6680 0.99632.2.3.2.2 MODERATOR: Validity evidence
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel1.validity <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Validity)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.validity, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 35.2468 -70.4937 -62.4937 -55.8394 -61.3172
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0053 0.0731 36 no STUDID
## sigma^2.2 0.0004 0.0202 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 711.9575, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 2.0428, p-val = 0.1609
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8736 0.0181 48.1664 39 <.0001 0.8369 0.9103 ***
## Validity -0.0426 0.0298 -1.4293 39 0.1609 -0.1028 0.0177
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.validity, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8736 0.0195 18.8 0.8327 0.9146
## Validity -0.0426 0.0277 24.7 -0.0997 0.0146## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8736 0.0181 0.8369 0.9103 0.7159 1.0314
## 2 0.8311 0.0236 0.7833 0.8788 0.6704 0.99182.2.3.2.3 MODERATOR: Test forms
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel1.forms <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ factor(Forms))
## Summarize the results
summary(MLMEMCSC.tfm.srel1.forms, digits=4)##
## Multivariate Meta-Analysis Model (k = 36; method: REML)
##
## logLik Deviance AIC BIC AICc
## 38.8235 -77.6470 -67.6470 -60.1645 -65.4248
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0023 0.0484 32 no STUDID
## sigma^2.2 0.0004 0.0209 36 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 33) = 718.8632, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 2.4598, p-val = 0.1010
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8817 0.0120 73.2497 33 <.0001 0.8572 0.9062 ***
## factor(Forms)B -0.0881 0.0397 -2.2178 33 0.0336 -0.1689 -0.0073 *
## factor(Forms)Both -0.0096 0.0492 -0.1949 33 0.8467 -0.1096 0.0905
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.forms, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.88168 0.0105 21.93 0.860 0.903
## factor(Forms)B -0.08811 0.0467 2.52 -0.254 0.078
## factor(Forms)Both -0.00958 0.1482 1.13 -1.447 1.428## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.forms, newmods = cbind(c(0,1,0),
c(0,0,1)))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8817 0.0120 0.8572 0.9062 0.7716 0.9917
## 2 0.7936 0.0379 0.7165 0.8706 0.6615 0.9256
## 3 0.8721 0.0477 0.7751 0.9691 0.7275 1.01672.2.3.2.4 MODERATOR: Test scores
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel1.scores <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Scores)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.scores, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 41.2898 -82.5795 -74.5795 -68.1359 -73.3295
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0026 0.0510 34 no STUDID
## sigma^2.2 0.0004 0.0201 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 770.1361, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.7340, p-val = 0.3971
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8610 0.0148 58.1850 37 <.0001 0.8310 0.8909 ***
## Scores 0.0197 0.0229 0.8568 37 0.3971 -0.0268 0.0661
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.scores, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8610 0.0153 15.6 0.8285 0.8934
## Scores 0.0197 0.0226 24.5 -0.0269 0.0662## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8610 0.0148 0.8310 0.8909 0.7459 0.9761
## 2 0.8806 0.0175 0.8451 0.9161 0.7640 0.99732.2.3.2.5 MODERATOR: Language English
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel1.lang <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ LanguageEnglish)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.lang, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 34.2111 -68.4223 -60.4223 -53.7680 -59.2458
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0062 0.0786 36 no STUDID
## sigma^2.2 0.0004 0.0203 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 498.6571, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.0630, p-val = 0.8032
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8487 0.0331 25.6500 39 <.0001 0.7818 0.9157 ***
## LanguageEnglish 0.0094 0.0373 0.2509 39 0.8032 -0.0660 0.0848
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.lang, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.84872 0.0566 5.65 0.708 0.989
## LanguageEnglish 0.00935 0.0579 8.95 -0.122 0.141## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8487 0.0331 0.7818 0.9157 0.6715 1.0260
## 2 0.8581 0.0172 0.8233 0.8928 0.6903 1.02582.2.3.2.6 MODERATOR: Western Culture
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel1.cult <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ CultureWestern)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.cult, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 34.5110 -69.0221 -61.0221 -54.3678 -59.8456
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0061 0.0783 36 no STUDID
## sigma^2.2 0.0004 0.0203 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 560.5630, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.5939, p-val = 0.4456
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8376 0.0285 29.3705 39 <.0001 0.7799 0.8953 ***
## CultureWestern 0.0260 0.0337 0.7706 39 0.4456 -0.0422 0.0941
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.cult, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.838 0.0433 7.96 0.7376 0.938
## CultureWestern 0.026 0.0451 14.72 -0.0704 0.122## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8376 0.0285 0.7799 0.8953 0.6641 1.0111
## 2 0.8636 0.0180 0.8272 0.8999 0.6960 1.03122.2.3.2.7 MODERATOR: Proportion of women in the sample
## Three-level MEM
## Model specification and estimation
## Note: The proportion is arcsine-square-root transformed to stabilize the distribution
## and approximate normality.
## Source: Schwarzer et al. (2019), https://doi.org/10.1002/jrsm.1348
MLMEMCSC.tfm.srel1.female <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ asin(sqrt(PropFemale/100)))
## Summarize the results
summary(MLMEMCSC.tfm.srel1.female, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 32.3550 -64.7099 -56.7099 -50.2662 -55.4599
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0058 0.0763 34 no STUDID
## sigma^2.2 0.0004 0.0206 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 759.1623, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.1570, p-val = 0.6942
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.8380 0.0469 17.8673 37 <.0001 0.7430
## asin(sqrt(PropFemale/100)) 0.0199 0.0502 0.3963 37 0.6942 -0.0819
## ci.ub
## intrcpt 0.9331 ***
## asin(sqrt(PropFemale/100)) 0.1217
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel1.female, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8380 0.0406 4.13 0.7266 0.949
## asin(sqrt(PropFemale/100)) 0.0199 0.0334 2.98 -0.0868 0.1272.2.3.3 Moderator Analyses for the Reliability of Factor 2
2.2.3.3.1 MODERATOR: Age groups
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel2.age <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Adults)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.age, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.8410 -31.6819 -23.6819 -17.0277 -22.5054
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0164 0.1281 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 335.1810, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.9387, p-val = 0.3386
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5992 0.0307 19.5350 39 <.0001 0.5372 0.6612 ***
## Adults 0.0454 0.0468 0.9689 39 0.3386 -0.0494 0.1401
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.age, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.5992 0.0288 14.2 0.5376 0.661
## Adults 0.0454 0.0455 26.8 -0.0479 0.139## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.5992 0.0307 0.5372 0.6612 0.3328 0.8656
## 2 0.6446 0.0354 0.5730 0.7162 0.3757 0.91342.2.3.3.2 MODERATOR: Validity evidence
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel2.validity <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Validity)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.validity, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.8191 -31.6383 -23.6383 -16.9840 -22.4618
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0171 0.1308 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 371.5694, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.8343, p-val = 0.3666
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6348 0.0298 21.2820 39 <.0001 0.5745 0.6952 ***
## Validity -0.0445 0.0487 -0.9134 39 0.3666 -0.1429 0.0540
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.validity, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6348 0.0307 15.4 0.570 0.7000
## Validity -0.0445 0.0468 24.9 -0.141 0.0519## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6348 0.0298 0.5745 0.6952 0.3634 0.9063
## 2 0.5904 0.0385 0.5126 0.6682 0.3145 0.86622.2.3.3.3 MODERATOR: Test forms
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel2.forms <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ factor(Forms))
## Summarize the results
summary(MLMEMCSC.tfm.srel2.forms, digits=4)##
## Multivariate Meta-Analysis Model (k = 36; method: REML)
##
## logLik Deviance AIC BIC AICc
## 13.1379 -26.2759 -16.2759 -8.7934 -14.0537
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 32 no STUDID
## sigma^2.2 0.0168 0.1297 36 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 33) = 319.8498, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 0.4781, p-val = 0.6242
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6066 0.0276 21.9570 33 <.0001 0.5504 0.6628 ***
## factor(Forms)B 0.0596 0.0722 0.8252 33 0.4152 -0.0873 0.2065
## factor(Forms)Both -0.0509 0.1142 -0.4460 33 0.6585 -0.2833 0.1814
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.forms, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6066 0.0277 19.33 0.549 0.665
## factor(Forms)B 0.0596 0.0341 5.23 -0.027 0.146
## factor(Forms)Both -0.0509 0.1967 1.13 -1.970 1.868## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.forms, newmods = cbind(c(0,1,0),
c(0,0,1)))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6066 0.0276 0.5504 0.6628 0.3367 0.8765
## 2 0.6661 0.0667 0.5304 0.8019 0.3693 0.9630
## 3 0.5556 0.1108 0.3302 0.7811 0.2085 0.90282.2.3.3.4 MODERATOR: Test scores
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel2.scores <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Scores)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.scores, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.2879 -30.5759 -22.5759 -16.1322 -21.3259
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 34 no STUDID
## sigma^2.2 0.0158 0.1257 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 319.5096, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.5922, p-val = 0.4465
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6005 0.0296 20.2893 37 <.0001 0.5406 0.6605 ***
## Scores 0.0376 0.0489 0.7695 37 0.4465 -0.0614 0.1367
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.scores, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6005 0.0278 14.2 0.5411 0.660
## Scores 0.0376 0.0480 23.1 -0.0616 0.137## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6005 0.0296 0.5406 0.6605 0.3388 0.8622
## 2 0.6382 0.0389 0.5593 0.7170 0.3715 0.90482.2.3.3.5 MODERATOR: Language English
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel2.lang <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ LanguageEnglish)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.lang, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.5063 -31.0126 -23.0126 -16.3584 -21.8362
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0173 0.1314 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 362.2982, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.3475, p-val = 0.5589
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5898 0.0534 11.0356 39 <.0001 0.4817 0.6979 ***
## LanguageEnglish 0.0351 0.0596 0.5895 39 0.5589 -0.0854 0.1557
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.lang, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.5898 0.0746 5.83 0.406 0.774
## LanguageEnglish 0.0351 0.0780 8.87 -0.142 0.212## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.5898 0.0534 0.4817 0.6979 0.3030 0.8766
## 2 0.6249 0.0264 0.5716 0.6783 0.3539 0.89592.2.3.3.6 MODERATOR: Western Culture
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srel2.cult <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ CultureWestern)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.cult, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 16.1320 -32.2641 -24.2641 -17.6098 -23.0876
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0166 0.1288 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 373.1420, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.5781, p-val = 0.2165
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5703 0.0449 12.6933 39 <.0001 0.4794 0.6611 ***
## CultureWestern 0.0660 0.0525 1.2562 39 0.2165 -0.0403 0.1722
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.cult, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.570 0.0612 8.65 0.4311 0.709
## CultureWestern 0.066 0.0651 15.23 -0.0726 0.205## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.5703 0.0449 0.4794 0.6611 0.2944 0.8461
