Supplementary Material
Reliability Generalization of the TTCT: Parameter-Based MASEM - Sensitivity Analyses
25 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,
semPower)
#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'
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'
Balci_mata <-
'1,
0.292, 1,
0, 0.221, 1,
0.176, 0.148, 0.304, 1,
-0.117, 0.154, 0.035, 0.047, 1'
Balci_matb <-
'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'
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'
Rubenstein_2020_a <-
'1,
0.828, 1,
0.331, 0.321, 1,
0.47, 0.55, 0.45, 1,
0.681, 0.64, 0.443, 0.526, 1'
Rubenstein_2022_b <-
'1,
0.629, 1,
0.238, 0.351, 1,
0.402, 0.509, 0.38, 1,
0.313, 0.394, 0.385, 0.305, 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'
#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(Balci_mata)
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(Balci_matb)
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")
Rubenstein_2020_a1 <-char2num(Rubenstein_2020_a)
Rubenstein_a <- getCov(Rubenstein_2020_a1, diag=T)
colnames(Rubenstein_a) <- c("Fl","Or", "El","Ab","Res")
rownames(Rubenstein_a) <- c("Fl","Or", "El","Ab","Res")
Rubenstein_2022_b1 <-char2num(Rubenstein_2022_b)
Rubenstein_b <- getCov(Rubenstein_2022_b1, diag=T)
colnames(Rubenstein_b) <- c("Fl","Or", "El","Ab","Res")
rownames(Rubenstein_b) <- c("Fl","Or", "El","Ab","Res")
#alphabetical order
data <- list(Acar, Acaretal,Auth, Balcia, Balcib, Barkul, Barkul2, Berman, Boynton, Callans,
Carter_a, Carter_b, Chi, Cho_F, Cho_M, Cockcroft,
Conway, Crawford, Digranes, Dufner, Fishkin, Forsyth, Gao, Garcia, Gollmar,
Hamlen, Hokanson, Houtz, Humble, Ibrahim,
Kiehn, Kim_1, Kim_2a, Kim_2b, Kim_2c, Kim_3a, Kim_3b,
Lew, Liu, Miranda, Morrison_a, Morrison_b, Morrison_c,
Nguyen, Rose, Rose_b, Roskos_Y, Roskos_O, Rubenstein_a, Rubenstein_b, Samuels, Shore, Stephens,
Storer_a, Storer_b, Tannehill, Tisone, Trigani,
Voss, Wan, Warne, Watson, Yoon, Zbarskaya, Zhang)
#Updated sample size counts
n <- c(477, 375, 30, 264, 105, 599, 147, 13, 62, 60, 24, 24, 203, 24, 35, 36, 25, 21, 17, 98, 116, 45, 319, 95, 128, 118, 1758,
42, 125, 99, 89, 500, 1000, 1000, 1000, 125, 137, 135, 1047, 12, 184, 122, 121, 187, 12, 19, 39, 31, 371,371,
51, 18, 84, 43, 46, 199, 24, 107, 120, 95, 432, 6, 163, 125, 1067)
#alphabetical order
names <- c("Acar", "Acaretal","Auth" , "Balcia", "Balcib", "Barkul" , "Barkul2" , "Berman" , "Boynton" , "Callans" ,
"Carter_a" , "Carter_b" , "Chi" , "Cho_F" , "Cho_M" , "Cockcroft" ,
"Conway" , "Crawford",
"Digranes" , "Dufner" , "Fishkin" , "Forsyth" , "Gao", "Garcia" , "Gollmar" ,
"Hamlen" , "Hokanson" , "Houtz" , "Humble" , "Ibrahim",
"Kiehn" , "Kim_1" , "Kim_2a" , "Kim_2b" , "Kim_2c" , "Kim_3a" , "Kim_3b" ,
"Lew" , "Liu", "Miranda" , "Morrison_a" , "Morrison_b" , "Morrison_c" ,
"Nguyen" , "Rose" , "Rose_b" , "Roskos_Y" , "Roskos_O" , "Rubenstein_a","Rubenstein_b", "Samuels" , "Shore" , "Stephens" ,
"Storer_a" , "Storer_b" , "Tannehill" , "Tisone" , "Trigani", "Voss" ,"Wan", "Warne" , "Watson" , "Yoon" , "Zbarskaya" , "Zhang")
#alphabetical order
study.names <- c("Acar", "Acaretal","Auth" , "Balcia", "Balcib", "Barkul" , "Barkul2" , "Berman" , "Boynton" , "Callans" ,
"Carter_a" , "Carter_b" , "Chi" , "Cho_F" , "Cho_M" , "Cockcroft" ,
"Conway" , "Crawford",
"Digranes" , "Dufner" , "Fishkin" , "Forsyth" , "Gao", "Garcia" , "Gollmar" ,
"Hamlen" , "Hokanson" , "Houtz" , "Humble" , "Ibrahim",
"Kiehn" , "Kim_1" , "Kim_2a" , "Kim_2b" , "Kim_2c" , "Kim_3a" , "Kim_3b" ,
"Lew" , "Liu", "Miranda" , "Morrison_a" , "Morrison_b" , "Morrison_c" ,