## 2 0.6362 0.0272 0.5812 0.6913 0.3700 0.90252.2.3.3.7 MODERATOR: Proportion of women in the sample
## Three-level MEM
## Model specification and estimation
## Note: The proportion is arcsine-square-root transformed to stabilize the distribution
## and approximate normality.
## Source: Schwarzer et al. (2019), https://doi.org/10.1002/jrsm.1348
MLMEMCSC.tfm.srel2.female <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ asin(sqrt(PropFemale/100)))
## Summarize the results
summary(MLMEMCSC.tfm.srel2.female, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.9733 -31.9465 -23.9465 -17.5029 -22.6965
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 34 no STUDID
## sigma^2.2 0.0153 0.1236 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 333.7264, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 4.2105, p-val = 0.0473
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.4557 0.0802 5.6800 37 <.0001 0.2931
## asin(sqrt(PropFemale/100)) 0.1779 0.0867 2.0520 37 0.0473 0.0022
## ci.ub
## intrcpt 0.6182 ***
## asin(sqrt(PropFemale/100)) 0.3537 *
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srel2.female, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.456 0.0543 5.42 0.319 0.592
## asin(sqrt(PropFemale/100)) 0.178 0.0491 4.02 0.042 0.3142.2.3.4 Moderator Analyses for the Composite Reliability
2.2.3.4.1 MODERATOR: Age groups
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srelcr.age <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Adults)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.age, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.1096 -80.2191 -72.2191 -65.5649 -71.0427
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0018 0.0427 36 no STUDID
## sigma^2.2 0.0028 0.0527 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 381.3183, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.0016, p-val = 0.9683
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8088 0.0167 48.4050 39 <.0001 0.7750 0.8426 ***
## Adults 0.0010 0.0257 0.0399 39 0.9683 -0.0510 0.0530
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.age, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.80881 0.0152 17.2 0.777 0.8409
## Adults 0.00103 0.0264 28.3 -0.053 0.0551## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8088 0.0167 0.7750 0.8426 0.6676 0.9500
## 2 0.8098 0.0195 0.7703 0.8494 0.6671 0.95262.2.3.4.2 MODERATOR: Validity evidence
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srelcr.validity <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Validity)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.validity, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.8366 -81.6732 -73.6732 -67.0189 -72.4967
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0020 0.0442 36 no STUDID
## sigma^2.2 0.0025 0.0498 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 414.8510, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.4562, p-val = 0.2348
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8213 0.0159 51.6675 39 <.0001 0.7891 0.8534 ***
## Validity -0.0313 0.0259 -1.2067 39 0.2348 -0.0837 0.0211
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.validity, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8213 0.0162 18.5 0.7874 0.855
## Validity -0.0313 0.0254 25.3 -0.0835 0.021## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8213 0.0159 0.7891 0.8534 0.6828 0.9598
## 2 0.7900 0.0205 0.7487 0.8314 0.6491 0.93102.2.3.4.3 MODERATOR: Test forms
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srelcr.forms <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ factor(Forms))
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.forms, digits=4)##
## Multivariate Meta-Analysis Model (k = 36; method: REML)
##
## logLik Deviance AIC BIC AICc
## 35.1124 -70.2248 -60.2248 -52.7423 -58.0026
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 32 no STUDID
## sigma^2.2 0.0037 0.0606 36 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 33) = 375.7742, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 0.2754, p-val = 0.7610
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8160 0.0131 62.2610 33 <.0001 0.7893 0.8426 ***
## factor(Forms)B -0.0166 0.0364 -0.4568 33 0.6508 -0.0908 0.0575
## factor(Forms)Both -0.0344 0.0554 -0.6216 33 0.5385 -0.1471 0.0783
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.forms, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8160 0.0116 18.29 0.7916 0.8403
## factor(Forms)B -0.0166 0.0246 4.56 -0.0818 0.0485
## factor(Forms)Both -0.0344 0.1597 1.12 -1.6098 1.5409## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.forms, newmods = cbind(c(0,1,0),
c(0,0,1)))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8160 0.0131 0.7893 0.8426 0.6899 0.9421
## 2 0.7993 0.0340 0.7302 0.8685 0.6580 0.9407
## 3 0.7815 0.0538 0.6721 0.8910 0.6167 0.94642.2.3.4.4 MODERATOR: Test scores
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srelcr.scores <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Scores)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.scores, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.0180 -80.0361 -72.0361 -65.5924 -70.7861
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 34 no STUDID
## sigma^2.2 0.0033 0.0574 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 381.6730, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.0219, p-val = 0.8833
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8110 0.0139 58.2455 37 <.0001 0.7828 0.8392 ***
## Scores 0.0034 0.0232 0.1478 37 0.8833 -0.0435 0.0503
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.scores, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.81096 0.0129 13.1 0.7832 0.8387
## Scores 0.00342 0.0238 23.1 -0.0457 0.0525## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8110 0.0139 0.7828 0.8392 0.6913 0.9306
## 2 0.8144 0.0185 0.7769 0.8519 0.6922 0.93662.2.3.4.5 MODERATOR: Language English
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srelcr.lang <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ LanguageEnglish)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.lang, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.0850 -80.1700 -72.1700 -65.5157 -70.9935
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0017 0.0415 36 no STUDID
## sigma^2.2 0.0029 0.0536 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 369.6889, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.1209, p-val = 0.7299
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8007 0.0277 28.8934 39 <.0001 0.7446 0.8567 ***
## LanguageEnglish 0.0108 0.0312 0.3477 39 0.7299 -0.0522 0.0739
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.lang, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8007 0.0420 5.74 0.6969 0.904
## LanguageEnglish 0.0108 0.0436 9.04 -0.0877 0.109## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8007 0.0277 0.7446 0.8567 0.6525 0.9489
## 2 0.8115 0.0143 0.7826 0.8404 0.6713 0.95172.2.3.4.6 MODERATOR: Western Culture
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfm.srelcr.cult <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ CultureWestern)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.cult, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.8511 -81.7022 -73.7022 -67.0480 -72.5258
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0014 0.0374 36 no STUDID
## sigma^2.2 0.0030 0.0543 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 403.4575, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.6160, p-val = 0.2112
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7848 0.0232 33.7903 39 <.0001 0.7378 0.8317 ***
## CultureWestern 0.0349 0.0274 1.2712 39 0.2112 -0.0206 0.0904
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.cult, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7848 0.0335 8.45 0.7082 0.861
## CultureWestern 0.0349 0.0353 15.52 -0.0402 0.110## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7848 0.0232 0.7378 0.8317 0.6433 0.9262
## 2 0.8196 0.0146 0.7901 0.8492 0.6829 0.95632.2.3.4.7 MODERATOR: Proportion of women in the sample
## Three-level MEM
## Model specification and estimation
## Note: The proportion is arcsine-square-root transformed to stabilize the distribution
## and approximate normality.
## Source: Schwarzer et al. (2019), https://doi.org/10.1002/jrsm.1348
MLMEMCSC.tfm.srelcr.female <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ asin(sqrt(PropFemale/100)))
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.female, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 38.0771 -76.1543 -68.1543 -61.7106 -66.9043
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0021 0.0459 34 no STUDID
## sigma^2.2 0.0025 0.0499 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 430.1098, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 1.2203, p-val = 0.2764
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.7616 0.0419 18.1767 37 <.0001 0.6767
## asin(sqrt(PropFemale/100)) 0.0499 0.0452 1.1046 37 0.2764 -0.0416
## ci.ub
## intrcpt 0.8465 ***
## asin(sqrt(PropFemale/100)) 0.1414
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfm.srelcr.female, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7616 0.0303 3.98 0.6773 0.846
## asin(sqrt(PropFemale/100)) 0.0499 0.0281 2.95 -0.0402 0.1402.2.3.5 Publication Bias and Infuential Effect Sizes
## Reliability of factor 1
## Egger's regression test (PET)
## Details: https://wviechtb.github.io/metafor/reference/regtest.html
## Three-level MEM
MLMEMCSC.tfm.srel1.pet <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ sqrt(SREL1.vg))
## Summarize the results
summary(MLMEMCSC.tfm.srel1.pet, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 51.6097 -103.2193 -95.2193 -88.5651 -94.0429
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0018 0.0418 36 no STUDID
## sigma^2.2 0.0003 0.0172 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 475.4547, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 43.4531, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.9358 0.0136 69.0432 39 <.0001 0.9084 0.9633 ***
## sqrt(SREL1.vg) -2.4456 0.3710 -6.5919 39 <.0001 -3.1960 -1.6952 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srel1.pet, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.936 0.0118 79.10 18.2 <0.001 ***
## sqrt(SREL1.vg) -2.446 0.3815 -6.41 11.4 <0.001 ***## Result: The standard errors are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Funnel plot test
## Three-level MEM
MLMEMCSC.tfm.srel1.fpt <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ N)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.fpt, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 34.5683 -69.1366 -61.1366 -54.4823 -59.9601
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0061 0.0779 36 no STUDID
## sigma^2.2 0.0004 0.0203 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 763.0805, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.6736, p-val = 0.4168
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8480 0.0182 46.5004 39 <.0001 0.8111 0.8848 ***
## N 0.0000 0.0000 0.8207 39 0.4168 -0.0000 0.0001
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srel1.fpt, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.8479531 0.0174547 48.58 27.6 <0.001 ***
## N 0.0000316 0.0000187 1.69 2.7 0.199## Contour-enhanced funnel plot
funnel(MLREMCSC.tfm.srel1,
main="Standard Error",
level = c(90, 95, 99),
shade = c("white", "gray55", "gray75"),
legend = TRUE)
## Result: No evidence for publication or selection bias.
## Precision-Effect Estimate with SE (PEESE)
## Three-level MEM
MLMEMCSC.tfm.srel1.peese <- rma.mv(SREL1,
SREL1.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ SREL1.vg)
## Summarize the results
summary(MLMEMCSC.tfm.srel1.peese, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 44.1491 -88.2981 -80.2981 -73.6439 -79.1217
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0032 0.0564 36 no STUDID
## sigma^2.2 0.0004 0.0205 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 760.0274, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 20.1637, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8810 0.0124 70.9910 39 <.0001 0.8559 0.9061 ***
## SREL1.vg -10.2054 2.2727 -4.4904 39 <.0001 -14.8024 -5.6084 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srel1.peese, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.881 0.012 73.6 28.25 <0.001 ***
## SREL1.vg -10.205 2.550 -4.0 2.15 0.0508 .## Result: The sampling variances are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Influential effect sizes
## Analyses based on the REM with variation between effect sizes
## Plots indicating potential influential effect sizes
inf.tfm.srel1 <- influence.rma.uni(rma(SREL1,
SREL1.vg,
data = srel.meta,
method = "REML"))
plot.infl.rma.uni(inf.tfm.srel1)
# Increase max print options to show all effect sizes
options(max.print = 1000000)
print(inf.tfm.srel1)##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -0.9080 -0.1242 0.0154 1.0093 0.0052 855.7637 0.0162 1.6153 -0.1244
## 2 1.6121 0.2363 0.0524 0.9812 0.0049 383.9964 0.0329 3.2932 0.2351
## 3 0.2616 0.0968 0.0098 1.0769 0.0055 857.7510 0.0276 2.7568 0.0968
## 4 0.8435 0.1762 0.0319 1.0583 0.0054 860.9922 0.0283 2.8339 0.1763
## 5 0.5940 0.1423 0.0210 1.0673 0.0055 860.3824 0.0267 2.6680 0.1422
## 6 -0.5687 -0.0615 0.0038 1.0283 0.0053 857.5364 0.0167 1.6668 -0.0613
## 7 -1.0432 -0.1393 0.0193 0.9997 0.0051 855.9912 0.0138 1.3822 -0.1398
## 8 -1.5321 -0.1207 0.0145 0.9853 0.0051 857.0020 0.0042 0.4241 -0.1217
## 9 0.4722 0.1223 0.0155 1.0679 0.0055 860.1487 0.0254 2.5360 0.1221
## 10 1.5105 0.2318 0.0515 0.9960 0.0050 856.5966 0.0319 3.1942 0.2312
## 11 0.0188 0.0374 0.0014 1.0495 0.0054 859.8234 0.0180 1.7992 0.0372
## 12 -1.1858 -0.2123 0.0440 0.9901 0.0050 849.1502 0.0215 2.1540 -0.2130
## 13 1.2642 0.2212 0.0485 1.0257 0.0052 860.5280 0.0318 3.1818 0.2210
## 14 -1.0903 -0.1955 0.0375 0.9994 0.0051 847.9700 0.0231 2.3137 -0.1959
## 15 0.4502 0.1389 0.0205 1.0865 0.0055 788.8704 0.0328 3.2751 0.1395
## 16 -0.7503 -0.0904 0.0082 1.0165 0.0052 857.2355 0.0148 1.4799 -0.0903
## 17 0.6862 0.1672 0.0292 1.0730 0.0055 858.2256 0.0313 3.1260 0.1676
## 18 0.6994 0.1731 0.0314 1.0753 0.0055 830.5765 0.0328 3.2770 0.1737
## 19 0.2872 0.1125 0.0135 1.0897 0.0056 794.4951 0.0326 3.2616 0.1130
## 20 0.9125 0.1968 0.0399 1.0605 0.0054 850.6060 0.0328 3.2827 0.1973
## 21 -0.9146 -0.0613 0.0038 0.9992 0.0052 859.3746 0.0038 0.3758 -0.0615
## 22 0.0056 0.0566 0.0034 1.0826 0.0055 847.4106 0.0303 3.0259 0.0567
## 23 -0.7125 -0.1093 0.0121 1.0386 0.0053 842.1365 0.0278 2.7831 -0.1093
## 24 0.3889 0.1038 0.0111 1.0633 0.0055 860.2916 0.0229 2.2922 0.1035
## 25 -2.1562 -0.1804 0.0324 0.9670 0.0050 853.8522 0.0042 0.4220 -0.1833
## 26 -1.7762 -0.0907 0.0082 0.9880 0.0051 856.8761 0.0018 0.1797 -0.0913
## 27 0.1631 0.0800 0.0067 1.0765 0.0055 856.9935 0.0273 2.7343 0.0799
## 28 0.8645 0.1877 0.0364 1.0619 0.0054 860.2282 0.0314 3.1390 0.1881
## 29 -0.2121 0.0054 0.0000 1.0587 0.0054 856.6562 0.0234 2.3446 0.0053
## 30 0.7342 0.1751 0.0320 1.0717 0.0055 856.7370 0.0320 3.2010 0.1756
## 31 -0.2371 -0.0025 0.0000 1.0479 0.0054 858.3110 0.0195 1.9542 -0.0025
## 32 -0.0250 0.0493 0.0026 1.0797 0.0055 850.4262 0.0294 2.9409 0.0494
## 33 -0.3093 -0.0114 0.0001 1.0667 0.0054 848.5876 0.0283 2.8270 -0.0114
## 34 -0.0738 0.0428 0.0019 1.0847 0.0055 822.8696 0.0318 3.1773 0.0430
## 35 0.0411 0.0642 0.0044 1.0843 0.0055 845.6657 0.0307 3.0685 0.0644
## 36 0.2762 0.1107 0.0130 1.0899 0.0056 786.8995 0.0326 3.2641 0.1112
## 37 -1.0326 -0.2119 0.0438 1.0082 0.0051 797.6141 0.0307 3.0738 -0.2117
## 38 0.0543 0.0683 0.0049 1.0869 0.0055 835.0969 0.0316 3.1592 0.0685
## 39 -2.4529 -0.4365 0.1785 0.8880 0.0045 844.7665 0.0142 1.4169 -0.4514
## 40 -4.7841 -1.2414 1.1456 0.6088 0.0028 808.8575 0.0183 1.8257 -1.3820 *
## 41 1.5212 0.2342 0.0523 0.9940 0.0050 840.2731 0.0327 3.2731 0.2334## Reliability of factor 2
## Egger's regression test (PET)
## Details: https://wviechtb.github.io/metafor/reference/regtest.html
## Three-level MEM
MLMEMCSC.tfm.srel2.pet <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ sqrt(SREL2.vg))
## Summarize the results
summary(MLMEMCSC.tfm.srel2.pet, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 20.9832 -41.9664 -33.9664 -27.3122 -32.7900
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0082 0.0903 36 no STUDID
## sigma^2.2 0.0062 0.0786 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 338.6261, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 12.6019, p-val = 0.0010
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7540 0.0437 17.2663 39 <.0001 0.6657 0.8424 ***
## sqrt(SREL2.vg) -2.0701 0.5831 -3.5499 39 0.0010 -3.2495 -0.8906 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srel2.pet, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.754 0.0433 17.42 16.6 < 0.001 ***
## sqrt(SREL2.vg) -2.070 0.6108 -3.39 18.5 0.00318 **## Result: The standard errors are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Funnel plot test
## Three-level MEM
MLMEMCSC.tfm.srel2.fpt <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ N)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.fpt, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.5067 -31.0133 -23.0133 -16.3591 -21.8368
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0169 0.1300 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 363.7350, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.4316, p-val = 0.5150
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6294 0.0289 21.7695 39 <.0001 0.5709 0.6879 ***
## N -0.0000 0.0001 -0.6570 39 0.5150 -0.0002 0.0001
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srel2.fpt, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.629398 0.0282163 22.306 27.95 <0.001 ***
## N -0.000037 0.0000544 -0.679 2.99 0.546## Contour-enhanced funnel plot
funnel(MLREMCSC.tfm.srel2,
main="Standard Error",
level = c(90, 95, 99),
shade = c("white", "gray55", "gray75"),
legend = TRUE)
## Result: No evidence for publication or selection bias.
## Precision-Effect Estimate with SE (PEESE)
## Three-level MEM
MLMEMCSC.tfm.srel2.peese <- rma.mv(SREL2,
SREL2.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ SREL2.vg)
## Summarize the results
summary(MLMEMCSC.tfm.srel2.peese, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 21.8252 -43.6505 -35.6505 -28.9962 -34.4740
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0061 0.0781 36 no STUDID
## sigma^2.2 0.0074 0.0859 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 342.8645, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 14.0149, p-val = 0.0006
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6942 0.0293 23.6763 39 <.0001 0.6349 0.7535 ***
## SREL2.vg -12.9876 3.4692 -3.7436 39 0.0006 -20.0048 -5.9704 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srel2.peese, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.694 0.0292 23.8 20.4 < 0.001 ***
## SREL2.vg -12.988 3.7068 -3.5 10.4 0.00533 **## Result: The sampling variances are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Influential effect sizes
## Analyses based on the REM with variation between effect sizes
## Plots indicating potential influential effect sizes
inf.tfm.srel2 <- influence.rma.uni(rma(SREL2,
SREL2.vg,
data = srel.meta,
method = "REML"))
plot.infl.rma.uni(inf.tfm.srel2)
# Increase max print options to show all effect sizes
options(max.print = 1000000)
print(inf.tfm.srel2)##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -0.7515 -0.0796 0.0063 1.0149 0.0168 380.5656 0.0116 1.1599 -0.0795
## 2 1.2609 0.2218 0.0484 1.0191 0.0164 316.5582 0.0322 3.2222 0.2214
## 3 0.2801 0.0650 0.0044 1.0586 0.0174 382.0657 0.0260 2.5979 0.0650
## 4 0.0552 0.0223 0.0005 1.0431 0.0172 381.9451 0.0188 1.8818 0.0223
## 5 -0.0452 0.0061 0.0000 1.0346 0.0171 381.9004 0.0154 1.5359 0.0060
## 6 1.1571 0.1836 0.0336 1.0230 0.0167 379.5245 0.0250 2.4999 0.1836
## 7 -0.4646 -0.0529 0.0028 1.0320 0.0170 380.8545 0.0173 1.7257 -0.0528
## 8 0.1487 0.0382 0.0015 1.0483 0.0173 382.0093 0.0210 2.1046 0.0381
## 9 1.5627 0.2390 0.0550 0.9921 0.0160 374.0921 0.0273 2.7343 0.2388
## 10 0.8501 0.1361 0.0187 1.0356 0.0170 381.3334 0.0221 2.2140 0.1360
## 11 0.7591 0.1184 0.0142 1.0357 0.0170 381.6384 0.0201 2.0074 0.1182
## 12 -2.7212 -0.4089 0.1558 0.9006 0.0144 365.9504 0.0157 1.5749 -0.4191
## 13 0.7214 0.1294 0.0171 1.0464 0.0171 381.5457 0.0257 2.5692 0.1294
## 14 0.8270 0.1524 0.0236 1.0465 0.0171 380.5462 0.0288 2.8752 0.1525
## 15 0.3868 0.0920 0.0089 1.0702 0.0175 382.0008 0.0323 3.2259 0.0924
## 16 0.0819 0.0282 0.0008 1.0479 0.0173 381.9302 0.0208 2.0849 0.0281
## 17 -1.0764 -0.1739 0.0299 1.0130 0.0165 374.9144 0.0235 2.3522 -0.1740
## 18 0.5603 0.1201 0.0150 1.0644 0.0174 380.6788 0.0321 3.2089 0.1205
## 19 -1.2372 -0.2410 0.0561 1.0030 0.0161 331.0745 0.0309 3.0916 -0.2404
## 20 -0.3436 -0.0425 0.0019 1.0647 0.0174 360.5545 0.0317 3.1678 -0.0426
## 21 -2.6700 -0.3278 0.1037 0.9287 0.0150 369.6898 0.0113 1.1283 -0.3359
## 22 -2.5453 -0.4424 0.1773 0.8940 0.0142 363.0471 0.0200 1.9972 -0.4496
## 23 0.6767 0.1332 0.0182 1.0554 0.0172 381.2293 0.0298 2.9808 0.1334
## 24 -0.3123 -0.0292 0.0009 1.0305 0.0170 381.4560 0.0149 1.4929 -0.0291
## 25 0.1934 0.0452 0.0021 1.0490 0.0173 382.0473 0.0214 2.1411 0.0451
## 26 0.3315 0.0665 0.0045 1.0496 0.0173 382.1107 0.0222 2.2206 0.0664
## 27 0.1032 0.0351 0.0013 1.0560 0.0174 381.8376 0.0244 2.4405 0.0351
## 28 -0.4397 -0.0555 0.0031 1.0448 0.0172 379.8626 0.0234 2.3401 -0.0554
## 29 -0.5008 -0.0592 0.0035 1.0323 0.0170 380.6512 0.0179 1.7919 -0.0591
## 30 0.3060 0.0745 0.0058 1.0660 0.0175 382.0144 0.0295 2.9536 0.0746
## 31 0.0214 0.0156 0.0002 1.0377 0.0172 381.9541 0.0165 1.6522 0.0156
## 32 0.0400 0.0279 0.0008 1.0640 0.0174 381.2416 0.0279 2.7942 0.0279
## 33 0.9160 0.1680 0.0286 1.0430 0.0170 378.9795 0.0299 2.9889 0.1682
## 34 0.2971 0.0754 0.0059 1.0697 0.0175 381.8007 0.0312 3.1176 0.0756
## 35 1.3689 0.2319 0.0523 1.0090 0.0163 361.5209 0.0312 3.1209 0.2314
## 36 -1.8888 -0.4171 0.1534 0.9289 0.0146 298.6579 0.0308 3.0766 -0.4129
## 37 -0.0098 0.0213 0.0005 1.0705 0.0175 378.4644 0.0310 3.0963 0.0214
## 38 -0.3624 -0.0454 0.0021 1.0600 0.0173 375.4625 0.0297 2.9684 -0.0455
## 39 -1.7603 -0.2768 0.0737 0.9651 0.0156 372.3120 0.0189 1.8941 -0.2789
## 40 -0.6897 -0.1094 0.0121 1.0425 0.0170 373.1924 0.0283 2.8324 -0.1094
## 41 1.8312 0.2851 0.0744 0.9600 0.0152 333.9787 0.0314 3.1372 0.2829## Reliability of factor 1
## Egger's regression test (PET)
## Details: https://wviechtb.github.io/metafor/reference/regtest.html
## Three-level MEM
MLMEMCSC.tfm.srelcr.pet <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ sqrt(SRELCR.vg))
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.pet, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 49.1677 -98.3355 -90.3355 -83.6812 -89.1590
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0014 0.0381 36 no STUDID
## sigma^2.2 0.0016 0.0401 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 354.3190, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 18.8547, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8786 0.0187 47.0916 39 <.0001 0.8409 0.9164 ***
## sqrt(SRELCR.vg) -2.1059 0.4850 -4.3422 39 <.0001 -3.0869 -1.1249 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srelcr.pet, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.879 0.0156 56.28 15.8 <0.001 ***
## sqrt(SRELCR.vg) -2.106 0.4200 -5.01 13.0 <0.001 ***## Result: The standard errors are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Funnel plot test
## Three-level MEM
MLMEMCSC.tfm.srelcr.fpt <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ N)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.fpt, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.0945 -80.1890 -72.1890 -65.5347 -71.0125
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0020 0.0446 36 no STUDID
## sigma^2.2 0.0027 0.0518 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 437.0096, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.0996, p-val = 0.7539
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8063 0.0156 51.7485 39 <.0001 0.7748 0.8378 ***
## N 0.0000 0.0000 0.3157 39 0.7539 -0.0001 0.0001
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srelcr.fpt, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.80628 0.0155475 51.859 28.33 <0.001 ***
## N 0.00001 0.0000183 0.547 2.89 0.624## Contour-enhanced funnel plot
funnel(MLREMCSC.tfm.srelcr,
main="Standard Error",
level = c(90, 95, 99),
shade = c("white", "gray55", "gray75"),
legend = TRUE)