"Nguyen" , "Rose" , "Rose_b" , "Roskos_Y" , "Roskos_O" , "Rubenstein_a","Rubenstein_b", "Samuels" , "Shore" , "Stephens" ,
"Storer_a" , "Storer_b" , "Tannehill" , "Tisone" , "Trigani", "Voss" ,"Wan", "Warne" , "Watson" , "Yoon" , "Zbarskaya" , "Zhang")
names(data) <- study.names
## Possible moderators
## Age group
## Code: 1 = Adults, 0 = Kindergarten up to High/Middle school
adults <- c(1,0,1,0,0,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,
0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0,0,0,1,0,1,1,1,0,1,0)
## Evidence against discriminant validity
## Coding: 1 = evidence present, 0 = evidence not present/reported
validity <- c(1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0)
## Test forms
## Subset the data
formsAB <- c("A","A",NA,"Both","Both","A","A","A","Both","A","A","A","A",NA,NA,"B","A","A","A","B","A","Both",NA,"B","A","A","A","B","A","A","A","A","A","A","A","A",
"A",NA,"A","A","A","A","A","A","A","A","B","B","A","B","A","A","A","A","A","A","A","A","A",NA,"A","B","A","A","A")
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(0,0,1,0,0,0,0,NA,0,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,1,1,0,
NA,NA,NA,1,0,0,1,1,0,0,1,0,1,1,1,1,0,1,1,NA,0,0,1,1,0)
scores <- as.vector(as.numeric(which(scoring %in% NA))) # which gives the positions of codes 1
head(data, 5)## $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
##
## $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
##
## $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
##
## $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
##
## $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 1.0001.3 Data checking and subsetting
## Check for positive definiteness
is.pd(data)## Acar Acaretal Auth Balcia Balcib Barkul
## TRUE TRUE TRUE TRUE TRUE TRUE
## Barkul2 Berman Boynton Callans Carter_a Carter_b
## NA TRUE TRUE TRUE TRUE TRUE
## Chi Cho_F Cho_M Cockcroft Conway Crawford
## TRUE TRUE TRUE TRUE TRUE TRUE
## Digranes Dufner Fishkin Forsyth Gao Garcia
## TRUE TRUE TRUE TRUE TRUE TRUE
## Gollmar Hamlen Hokanson Houtz Humble Ibrahim
## TRUE TRUE TRUE TRUE TRUE TRUE
## Kiehn Kim_1 Kim_2a Kim_2b Kim_2c Kim_3a
## TRUE TRUE TRUE TRUE TRUE TRUE
## Kim_3b Lew Liu Miranda Morrison_a Morrison_b
## TRUE TRUE TRUE TRUE TRUE TRUE
## Morrison_c Nguyen Rose Rose_b Roskos_Y Roskos_O
## TRUE TRUE TRUE TRUE TRUE TRUE
## Rubenstein_a Rubenstein_b Samuels Shore Stephens Storer_a
## TRUE TRUE TRUE TRUE TRUE TRUE
## Storer_b Tannehill Tisone Trigani Voss Wan
## TRUE TRUE TRUE TRUE TRUE TRUE
## Warne Watson Yoon Zbarskaya Zhang
## 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 65 65 58 59 57
## Or 65 65 58 59 57
## El 58 58 58 58 55
## Ab 59 59 58 59 56
## Res 57 57 55 56 57# 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 FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
## [25] FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE TRUE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE TRUE FALSE FALSE FALSEtable(y)## y
## FALSE TRUE
## 55 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
## $data$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
##
## $data$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
##
## $data$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
##
## $data$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_a
## 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_b
## 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_F
## 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_M
## 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
##
## $data$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