## Result: No evidence for publication or selection bias.
## Precision-Effect Estimate with SE (PEESE)
## Three-level MEM
MLMEMCSC.tfm.srelcr.peese <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ SRELCR.vg)
## Summarize the results
summary(MLMEMCSC.tfm.srelcr.peese, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 47.4656 -94.9312 -86.9312 -80.2770 -85.7548
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0030 0.0549 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 396.1237, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 14.0239, p-val = 0.0006
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8328 0.0117 71.4146 39 <.0001 0.8092 0.8564 ***
## SRELCR.vg -13.7004 3.6585 -3.7448 39 0.0006 -21.1004 -6.3005 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfm.srelcr.peese, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.833 0.0131 63.59 18.66 <0.001 ***
## SRELCR.vg -13.700 6.7669 -2.02 2.31 0.163## Result: The sampling variances are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Influential effect sizes
## Analyses based on the REM with variation between effect sizes
## Plots indicating potential influential effect sizes
inf.tfm.srelcr <- influence.rma.uni(rma(SRELCR,
SRELCR.vg,
data = srel.meta,
method = "REML"))
plot.infl.rma.uni(inf.tfm.srelcr)
# Increase max print options to show all effect sizes
options(max.print = 1000000)
print(inf.tfm.srelcr)##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -1.1274 -0.1306 0.0170 1.0006 0.0041 447.8364 0.0115 1.1541 -0.1310
## 2 1.7379 0.2664 0.0652 0.9675 0.0038 272.3760 0.0333 3.3305 0.2642
## 3 0.1794 0.0592 0.0036 1.0633 0.0044 450.5628 0.0260 2.6005 0.0592
## 4 0.5398 0.1030 0.0108 1.0488 0.0043 451.2214 0.0218 2.1839 0.1027
## 5 0.4832 0.0926 0.0088 1.0476 0.0043 451.2220 0.0207 2.0731 0.0924
## 6 0.7120 0.1288 0.0169 1.0464 0.0043 451.1187 0.0232 2.3187 0.1286
## 7 -0.4404 -0.0460 0.0021 1.0341 0.0043 449.4957 0.0177 1.7712 -0.0459
## 8 -0.8162 -0.0994 0.0099 1.0158 0.0042 448.5027 0.0148 1.4796 -0.0993
## 9 1.4102 0.2196 0.0472 1.0072 0.0041 447.5377 0.0277 2.7655 0.2195
## 10 1.2577 0.1983 0.0391 1.0193 0.0041 449.2160 0.0257 2.5744 0.1984
## 11 0.9378 0.1528 0.0236 1.0356 0.0042 450.7135 0.0224 2.2352 0.1526
## 12 -2.9397 -0.4852 0.2163 0.8693 0.0034 432.1863 0.0154 1.5365 -0.5024 *
## 13 1.2253 0.2060 0.0421 1.0234 0.0041 448.4871 0.0289 2.8868 0.2059
## 14 0.3833 0.0960 0.0096 1.0668 0.0044 450.9407 0.0285 2.8482 0.0961
## 15 0.3912 0.1063 0.0119 1.0771 0.0044 443.9392 0.0332 3.3224 0.1068
## 16 -0.2182 -0.0110 0.0001 1.0458 0.0043 449.9075 0.0204 2.0420 -0.0109
## 17 -0.5274 -0.0698 0.0050 1.0478 0.0043 445.5624 0.0264 2.6436 -0.0698
## 18 0.8965 0.1808 0.0334 1.0529 0.0043 444.3880 0.0332 3.3175 0.1812
## 19 -0.8011 -0.1411 0.0200 1.0395 0.0042 394.9484 0.0323 3.2306 -0.1412
## 20 0.2652 0.0845 0.0075 1.0788 0.0044 443.3548 0.0329 3.2920 0.0849
## 21 -1.5063 -0.0825 0.0068 0.9943 0.0041 448.1768 0.0025 0.2533 -0.0828
## 22 -2.0347 -0.4146 0.1561 0.9168 0.0036 431.0199 0.0237 2.3669 -0.4175
## 23 -0.2105 -0.0072 0.0001 1.0648 0.0043 446.7857 0.0286 2.8628 -0.0073
## 24 0.0674 0.0286 0.0008 1.0406 0.0043 450.9298 0.0167 1.6694 0.0284
## 25 -0.9845 -0.1242 0.0154 1.0084 0.0041 447.8198 0.0144 1.4430 -0.1244
## 26 -1.4319 -0.1538 0.0235 0.9891 0.0041 446.9916 0.0092 0.9206 -0.1549
## 27 -0.4303 -0.0479 0.0023 1.0443 0.0043 448.4390 0.0226 2.2572 -0.0479
## 28 0.1434 0.0546 0.0031 1.0654 0.0044 450.2916 0.0269 2.6860 0.0546
## 29 -0.1839 -0.0052 0.0000 1.0481 0.0043 449.9304 0.0211 2.1118 -0.0052
## 30 0.4223 0.1069 0.0119 1.0712 0.0044 450.7580 0.0309 3.0883 0.1072
## 31 -0.4047 -0.0381 0.0015 1.0290 0.0042 450.0017 0.0148 1.4773 -0.0379
## 32 0.1012 0.0498 0.0026 1.0695 0.0044 449.5834 0.0286 2.8586 0.0499
## 33 0.8808 0.1723 0.0303 1.0506 0.0043 450.3480 0.0308 3.0821 0.1725
## 34 0.3805 0.1028 0.0111 1.0753 0.0044 449.5784 0.0323 3.2266 0.1032
## 35 0.6803 0.1461 0.0221 1.0623 0.0043 451.1639 0.0311 3.1147 0.1465
## 36 -0.5962 -0.0911 0.0085 1.0547 0.0043 404.4712 0.0324 3.2429 -0.0913
## 37 -0.2090 -0.0059 0.0000 1.0720 0.0044 437.5321 0.0318 3.1794 -0.0059
## 38 -0.0987 0.0157 0.0003 1.0732 0.0044 443.9291 0.0311 3.1133 0.0158
## 39 -2.7894 -0.4535 0.1906 0.8829 0.0035 433.8214 0.0152 1.5248 -0.4680
## 40 -2.0264 -0.4520 0.1807 0.9078 0.0036 421.8942 0.0268 2.6756 -0.4522
## 41 1.8557 0.2709 0.0665 0.9537 0.0038 412.7923 0.0324 3.2394 0.26852.2.3.6 Forest Plots
## Reliability of factor 1
#pdf(file = "ForestPlots-TwoFactorModel4.pdf", onefile = TRUE)
forest.rma(MLREMCSC.tfm.srel1,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfm.srel1$k,
digits = 3,
level = 95,
cex = .9,
xlab = "Omega Coefficient",
main = "Reliability Factor 1 (Model 4)")
## Reliability of factor 2
forest.rma(MLREMCSC.tfm.srel2,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfm.srel2$k,
digits = 3,
level = 95,
cex = .9,
xlab = "Omega Coefficient",
main = "Reliability Factor 2 (Model 4)")
## Composite reliability
forest.rma(MLREMCSC.tfm.srelcr,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfm.srelcr$k,
digits = 3,
level = 95,
cex = .9,
xlab = "Omega Coefficient",
main = "Composite Reliability (Model 4)")
#dev.off()2.2.4 Meta-Analysis of the Two-Factor Model with Cross-Loadings
2.2.4.1 Meta-Analytic Baseline Models
## Reliability of factor 1
## Three-level REM
## Model specification and estimation
MLREMCSC.tfmc.srel1 <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t")
## Summarize the results
summary(MLREMCSC.tfmc.srel1, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 14.9258 -29.8516 -23.8516 -18.7849 -23.1849
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0170 0.1306 36 no STUDID
## sigma^2.2 0.0011 0.0326 41 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 40) = 443.4631, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.7811 0.0251 31.1512 40 <.0001 0.7304 0.8318 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## 95% confidence intervals
confint(MLREMCSC.tfmc.srel1, digits=4)##
## estimate ci.lb ci.ub
## sigma^2.1 0.0170 0.0021 0.0357
## sigma.1 0.1306 0.0455 0.1890
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0011 0.0002 0.0144
## sigma.2 0.0326 0.0150 0.1200## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfmc.srel1))## % of total variance I2
## Level 1 1.662360 ---
## Level 2 5.772129 5.77
## Level 3 92.565511 92.57
## Total I2: 98.34%plot(dmetar::var.comp(MLREMCSC.tfmc.srel1))
## RVE standard errors
clubSandwich::conf_int(MLREMCSC.tfmc.srel1, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.781 0.025 31.4 0.73 0.832# Profile plots
profile.rma.mv(MLREMCSC.tfmc.srel1, sigma2=1)
profile.rma.mv(MLREMCSC.tfmc.srel1, sigma2=2)
## Reliability of factor 2
## Three-level REM
## Model specification and estimation
MLREMCSC.tfmc.srel2 <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t")
## Summarize the results
summary(MLREMCSC.tfmc.srel2, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 12.0152 -24.0305 -18.0305 -12.9638 -17.3638
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0151 0.1227 41 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 40) = 259.6685, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.6471 0.0243 26.6853 40 <.0001 0.5981 0.6961 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## 95% confidence intervals
confint(MLREMCSC.tfmc.srel2, digits=4)##
## estimate ci.lb ci.ub
## sigma^2.1 0.0000 0.0000 0.0208
## sigma.1 0.0000 0.0000 0.1441
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0151 0.0025 0.0298
## sigma.2 0.1227 0.0502 0.1727## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfmc.srel2))## % of total variance I2
## Level 1 10.7879655814187 ---
## Level 2 89.2120342739435 89.21
## Level 3 0.0000001446378 0
## Total I2: 89.21%plot(dmetar::var.comp(MLREMCSC.tfmc.srel2))
## RVE standard errors
clubSandwich::conf_int(MLREMCSC.tfmc.srel2, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.647 0.0236 23.9 0.599 0.696# Profile plots
profile.rma.mv(MLREMCSC.tfmc.srel2, sigma2=1)
profile.rma.mv(MLREMCSC.tfmc.srel2, sigma2=2)
## Composite reliability
## Three-level REM
## Model specification and estimation
MLREMCSC.tfmc.srelcr <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t")
## Summarize the results
summary(MLREMCSC.tfmc.srelcr, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 43.3551 -86.7102 -80.7102 -75.6436 -80.0435
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0016 0.0406 36 no STUDID
## sigma^2.2 0.0026 0.0509 41 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 40) = 358.2204, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.8265 0.0123 67.2501 40 <.0001 0.8016 0.8513 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## 95% confidence intervals
confint(MLREMCSC.tfmc.srelcr, digits=4)##
## estimate ci.lb ci.ub
## sigma^2.1 0.0016 0.0000 0.0066
## sigma.1 0.0406 0.0000 0.0809
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0026 0.0006 0.0075
## sigma.2 0.0509 0.0245 0.0866## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfmc.srelcr))## % of total variance I2
## Level 1 5.806589 ---
## Level 2 57.605521 57.61
## Level 3 36.587889 36.59
## Total I2: 94.19%plot(dmetar::var.comp(MLREMCSC.tfmc.srelcr))
## RVE standard errors
clubSandwich::conf_int(MLREMCSC.tfmc.srelcr, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.826 0.0123 30.8 0.801 0.851# Profile plots
profile.rma.mv(MLREMCSC.tfmc.srel1, sigma2=1)
profile.rma.mv(MLREMCSC.tfmc.srel1, sigma2=2)
2.2.4.2 Moderator Analyses for the Reliability of Factor 1
2.2.4.2.1 MODERATOR: Age groups
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel1.age <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Adults)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.age, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 14.0957 -28.1913 -20.1913 -13.5371 -19.0149
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0181 0.1345 36 no STUDID
## sigma^2.2 0.0011 0.0325 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 422.5866, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.1227, p-val = 0.7280
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7725 0.0337 22.9203 39 <.0001 0.7044 0.8407 ***
## Adults 0.0182 0.0521 0.3503 39 0.7280 -0.0871 0.1236
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.age, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7725 0.0402 17.7 0.6879 0.857
## Adults 0.0182 0.0470 27.6 -0.0781 0.115## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7725 0.0337 0.7044 0.8407 0.4845 1.0606
## 2 0.7908 0.0397 0.7105 0.8711 0.4996 1.08202.2.4.2.2 MODERATOR: Validity evidence
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel1.validity <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Validity)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.validity, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 14.2361 -28.4723 -20.4723 -13.8180 -19.2958
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0176 0.1328 36 no STUDID
## sigma^2.2 0.0011 0.0326 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 395.1654, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.3905, p-val = 0.5357
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7930 0.0323 24.5444 39 <.0001 0.7277 0.8584 ***
## Validity -0.0328 0.0524 -0.6249 39 0.5357 -0.1388 0.0733
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.validity, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7930 0.0347 18.9 0.720 0.8657
## Validity -0.0328 0.0492 24.5 -0.134 0.0686## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7930 0.0323 0.7277 0.8584 0.5087 1.0773
## 2 0.7602 0.0413 0.6768 0.8437 0.4712 1.04932.2.4.2.3 MODERATOR: Test forms
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel1.forms <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ factor(Forms))
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.forms, digits=4)##
## Multivariate Meta-Analysis Model (k = 36; method: REML)
##
## logLik Deviance AIC BIC AICc
## 10.1275 -20.2550 -10.2550 -2.7724 -8.0327
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0204 0.1427 32 no STUDID
## sigma^2.2 0.0011 0.0333 36 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 33) = 403.2732, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 0.1190, p-val = 0.8882
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7859 0.0310 25.3666 33 <.0001 0.7229 0.8490 ***
## factor(Forms)B -0.0235 0.1067 -0.2199 33 0.8273 -0.2406 0.1936
## factor(Forms)Both -0.0538 0.1193 -0.4508 33 0.6551 -0.2964 0.1889
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.forms, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7859 0.0292 23.63 0.726 0.846
## factor(Forms)B -0.0235 0.0599 1.66 -0.340 0.293
## factor(Forms)Both -0.0538 0.2588 1.15 -2.484 2.377## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.forms, newmods = cbind(c(0,1,0),
c(0,0,1)))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7859 0.0310 0.7229 0.8490 0.4812 1.0907
## 2 0.7625 0.1022 0.5546 0.9703 0.3990 1.1259
## 3 0.7322 0.1152 0.4979 0.9665 0.3530 1.11142.2.4.2.4 MODERATOR: Test scores
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel1.scores <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Scores)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.scores, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 13.3928 -26.7856 -18.7856 -12.3419 -17.5356
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0177 0.1331 34 no STUDID
## sigma^2.2 0.0011 0.0326 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 430.1029, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.0595, p-val = 0.8086
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7881 0.0343 22.9719 37 <.0001 0.7186 0.8577 ***
## Scores -0.0130 0.0533 -0.2440 37 0.8086 -0.1209 0.0949
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.scores, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.788 0.0260 16.5 0.733 0.843
## Scores -0.013 0.0575 25.8 -0.131 0.105## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7881 0.0343 0.7186 0.8577 0.5018 1.0744
## 2 0.7751 0.0408 0.6926 0.8577 0.4854 1.06492.2.4.2.5 MODERATOR: Language English
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel1.lang <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ LanguageEnglish)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.lang, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.9052 -31.8104 -23.8104 -17.1562 -22.6339
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0166 0.1288 36 no STUDID
## sigma^2.2 0.0011 0.0326 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 380.8877, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 3.9331, p-val = 0.0544
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6835 0.0553 12.3608 39 <.0001 0.5717 0.7953 ***
## LanguageEnglish 0.1227 0.0619 1.9832 39 0.0544 -0.0024 0.2478 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.lang, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.683 0.106 5.69 0.420 0.947
## LanguageEnglish 0.123 0.108 8.78 -0.122 0.367## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6835 0.0553 0.5717 0.7953 0.3924 0.9746
## 2 0.8062 0.0277 0.7501 0.8623 0.5316 1.08072.2.4.2.6 MODERATOR: Western Culture
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel1.cult <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ CultureWestern)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.cult, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 15.8606 -31.7212 -23.7212 -17.0670 -22.5447
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0164 0.1281 36 no STUDID
## sigma^2.2 0.0011 0.0326 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 409.7589, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 3.8009, p-val = 0.0584
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7028 0.0474 14.8241 39 <.0001 0.6069 0.7987 ***
## CultureWestern 0.1082 0.0555 1.9496 39 0.0584 -0.0041 0.2205 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.cult, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.703 0.0774 7.82 0.5235 0.882
## CultureWestern 0.108 0.0796 14.03 -0.0624 0.279## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7028 0.0474 0.6069 0.7987 0.4188 0.9868
## 2 0.8110 0.0289 0.7526 0.8695 0.5374 1.08472.2.4.2.7 MODERATOR: Proportion of women in the sample
## Three-level MEM
## Model specification and estimation
## Note: The proportion is arcsine-square-root transformed to stabilize the distribution
## and approximate normality.
## Source: Schwarzer et al. (2019), https://doi.org/10.1002/jrsm.1348
MLMEMCSC.tfmc.srel1.female <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ asin(sqrt(PropFemale/100)))
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.female, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 12.3088 -24.6177 -16.6177 -10.1740 -15.3677
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0180 0.1342 34 no STUDID
## sigma^2.2 0.0011 0.0331 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 384.2668, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.5312, p-val = 0.4707
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.8070 0.0502 16.0676 37 <.0001 0.7052
## asin(sqrt(PropFemale/100)) -0.0360 0.0494 -0.7288 37 0.4707 -0.1360
## ci.ub
## intrcpt 0.9088 ***
## asin(sqrt(PropFemale/100)) 0.0641
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel1.female, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.807 0.0369 2.35 0.669 0.945
## asin(sqrt(PropFemale/100)) -0.036 0.0221 1.30 -0.202 0.1302.2.4.3 Moderator Analyses for the Reliability of Factor 2
2.2.4.3.1 MODERATOR: Age groups
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel2.age <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Adults)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.age, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.0963 -22.1926 -14.1926 -7.5383 -13.0161
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0157 0.1253 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 236.1680, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.0149, p-val = 0.9036
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6441 0.0322 20.0161 39 <.0001 0.5790 0.7092 ***
## Adults 0.0061 0.0501 0.1219 39 0.9036 -0.0952 0.1074
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.age, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.64409 0.0267 11.9 0.586 0.702
## Adults 0.00611 0.0514 23.4 -0.100 0.112## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6441 0.0322 0.5790 0.7092 0.3823 0.9059
## 2 0.6502 0.0384 0.5725 0.7279 0.3850 0.91542.2.4.3.2 MODERATOR: Validity evidence
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel2.validity <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Validity)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.validity, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.4247 -22.8493 -14.8493 -8.1951 -13.6729
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0151 0.1230 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 247.3802, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.6479, p-val = 0.4258
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6617 0.0303 21.8281 39 <.0001 0.6004 0.7230 ***
## Validity -0.0408 0.0507 -0.8049 39 0.4258 -0.1433 0.0617
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.validity, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6617 0.033 13.4 0.591 0.7328
## Validity -0.0408 0.045 20.1 -0.135 0.0531## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6617 0.0303 0.6004 0.7230 0.4055 0.9178
## 2 0.6209 0.0406 0.5387 0.7030 0.3590 0.88282.2.4.3.3 MODERATOR: Test forms
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel2.forms <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ factor(Forms))
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.forms, digits=4)##
## Multivariate Meta-Analysis Model (k = 36; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.4340 -22.8680 -12.8680 -5.3855 -10.6458
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 32 no STUDID
## sigma^2.2 0.0127 0.1127 36 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 33) = 198.3256, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 0.1600, p-val = 0.8528
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6489 0.0260 24.9558 33 <.0001 0.5960 0.7018 ***
## factor(Forms)B 0.0234 0.0828 0.2830 33 0.7789 -0.1450 0.1918
## factor(Forms)Both -0.0509 0.1090 -0.4672 33 0.6434 -0.2726 0.1708
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.forms, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6489 0.0257 16.27 0.594 0.703
## factor(Forms)B 0.0234 0.0356 2.12 -0.121 0.168
## factor(Forms)Both -0.0509 0.1666 1.12 -1.688 1.586## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.forms, newmods = cbind(c(0,1,0),
c(0,0,1)))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6489 0.0260 0.5960 0.7018 0.4136 0.8842
## 2 0.6724 0.0786 0.5125 0.8322 0.3929 0.9518
## 3 0.5980 0.1058 0.3827 0.8133 0.2835 0.91252.2.4.3.4 MODERATOR: Test scores
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel2.scores <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Scores)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.scores, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 13.7012 -27.4025 -19.4025 -12.9588 -18.1525
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 34 no STUDID
## sigma^2.2 0.0111 0.1052 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 188.4431, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 1.0048, p-val = 0.3227
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6348 0.0274 23.2065 37 <.0001 0.5794 0.6903 ***
## Scores 0.0469 0.0468 1.0024 37 0.3227 -0.0479 0.1418
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.scores, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6348 0.0228 11.4 0.5848 0.685
## Scores 0.0469 0.0491 19.5 -0.0556 0.149## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6348 0.0274 0.5794 0.6903 0.4147 0.8550
## 2 0.6818 0.0380 0.6048 0.7588 0.4552 0.90832.2.4.3.5 MODERATOR: Language English
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel2.lang <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ LanguageEnglish)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.lang, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.0553 -22.1106 -14.1106 -7.4563 -12.9341
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0155 0.1246 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 203.3114, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.1133, p-val = 0.7382
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6627 0.0534 12.4047 39 <.0001 0.5547 0.7708 ***
## LanguageEnglish -0.0202 0.0602 -0.3366 39 0.7382 -0.1419 0.1014
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.lang, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6627 0.0772 5.65 0.471 0.855
## LanguageEnglish -0.0202 0.0804 8.87 -0.203 0.162## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6627 0.0534 0.5547 0.7708 0.3885 0.9369
## 2 0.6425 0.0276 0.5866 0.6984 0.3844 0.90062.2.4.3.6 MODERATOR: Western Culture
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srel2.cult <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ CultureWestern)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.cult, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.3920 -22.7841 -14.7841 -8.1298 -13.6076
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0158 0.1255 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 231.8263, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.7137, p-val = 0.4034
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6132 0.0466 13.1631 39 <.0001 0.5190 0.7074 ***
## CultureWestern 0.0464 0.0549 0.8448 39 0.4034 -0.0647 0.1575
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.cult, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.6132 0.0712 8.16 0.450 0.777
## CultureWestern 0.0464 0.0739 14.62 -0.111 0.204## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6132 0.0466 0.5190 0.7074 0.3423 0.8841
## 2 0.6596 0.0291 0.6007 0.7185 0.3989 0.92032.2.4.3.7 MODERATOR: Proportion of women in the sample
## Three-level MEM
## Model specification and estimation
## Note: The proportion is arcsine-square-root transformed to stabilize the distribution
## and approximate normality.
## Source: Schwarzer et al. (2019), https://doi.org/10.1002/jrsm.1348
MLMEMCSC.tfmc.srel2.female <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ asin(sqrt(PropFemale/100)))
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.female, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 10.9796 -21.9592 -13.9592 -7.5156 -12.7092
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 34 no STUDID
## sigma^2.2 0.0147 0.1214 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 230.6334, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 3.4800, p-val = 0.0701
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.4920 0.0846 5.8133 37 <.0001 0.3205