##
## $data$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_2a
## 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_2b
## 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_2c
## 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_3a
## 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_3b
## 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
##
## $data$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
##
## $data$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
##
## $data$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_b
## 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_Y
## 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_O
## 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
##
## $data$Rubenstein_a
## Fl Or El Ab Res
## Fl 1.000 0.828 0.331 0.470 0.681
## Or 0.828 1.000 0.321 0.550 0.640
## El 0.331 0.321 1.000 0.450 0.443
## Ab 0.470 0.550 0.450 1.000 0.526
## Res 0.681 0.640 0.443 0.526 1.000
##
## $data$Rubenstein_b
## Fl Or El Ab Res
## Fl 1.000 0.629 0.238 0.402 0.313
## Or 0.629 1.000 0.351 0.509 0.394
## El 0.238 0.351 1.000 0.380 0.385
## Ab 0.402 0.509 0.380 1.000 0.305
## Res 0.313 0.394 0.385 0.305 1.000
##
## $data$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_a
## 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_b
## 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
##
## $data$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
##
## $data$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
##
## $data$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
##
## $data$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
##
##
## $n
## [1] 477 375 30 264 105 599 13 60 24 24 203 24 35 36 25
## [16] 21 17 116 45 319 95 128 1758 42 125 99 500 1000 1000 1000
## [31] 125 137 1047 12 187 12 19 39 31 371 371 51 18 84 43
## [46] 46 199 24 107 120 95 432 163 125 10672 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]]$coefs
## L1 L2 L3 L4 L5
## 0.7806757 0.7970722 0.3850632 0.4928744 0.6544310
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0018747607 0.0004414647 0.0002888422 0.0003672497 0.0004744853
## L2 0.0004414647 0.0018586283 0.0002859710 0.0003626627 0.0004635303
## L3 0.0002888422 0.0002859710 0.0023570479 0.0001926207 0.0002535575
## L4 0.0003672497 0.0003626627 0.0001926207 0.0022354054 0.0003235835
## L5 0.0004744853 0.0004635303 0.0002535575 0.0003235835 0.0020128976
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 14 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 477
##
## Model Test User Model:
##
## Test statistic 83.333
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.8539468 0.8834395 0.2320228 0.4090740 0.6433003
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0020687540 0.0007157960 0.0002623920 0.0004625366 0.0007268287
## L2 0.0007157960 0.0020239678 0.0002524888 0.0004436589 0.0006875786
## L3 0.0002623920 0.0002524888 0.0029423964 0.0001260761 0.0001982261
## L4 0.0004625366 0.0004436589 0.0001260761 0.0027619526 0.0003494688
## L5 0.0007268287 0.0006875786 0.0001982261 0.0003494688 0.0023771537
##
## [[2]]$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 375
##
## Model Test User Model:
##
## Test statistic 108.835
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## 0.5976890 0.8960524 0.4174755 0.2081323 0.3135450
##
## [[3]]$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
##
## [[3]]$fit
## lavaan 0.6.16 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 30
##
## Model Test User Model:
##
## Test statistic 6.068
## Degrees of freedom 5
## P-value (Chi-square) 0.300
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.3384332 0.5238644 0.4325338 0.4546676 0.1122193