## asin(sqrt(PropFemale/100)) 0.1686 0.0904 1.8655 37 0.0701 -0.0145
## ci.ub
## intrcpt 0.6635 ***
## asin(sqrt(PropFemale/100)) 0.3516 .
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srel2.female, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.492 0.0594 5.88 0.3459 0.638
## asin(sqrt(PropFemale/100)) 0.169 0.0535 3.98 0.0197 0.3172.2.4.4 Moderator Analyses for the Composite Reliability
2.2.4.4.1 MODERATOR: Age groups
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srelcr.age <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Adults)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.age, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 41.7665 -83.5330 -75.5330 -68.8787 -74.3565
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0019 0.0435 36 no STUDID
## sigma^2.2 0.0026 0.0506 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 331.2973, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.0336, p-val = 0.8554
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8280 0.0165 50.2631 39 <.0001 0.7946 0.8613 ***
## Adults -0.0047 0.0255 -0.1834 39 0.8554 -0.0562 0.0469
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.age, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.82795 0.0141 17.1 0.7982 0.8577
## Adults -0.00467 0.0267 27.6 -0.0594 0.0501## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8280 0.0165 0.7946 0.8613 0.6889 0.9670
## 2 0.8233 0.0194 0.7840 0.8626 0.6827 0.96382.2.4.4.2 MODERATOR: Validity evidence
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srelcr.validity <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Validity)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.validity, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 42.5397 -85.0793 -77.0793 -70.4251 -75.9029
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0020 0.0444 36 no STUDID
## sigma^2.2 0.0023 0.0476 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 321.4724, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.5896, p-val = 0.2149
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8383 0.0156 53.8540 39 <.0001 0.8068 0.8698 ***
## Validity -0.0322 0.0256 -1.2608 39 0.2149 -0.0839 0.0195
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.validity, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8383 0.0158 18.5 0.8052 0.8714
## Validity -0.0322 0.0251 24.1 -0.0841 0.0197## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8383 0.0156 0.8068 0.8698 0.7029 0.9737
## 2 0.8061 0.0203 0.7651 0.8471 0.6681 0.94402.2.4.4.3 MODERATOR: Test forms
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srelcr.forms <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ factor(Forms))
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.forms, digits=4)##
## Multivariate Meta-Analysis Model (k = 36; method: REML)
##
## logLik Deviance AIC BIC AICc
## 36.9442 -73.8885 -63.8885 -56.4059 -61.6662
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 32 no STUDID
## sigma^2.2 0.0035 0.0588 36 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 33) = 289.1370, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 0.3012, p-val = 0.7420
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8345 0.0127 65.7057 33 <.0001 0.8087 0.8604 ***
## factor(Forms)B -0.0254 0.0372 -0.6838 33 0.4989 -0.1010 0.0502
## factor(Forms)Both -0.0227 0.0538 -0.4211 33 0.6764 -0.1322 0.0868
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.forms, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8345 0.0108 18.09 0.812 0.8573
## factor(Forms)B -0.0254 0.0293 3.97 -0.107 0.0563
## factor(Forms)Both -0.0227 0.1687 1.12 -1.689 1.6441## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.forms, newmods = cbind(c(0,1,0),
c(0,0,1)))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8345 0.0127 0.8087 0.8604 0.7121 0.9569
## 2 0.8091 0.0349 0.7381 0.8802 0.6700 0.9483
## 3 0.8119 0.0523 0.7054 0.9183 0.6517 0.97202.2.4.4.4 MODERATOR: Test scores
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srelcr.scores <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ Scores)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.scores, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 42.1575 -84.3149 -76.3149 -69.8713 -75.0649
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0003 0.0176 34 no STUDID
## sigma^2.2 0.0028 0.0528 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 294.9259, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 0.0129, p-val = 0.9103
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8320 0.0138 60.2559 37 <.0001 0.8040 0.8600 ***
## Scores -0.0026 0.0227 -0.1134 37 0.9103 -0.0485 0.0433
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.scores, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.83199 0.0130 13.6 0.8041 0.8599
## Scores -0.00257 0.0233 23.4 -0.0508 0.0456## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8320 0.0138 0.8040 0.8600 0.7159 0.9481
## 2 0.8294 0.0180 0.7930 0.8658 0.7110 0.94782.2.4.4.5 MODERATOR: Language English
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srelcr.lang <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ LanguageEnglish)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.lang, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.0850 -80.1700 -72.1700 -65.5157 -70.9935
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0017 0.0415 36 no STUDID
## sigma^2.2 0.0029 0.0536 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 369.6889, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.1209, p-val = 0.7299
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8007 0.0277 28.8934 39 <.0001 0.7446 0.8567 ***
## LanguageEnglish 0.0108 0.0312 0.3477 39 0.7299 -0.0522 0.0739
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.lang, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.8007 0.0420 5.74 0.6969 0.904
## LanguageEnglish 0.0108 0.0436 9.04 -0.0877 0.109## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8007 0.0277 0.7446 0.8567 0.6525 0.9489
## 2 0.8115 0.0143 0.7826 0.8404 0.6713 0.95172.2.4.4.6 MODERATOR: Western Culture
## Three-level MEM
## Model specification and estimation
MLMEMCSC.tfmc.srelcr.cult <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ CultureWestern)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.cult, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 40.8511 -81.7022 -73.7022 -67.0480 -72.5258
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0014 0.0374 36 no STUDID
## sigma^2.2 0.0030 0.0543 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 403.4575, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.6160, p-val = 0.2112
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7848 0.0232 33.7903 39 <.0001 0.7378 0.8317 ***
## CultureWestern 0.0349 0.0274 1.2712 39 0.2112 -0.0206 0.0904
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.cult, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7848 0.0335 8.45 0.7082 0.861
## CultureWestern 0.0349 0.0353 15.52 -0.0402 0.110## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7848 0.0232 0.7378 0.8317 0.6433 0.9262
## 2 0.8196 0.0146 0.7901 0.8492 0.6829 0.95632.2.4.4.7 MODERATOR: Proportion of women in the sample
## Three-level MEM
## Model specification and estimation
## Note: The proportion is arcsine-square-root transformed to stabilize the distribution
## and approximate normality.
## Source: Schwarzer et al. (2019), https://doi.org/10.1002/jrsm.1348
MLMEMCSC.tfmc.srelcr.female <- rma.mv(SRELCR,
SRELCR.vg,
random = list(~ 1 | STUDID/ESID),
data = srel.meta,
method = "REML",
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ asin(sqrt(PropFemale/100)))
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.female, digits=4)##
## Multivariate Meta-Analysis Model (k = 39; method: REML)
##
## logLik Deviance AIC BIC AICc
## 38.0771 -76.1543 -68.1543 -61.7106 -66.9043
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0021 0.0459 34 no STUDID
## sigma^2.2 0.0025 0.0499 39 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 37) = 430.1098, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 37) = 1.2203, p-val = 0.2764
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.7616 0.0419 18.1767 37 <.0001 0.6767
## asin(sqrt(PropFemale/100)) 0.0499 0.0452 1.1046 37 0.2764 -0.0416
## ci.ub
## intrcpt 0.8465 ***
## asin(sqrt(PropFemale/100)) 0.1414
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
clubSandwich::conf_int(MLMEMCSC.tfmc.srelcr.female, vcov = "CR2")## Coef. Estimate SE d.f. Lower 95% CI Upper 95% CI
## intrcpt 0.7616 0.0303 3.98 0.6773 0.846
## asin(sqrt(PropFemale/100)) 0.0499 0.0281 2.95 -0.0402 0.1402.2.4.5 Publication Bias and Infuential Effect Sizes
## Reliability of factor 1
## Egger's regression test (PET)
## Details: https://wviechtb.github.io/metafor/reference/regtest.html
## Three-level MEM
MLMEMCSC.tfmc.srel1.pet <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ sqrt(SREL1C.vg))
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.pet, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 22.8446 -45.6891 -37.6891 -31.0349 -36.5127
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0069 0.0830 36 no STUDID
## sigma^2.2 0.0008 0.0281 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 320.2990, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 20.7394, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8658 0.0231 37.5224 39 <.0001 0.8191 0.9125 ***
## sqrt(SREL1C.vg) -1.7132 0.3762 -4.5541 39 <.0001 -2.4742 -0.9523 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srel1.pet, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.866 0.0181 47.75 20.76 <0.001 ***
## sqrt(SREL1C.vg) -1.713 0.5239 -3.27 8.78 0.01 *## Result: The standard errors are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Funnel plot test
## Three-level MEM
MLMEMCSC.tfmc.srel1.fpt <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ N)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.fpt, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 14.2656 -28.5312 -20.5312 -13.8770 -19.3548
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0180 0.1342 36 no STUDID
## sigma^2.2 0.0011 0.0326 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 443.4089, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.5214, p-val = 0.4746
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7679 0.0308 24.9064 39 <.0001 0.7055 0.8303 ***
## N 0.0000 0.0001 0.7221 39 0.4746 -0.0001 0.0002
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srel1.fpt, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.7679016 0.0317598 24.18 26.9 <0.001 ***
## N 0.0000475 0.0000416 1.14 2.7 0.344## Contour-enhanced funnel plot
funnel(MLREMCSC.tfmc.srel1,
main="Standard Error",
level = c(90, 95, 99),
shade = c("white", "gray55", "gray75"),
legend = TRUE)
## Result: No evidence for publication or selection bias.
## Precision-Effect Estimate with SE (PEESE)
## Three-level MEM
MLMEMCSC.tfmc.srel1.peese <- rma.mv(SREL1C,
SREL1C.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ SREL1C.vg)
## Summarize the results
summary(MLMEMCSC.tfmc.srel1.peese, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 16.8230 -33.6459 -25.6459 -18.9917 -24.4695
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0159 0.1261 36 no STUDID
## sigma^2.2 0.0010 0.0324 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 431.8799, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.8137, p-val = 0.1858
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7867 0.0246 31.9999 39 <.0001 0.7370 0.8364 ***
## SREL1C.vg -0.8958 0.6652 -1.3467 39 0.1858 -2.2413 0.4496
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srel1.peese, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.787 0.0244 32.287 31.05 <0.001 ***
## SREL1C.vg -0.896 0.9493 -0.944 1.46 0.475## Result: The sampling variances are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Influential effect sizes
## Analyses based on the REM with variation between effect sizes
## Plots indicating potential influential effect sizes
inf.tfmc.srel1 <- influence.rma.uni(rma(SREL1C,
SREL1C.vg,
data = srel.meta,
method = "REML"))
plot.infl.rma.uni(inf.tfmc.srel1)
# Increase max print options to show all effect sizes
options(max.print = 1000000)
print(inf.tfmc.srel1)##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -0.8359 -0.1133 0.0129 1.0199 0.0156 439.4003 0.0183 1.8329 -0.1133
## 2 -0.0131 0.0383 0.0016 1.0869 0.0166 434.8728 0.0304 3.0417 0.0384
## 3 0.5036 0.1209 0.0153 1.0760 0.0164 443.3335 0.0289 2.8909 0.1210
## 4 1.0872 0.1974 0.0392 1.0368 0.0157 438.6403 0.0307 3.0703 0.1974
## 5 0.2193 0.0304 0.0009 1.0218 0.0158 443.4520 0.0074 0.7391 0.0302
## 6 0.2001 0.0679 0.0048 1.0740 0.0164 442.7485 0.0255 2.5510 0.0678
## 7 0.7106 0.1514 0.0238 1.0671 0.0162 443.3571 0.0298 2.9778 0.1516
## 8 -0.9148 -0.0438 0.0019 0.9996 0.0155 442.2185 0.0021 0.2088 -0.0438
## 9 0.1239 0.0539 0.0030 1.0711 0.0164 442.6303 0.0244 2.4404 0.0537
## 10 1.1288 0.1994 0.0398 1.0319 0.0156 439.5774 0.0300 3.0039 0.1994
## 11 0.9542 0.1792 0.0327 1.0480 0.0159 442.1906 0.0293 2.9269 0.1792
## 12 -0.9081 -0.1553 0.0240 1.0244 0.0155 428.0409 0.0274 2.7381 -0.1553
## 13 1.1933 0.2098 0.0437 1.0255 0.0155 426.4873 0.0315 3.1459 0.2097
## 14 -0.4010 -0.0399 0.0016 1.0646 0.0162 436.6346 0.0273 2.7279 -0.0399
## 15 0.1218 0.0649 0.0045 1.0920 0.0166 370.4276 0.0319 3.1868 0.0651
## 16 -0.2580 -0.0040 0.0000 1.0008 0.0156 443.3594 0.0003 0.0301 -0.0040
## 17 -6.2509 -1.5501 1.5063 0.4239 0.0056 376.4468 0.0186 1.8557 -1.8968 *
## 18 0.7044 0.1562 0.0254 1.0719 0.0163 442.2148 0.0319 3.1903 0.1565
## 19 0.2762 0.0915 0.0089 1.0903 0.0166 418.3144 0.0318 3.1815 0.0918
## 20 0.7915 0.1675 0.0291 1.0656 0.0162 432.2573 0.0319 3.1931 0.1679
## 21 -0.6084 -0.0597 0.0036 1.0199 0.0157 441.9140 0.0116 1.1562 -0.0596
## 22 -0.1021 0.0213 0.0005 1.0851 0.0165 432.2585 0.0304 3.0427 0.0214
## 23 -1.0939 -0.2056 0.0412 1.0041 0.0152 421.0703 0.0280 2.8024 -0.2056
## 24 -0.4261 -0.0400 0.0016 1.0376 0.0160 441.8028 0.0166 1.6639 -0.0399
## 25 -0.2542 -0.0092 0.0001 1.0041 0.0156 443.2855 0.0018 0.1845 -0.0092
## 26 -1.0934 -0.0598 0.0036 0.9976 0.0155 441.6889 0.0026 0.2622 -0.0600
## 27 -0.9226 -0.1484 0.0219 1.0195 0.0155 434.8731 0.0240 2.3969 -0.1485
## 28 0.6042 0.1312 0.0179 1.0681 0.0163 443.4629 0.0274 2.7391 0.1312
## 29 0.3385 0.0936 0.0092 1.0779 0.0165 442.9558 0.0276 2.7595 0.0935
## 30 -0.1326 0.0150 0.0002 1.0832 0.0165 433.7421 0.0301 3.0056 0.0151
## 31 -0.2629 -0.0135 0.0002 1.0590 0.0162 441.2037 0.0227 2.2677 -0.0134
## 32 0.5274 0.1292 0.0175 1.0799 0.0164 443.0895 0.0310 3.0974 0.1295
## 33 0.6883 0.1522 0.0241 1.0714 0.0163 443.3655 0.0312 3.1195 0.1525
## 34 0.3352 0.1009 0.0108 1.0884 0.0166 435.6413 0.0316 3.1599 0.1012
## 35 0.1368 0.0652 0.0045 1.0877 0.0166 438.5626 0.0304 3.0374 0.0654
## 36 0.9872 0.1907 0.0370 1.0483 0.0159 330.2582 0.0320 3.1959 0.1909
## 37 -0.1640 0.0096 0.0001 1.0854 0.0165 416.3218 0.0312 3.1215 0.0097
## 38 0.3635 0.1052 0.0117 1.0874 0.0165 438.5402 0.0315 3.1483 0.1055
## 39 -2.4209 -0.4474 0.1810 0.8623 0.0129 426.5189 0.0178 1.7757 -0.4620
## 40 -1.6361 -0.2937 0.0817 0.9456 0.0143 431.5993 0.0203 2.0304 -0.2969
## 41 0.7182 0.1556 0.0252 1.0691 0.0162 443.2524 0.0310 3.1000 0.1559## Reliability of factor 2
## Egger's regression test (PET)
## Details: https://wviechtb.github.io/metafor/reference/regtest.html
## Three-level MEM
MLMEMCSC.tfmc.srel2.pet <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ sqrt(SREL2C.vg))
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.pet, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 14.8114 -29.6227 -21.6227 -14.9685 -20.4462
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0039 0.0627 36 no STUDID
## sigma^2.2 0.0092 0.0957 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 248.6284, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 5.7080, p-val = 0.0218
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7083 0.0337 21.0261 39 <.0001 0.6402 0.7764 ***
## sqrt(SREL2C.vg) -0.8558 0.3582 -2.3891 39 0.0218 -1.5803 -0.1313 *
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srel2.pet, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.708 0.027 26.27 19.8 < 0.001 ***
## sqrt(SREL2C.vg) -0.856 0.247 -3.46 13.1 0.00415 **## Result: The standard errors are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Funnel plot test
## Three-level MEM
MLMEMCSC.tfmc.srel2.fpt <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ N)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.fpt, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.2522 -22.5044 -14.5044 -7.8501 -13.3279
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0151 0.1228 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 227.8196, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.6318, p-val = 0.4315
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6622 0.0308 21.4953 39 <.0001 0.5999 0.7245 ***
## N -0.0000 0.0001 -0.7948 39 0.4315 -0.0002 0.0001
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srel2.fpt, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.6622039 0.0293993 22.52 25.20 <0.001 ***
## N -0.0000442 0.0000335 -1.32 2.91 0.281## Contour-enhanced funnel plot
funnel(MLREMCSC.tfmc.srel2,
main="Standard Error",
level = c(90, 95, 99),
shade = c("white", "gray55", "gray75"),
legend = TRUE)
## Result: No evidence for publication or selection bias.
## Precision-Effect Estimate with SE (PEESE)
## Three-level MEM
MLMEMCSC.tfmc.srel2.peese <- rma.mv(SREL2C,
SREL2C.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ SREL2C.vg)
## Summarize the results
summary(MLMEMCSC.tfmc.srel2.peese, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 13.5449 -27.0898 -19.0898 -12.4355 -17.9133
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0145 0.1204 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 255.5011, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 1.7756, p-val = 0.1904
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6547 0.0245 26.7371 39 <.0001 0.6052 0.7043 ***
## SREL2C.vg -0.8013 0.6014 -1.3325 39 0.1904 -2.0177 0.4150
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srel2.peese, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.655 0.0236 27.7 22.72 <0.001 ***
## SREL2C.vg -0.801 0.2502 -3.2 3.61 0.0379 *## Result: The sampling variances are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Influential effect sizes
## Analyses based on the REM with variation between effect sizes
## Plots indicating potential influential effect sizes
inf.tfmc.srel2 <- influence.rma.uni(rma(SREL2C,
SREL2C.vg,
data = srel.meta,
method = "REML"))
plot.infl.rma.uni(inf.tfmc.srel2)
# Increase max print options to show all effect sizes
options(max.print = 1000000)
print(inf.tfmc.srel2)##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -0.8381 -0.0787 0.0062 1.0086 0.0150 258.4725 0.0087 0.8719 -0.0787
## 2 1.4725 0.2696 0.0692 0.9993 0.0143 206.1075 0.0380 3.8013 0.2683
## 3 -0.1740 -0.0100 0.0001 1.0594 0.0156 259.1436 0.0269 2.6864 -0.0100
## 4 0.8447 0.1540 0.0241 1.0459 0.0154 258.3607 0.0280 2.8032 0.1539
## 5 -0.2275 -0.0068 0.0000 1.0019 0.0151 259.5922 0.0011 0.1057 -0.0068
## 6 1.0677 0.1867 0.0350 1.0338 0.0151 257.0726 0.0289 2.8908 0.1867
## 7 -0.5572 -0.0607 0.0037 1.0230 0.0152 258.8709 0.0138 1.3812 -0.0606
## 8 0.1234 0.0220 0.0005 1.0255 0.0153 259.6677 0.0110 1.1040 0.0219
## 9 1.3167 0.2251 0.0499 1.0157 0.0147 254.3684 0.0309 3.0947 0.2251
## 10 0.4579 0.0850 0.0074 1.0484 0.0155 259.5250 0.0222 2.2176 0.0847
## 11 -0.9653 -0.0512 0.0026 1.0007 0.0150 258.5173 0.0027 0.2679 -0.0512
## 12 -1.7773 -0.3725 0.1272 0.9426 0.0134 243.6190 0.0301 3.0149 -0.3729
## 13 0.5742 0.1159 0.0138 1.0583 0.0156 259.2463 0.0285 2.8488 0.1158
## 14 0.4250 0.0995 0.0103 1.0705 0.0157 259.4935 0.0323 3.2251 0.0996
## 15 -0.0955 0.0086 0.0001 1.0869 0.0159 248.8420 0.0385 3.8465 0.0086
## 16 0.3088 0.0190 0.0004 1.0068 0.0151 259.6090 0.0028 0.2821 0.0189
## 17 1.4517 0.2333 0.0531 1.0036 0.0146 254.2868 0.0289 2.8861 0.2335
## 18 0.0656 0.0411 0.0018 1.0877 0.0159 257.8419 0.0380 3.8033 0.0413
## 19 -1.3796 -0.3083 0.0892 0.9850 0.0141 211.7303 0.0370 3.6962 -0.3066
## 20 0.2645 0.0800 0.0068 1.0874 0.0159 259.6607 0.0385 3.8468 0.0805
## 21 -0.5462 -0.0140 0.0002 1.0006 0.0150 259.3246 0.0007 0.0657 -0.0140
## 22 -3.0164 -0.5823 0.2913 0.8271 0.0114 238.4035 0.0230 2.2970 -0.6000 *
## 23 0.4808 0.1142 0.0136 1.0750 0.0158 259.1649 0.0353 3.5281 0.1145
## 24 -0.4876 -0.0510 0.0026 1.0241 0.0152 259.0273 0.0135 1.3531 -0.0509
## 25 -0.3737 -0.0098 0.0001 1.0010 0.0151 259.4969 0.0007 0.0708 -0.0098
## 26 0.1396 0.0373 0.0014 1.0491 0.0156 259.6595 0.0212 2.1159 0.0371
## 27 -0.0224 0.0177 0.0003 1.0658 0.0157 259.4126 0.0287 2.8657 0.0177
## 28 -0.2510 -0.0127 0.0002 1.0067 0.0151 259.5480 0.0034 0.3413 -0.0126
## 29 -1.0797 -0.1053 0.0111 1.0029 0.0149 257.7956 0.0088 0.8827 -0.1055
## 30 0.2377 0.0702 0.0052 1.0791 0.0159 259.6640 0.0345 3.4510 0.0704
## 31 0.1135 0.0354 0.0013 1.0533 0.0156 259.6447 0.0230 2.2967 0.0353
## 32 0.4121 0.1010 0.0106 1.0755 0.0158 259.4668 0.0345 3.4472 0.1012
## 33 0.4960 0.1137 0.0134 1.0711 0.0157 259.2523 0.0336 3.3597 0.1139
## 34 -0.0299 0.0212 0.0005 1.0841 0.0159 258.0639 0.0368 3.6772 0.0213
## 35 1.1946 0.2296 0.0522 1.0297 0.0149 242.0250 0.0372 3.7175 0.2294
## 36 -0.7783 -0.1316 0.0174 1.0388 0.0152 255.3265 0.0298 2.9827 -0.1316
## 37 -0.6336 -0.1093 0.0122 1.0576 0.0154 249.9168 0.0358 3.5777 -0.1095
## 38 -0.2977 -0.0343 0.0012 1.0739 0.0157 256.4368 0.0352 3.5157 -0.0344
## 39 -1.4809 -0.2248 0.0495 0.9841 0.0144 254.4721 0.0188 1.8838 -0.2263
## 40 -2.4793 -0.4442 0.1798 0.8912 0.0126 245.2651 0.0216 2.1615 -0.4539
## 41 1.6818 0.2924 0.0789 0.9731 0.0138 217.3303 0.0373 3.7348 0.2903## Reliability of factor 1
## Egger's regression test (PET)
## Details: https://wviechtb.github.io/metafor/reference/regtest.html
## Three-level MEM
MLMEMCSC.tfmc.srelcr.pet <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ sqrt(SRELCRC.vg))
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.pet, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 50.1284 -100.2567 -92.2567 -85.6025 -91.0802
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0010 0.0319 36 no STUDID
## sigma^2.2 0.0017 0.0410 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 278.2128, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 17.6714, p-val = 0.0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8862 0.0168 52.8237 39 <.0001 0.8523 0.9201 ***
## sqrt(SRELCRC.vg) -1.8829 0.4479 -4.2037 39 0.0001 -2.7889 -0.9769 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srelcr.pet, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.886 0.0129 68.83 16.3 <0.001 ***
## sqrt(SRELCRC.vg) -1.883 0.3810 -4.94 13.1 <0.001 ***## Result: The standard errors are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Funnel plot test
## Three-level MEM
MLMEMCSC.tfmc.srelcr.fpt <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ N)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.fpt, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 41.9300 -83.8600 -75.8600 -69.2058 -74.6836
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0020 0.0444 36 no STUDID
## sigma^2.2 0.0025 0.0500 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 350.6041, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 0.4900, p-val = 0.4881
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8198 0.0154 53.3885 39 <.0001 0.7887 0.8509 ***
## N 0.0000 0.0000 0.7000 39 0.4881 -0.0000 0.0001
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srelcr.fpt, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.8197964 0.0155592 52.69 27.70 <0.001 ***
## N 0.0000218 0.0000166 1.31 2.87 0.285## Contour-enhanced funnel plot
funnel(MLREMCSC.tfmc.srelcr,
main="Standard Error",
level = c(90, 95, 99),
shade = c("white", "gray55", "gray75"),
legend = TRUE)
## Result: No evidence for publication or selection bias.
## Precision-Effect Estimate with SE (PEESE)
## Three-level MEM
MLMEMCSC.tfmc.srelcr.peese <- rma.mv(SRELCRC,
SRELCRC.vg,
random = list(~ 1 | STUDID/ESID),
method = "REML",
data = srel.meta,
slab = paste(Reference),
tdist = TRUE,
test = "t",
mods =~ SRELCRC.vg)
## Summarize the results
summary(MLMEMCSC.tfmc.srelcr.peese, digits=4)##
## Multivariate Meta-Analysis Model (k = 41; method: REML)
##
## logLik Deviance AIC BIC AICc
## 46.3360 -92.6721 -84.6721 -78.0179 -83.4956
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0000 0.0000 36 no STUDID
## sigma^2.2 0.0032 0.0569 41 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 39) = 322.6363, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 39) = 7.3839, p-val = 0.0098
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8409 0.0114 73.5926 39 <.0001 0.8178 0.8640 ***
## SRELCRC.vg -7.7141 2.8388 -2.7173 39 0.0098 -13.4562 -1.9720 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## RVE standard errors
coef_test(MLMEMCSC.tfmc.srelcr.peese, vcov = "CR2")## Coef. Estimate SE t-stat d.f. (Satt) p-val (Satt) Sig.
## intrcpt 0.841 0.0133 63.06 21.2 <0.001 ***
## SRELCRC.vg -7.714 6.7213 -1.15 1.7 0.387## Result: The sampling variances are significantly moderating the effect size.
## This can be considered evidence for publication or selection bias.
## Influential effect sizes
## Analyses based on the REM with variation between effect sizes
## Plots indicating potential influential effect sizes
inf.tfmc.srelcr <- influence.rma.uni(rma(SRELCRC,
SRELCRC.vg,
data = srel.meta,
method = "REML"))
plot.infl.rma.uni(inf.tfmc.srelcr)
# Increase max print options to show all effect sizes
options(max.print = 1000000)
print(inf.tfmc.srelcr)##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -1.0690 -0.1166 0.0136 1.0027 0.0040 355.3463 0.0105 1.0533 -0.1169
## 2 1.4612 0.2457 0.0580 1.0027 0.0038 257.4534 0.0334 3.3448 0.2448
## 3 -0.2035 -0.0085 0.0001 1.0538 0.0041 356.2923 0.0243 2.4344 -0.0085
## 4 1.2350 0.2040 0.0414 1.0226 0.0040 355.7174 0.0279 2.7898 0.2040
## 5 0.2570 0.0594 0.0036 1.0476 0.0041 358.0984 0.0201 2.0090 0.0593
## 6 0.6864 0.1276 0.0166 1.0482 0.0041 358.1292 0.0242 2.4190 0.1275
## 7 0.0063 0.0240 0.0006 1.0495 0.0041 357.5952 0.0211 2.1060 0.0239
## 8 -1.0404 -0.1322 0.0174 1.0061 0.0040 354.6537 0.0143 1.4328 -0.1325
## 9 1.1781 0.1973 0.0388 1.0267 0.0040 356.1754 0.0277 2.7677 0.1972
## 10 1.0421 0.1748 0.0308 1.0336 0.0040 357.2096 0.0255 2.5468 0.1748
## 11 0.2779 0.0528 0.0028 1.0368 0.0041 358.1830 0.0155 1.5482 0.0525
## 12 -2.2295 -0.4475 0.1809 0.9030 0.0034 337.9267 0.0226 2.2596 -0.4526
## 13 1.4464 0.2334 0.0529 1.0048 0.0039 351.3941 0.0303 3.0317 0.2331
## 14 0.2014 0.0656 0.0045 1.0678 0.0042 357.2906 0.0287 2.8679 0.0656
## 15 0.2406 0.0796 0.0067 1.0785 0.0042 340.3447 0.0334 3.3394 0.0800
## 16 -0.1351 -0.0031 0.0000 1.0239 0.0041 357.8784 0.0107 1.0708 -0.0031
## 17 -0.0551 0.0210 0.0005 1.0677 0.0042 355.1910 0.0292 2.9198 0.0211
## 18 0.8764 0.1782 0.0325 1.0538 0.0041 350.0971 0.0334 3.3390 0.1785
## 19 -0.7886 -0.1388 0.0194 1.0404 0.0040 299.8678 0.0326 3.2555 -0.1389
## 20 0.6729 0.1496 0.0232 1.0657 0.0042 357.8493 0.0334 3.3372 0.1501
## 21 -0.9291 -0.0354 0.0013 0.9997 0.0040 357.0700 0.0013 0.1338 -0.0354
## 22 -2.0920 -0.4383 0.1728 0.9111 0.0035 335.5575 0.0246 2.4600 -0.4409
## 23 -0.4658 -0.0597 0.0037 1.0535 0.0041 351.2836 0.0285 2.8472 -0.0597
## 24 -0.1085 0.0031 0.0000 1.0372 0.0041 357.6553 0.0163 1.6344 0.0031
## 25 -1.2454 -0.1596 0.0252 0.9963 0.0039 353.8343 0.0135 1.3520 -0.1603
## 26 -1.5531 -0.1623 0.0261 0.9862 0.0039 353.6172 0.0086 0.8618 -0.1635
## 27 -0.7633 -0.1089 0.0119 1.0269 0.0040 353.9262 0.0214 2.1447 -0.1089
## 28 -0.1036 0.0079 0.0001 1.0523 0.0041 357.0497 0.0228 2.2825 0.0079
## 29 -0.1507 -0.0007 0.0000 1.0483 0.0041 357.0754 0.0214 2.1437 -0.0006
## 30 0.1744 0.0642 0.0043 1.0731 0.0042 356.0302 0.0309 3.0945 0.0644
## 31 -0.3078 -0.0260 0.0007 1.0366 0.0041 357.0223 0.0177 1.7662 -0.0259
## 32 0.4443 0.1079 0.0121 1.0678 0.0042 358.0144 0.0303 3.0316 0.1081
## 33 0.9934 0.1883 0.0359 1.0436 0.0041 355.7977 0.0316 3.1592 0.1884
## 34 0.3816 0.1024 0.0110 1.0744 0.0042 356.6039 0.0326 3.2586 0.1028
## 35 0.4220 0.1061 0.0117 1.0702 0.0042 357.8106 0.0312 3.1184 0.1064
## 36 0.4658 0.1145 0.0137 1.0705 0.0042 357.8599 0.0319 3.1919 0.1149
## 37 -0.3512 -0.0369 0.0014 1.0656 0.0042 339.9583 0.0320 3.1975 -0.0370
## 38 0.2261 0.0747 0.0058 1.0750 0.0042 355.4784 0.0319 3.1912 0.0749
## 39 -2.9093 -0.4463 0.1864 0.8860 0.0034 340.9867 0.0139 1.3934 -0.4617
## 40 -2.6061 -0.6201 0.3181 0.8405 0.0031 321.7650 0.0261 2.6148 -0.6233 *
## 41 1.5693 0.2522 0.0605 0.9912 0.0038 334.4151 0.0325 3.2499 0.25112.2.4.6 Forest Plots
## Reliability of factor 1
#pdf(file = "ForestPlots-TwoFactorModel3.pdf", onefile = TRUE)
forest.rma(MLREMCSC.tfmc.srel1,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfmc.srel1$k,
digits = 3,
level = 95,
cex = .9,
xlab = "Omega Coefficient",
main = "Reliability Factor 1 (Model 3)")
## Reliability of factor 2
forest.rma(MLREMCSC.tfmc.srel2,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfmc.srel2$k,
digits = 3,
level = 95,
cex = .9,
xlab = "Omega Coefficient",
main = "Reliability Factor 2 (Model 3)")
## Composite reliability
forest.rma(MLREMCSC.tfmc.srelcr,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfmc.srelcr$k,
digits = 3,
level = 95,
cex = .9,
xlab = "Omega Coefficient",
main = "Composite Reliability (Model 3)")
#dev.off()3 R session info
sessionInfo()## R version 4.3.1 (2023-06-16)
## Platform: x86_64-apple-darwin20 (64-bit)
## Running under: macOS Ventura 13.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Europe/Oslo
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] dmetar_0.1.0 devtools_2.4.5 usethis_2.2.1
## [4] dplyr_1.1.3 lavaan_0.6-16 clubSandwich_0.5.8
## [7] robumeta_2.1 metafor_4.2-0 numDeriv_2016.8-1.1
## [10] metadat_1.2-0 Matrix_1.6-1 metaSEM_1.3.0
## [13] OpenMx_2.21.8 reshape2_1.4.4 psych_2.3.6
## [16] pacman_0.5.1
##
## loaded via a namespace (and not attached):
## [1] mathjaxr_1.6-0 rstudioapi_0.14 jsonlite_1.8.7
## [4] magrittr_2.0.3 modeltools_0.2-23 farver_2.1.1
## [7] nloptr_2.0.3 rmarkdown_2.22 fs_1.6.3
## [10] vctrs_0.6.3 memoise_2.0.1 minqa_1.2.6
## [13] CompQuadForm_1.4.3 htmltools_0.5.5 sass_0.4.6
## [16] bslib_0.5.0 htmlwidgets_1.6.2 plyr_1.8.8
## [19] poibin_1.5 sandwich_3.0-2 zoo_1.8-12
## [22] cachem_1.0.8 mime_0.12 lifecycle_1.0.3
## [25] pkgconfig_2.0.3 R6_2.5.1 fastmap_1.1.1
## [28] shiny_1.7.4 magic_1.6-1 digest_0.6.33
## [31] colorspace_2.1-0 ps_1.7.5 pkgload_1.3.2.1
## [34] ellipse_0.4.5 labeling_0.4.3 fansi_1.0.4
## [37] abind_1.4-5 compiler_4.3.1 remotes_2.4.2
## [40] withr_2.5.0 meta_6.5-0 highr_0.10
## [43] pkgbuild_1.4.2 MASS_7.3-60 sessioninfo_1.2.2
## [46] tools_4.3.1 pbivnorm_0.6.0 prabclus_2.3-2
## [49] httpuv_1.6.11 nnet_7.3-19 glue_1.6.2
## [52] quadprog_1.5-8 callr_3.7.3 nlme_3.1-162
## [55] promises_1.2.0.1 grid_4.3.1 cluster_2.1.4
## [58] generics_0.1.3 gtable_0.3.4 class_7.3-22
## [61] xml2_1.3.4 utf8_1.2.3 flexmix_2.3-19
## [64] ggrepel_0.9.3 pillar_1.9.0 stringr_1.5.0
## [67] later_1.3.1 robustbase_0.99-0 splines_4.3.1
## [70] lattice_0.21-8 tidyselect_1.2.0 miniUI_0.1.1.1
## [73] pbapply_1.7-2 knitr_1.43 gridExtra_2.3
## [76] stats4_4.3.1 xfun_0.39 diptest_0.76-0
## [79] DEoptimR_1.0-14 MuMIn_1.47.5 netmeta_2.8-2
## [82] stringi_1.7.12 yaml_2.3.7 boot_1.3-28.1
## [85] evaluate_0.21 codetools_0.2-19 kernlab_0.9-32
## [88] tibble_3.2.1 cli_3.6.1 RcppParallel_5.1.7
## [91] xtable_1.8-4 munsell_0.5.0 processx_3.8.2
## [94] jquerylib_0.1.4 Rcpp_1.0.11 parallel_4.3.1
## [97] ellipsis_0.3.2 ggplot2_3.4.3 prettyunits_1.1.1
## [100] mclust_6.0.0 profvis_0.3.8 urlchecker_1.0.1
## [103] lme4_1.1-34 mvtnorm_1.2-2 scales_1.2.1
## [106] purrr_1.0.2 crayon_1.5.2 fpc_2.2-10
## [109] rlang_1.1.1 mnormt_2.1.1