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 7.787576e-03 -0.0006302157 -9.201167e-05 -1.448375e-04 1.826983e-05
## L2 -6.302157e-04 0.0095965837 -1.256685e-03 -1.541087e-03 -1.332804e-04
## L3 -9.201167e-05 -0.0012566850 8.347094e-03 -3.886514e-04 -1.621477e-06
## L4 -1.448375e-04 -0.0015410869 -3.886514e-04 8.596114e-03 -1.388429e-05
## L5 1.826983e-05 -0.0001332804 -1.621477e-06 -1.388429e-05 7.516828e-03
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 23 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 36.623
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.6505729 0.5767207 0.3335709 0.4680604 -0.1908895
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 1.718667e-02 -0.0026844610 -0.0002037401 -0.0007658679 3.988347e-05
## L2 -2.684461e-03 0.0159257850 0.0005739521 0.0006749661 -3.492890e-04
## L3 -2.037401e-04 0.0005739521 0.0146980847 0.0005715674 -2.534976e-04
## L4 -7.658679e-04 0.0006749661 0.0005715674 0.0147126561 -3.373881e-04
## L5 3.988347e-05 -0.0003492890 -0.0002534976 -0.0003373881 1.491776e-02
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 17 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
## Number of inequality constraints 5
##
## Number of observations 105
##
## Model Test User Model:
##
## Test statistic 14.475
## Degrees of freedom 5
## P-value (Chi-square) 0.013## Extract relevant model parameters
## FIT INDICES
## Chi-squares and p values of the parameter-based models
## Select CFI and SRMR
## SRMR performs well in small samples (see Pavlov et al., 2021, EPM)
sfm_model_fit <- t(sapply(sfm.fit.all, function(x) {
fitMeasures(x$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
## Acar 83.3332 0.0000 477 0.8816 0.0710
## Acaretal 108.8346 0.0000 375 0.8421 0.1082
## Auth 6.0684 0.2996 30 0.9263 0.0915
## Balcia 36.6229 0.0000 264 0.5953 0.0766
## Balcib 14.4754 0.0129 105 0.7828 0.0752
## 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_a 13.2179 0.0214 24 0.8721 0.1466
## Carter_b 2.1289 0.8310 24 1.0000 0.0348
## Chi 97.7060 0.0000 203 0.6591 0.1254
## Cho_F 13.9922 0.0157 24 0.8011 0.0947
## Cho_M 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
## Gao 14.0567 0.0153 319 0.9583 0.0368
## 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_2a 262.3095 0.0000 1000 0.9004 0.0802
## Kim_2b 134.6176 0.0000 1000 0.9102 0.0849
## Kim_2c 305.3774 0.0000 1000 0.8737 0.1028
## Kim_3a 181.6475 0.0000 125 0.2080 0.3009
## Kim_3b 69.7880 0.0000 137 0.7345 0.1431
## Liu 1025.4772 0.0000 1047 0.7377 0.2090
## Miranda 1.9213 0.8599 12 1.0000 0.0801
## Nguyen 6.3830 0.2707 187 0.9927 0.0418
## Rose 9.2189 0.1006 12 0.7898 0.1172
## Rose_b 11.3207 0.0454 19 0.7149 0.1517
## Roskos_Y 8.9598 0.1107 39 0.8776 0.0875
## Roskos_O 2.6746 0.7500 31 1.0000 0.0691
## Rubenstein_a 84.3037 0.0000 371 0.9157 0.0721
## Rubenstein_b 36.0357 0.0000 371 0.9332 0.0574
## 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_a 33.0343 0.0000 43 0.7132 0.1172
## Storer_b 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
## Wan 7.7501 0.1706 95 0.9231 0.0581
## Warne 89.9866 0.0000 432 0.8950 0.0731
## Yoon 161.6311 0.0000 163 0.4854 0.2409
## Zbarskaya 60.8402 0.0000 125 0.5753 0.1558
## Zhang 131.0945 0.0000 1067 0.9490 0.0807## 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
## Acar 83.333237 0.0000000000000002220446 477 0.8816320 0.07096241
## Acaretal 108.834597 0.0000000000000000000000 375 0.8420727 0.10816058
## Auth 6.068386 0.2996214212440039270646 30 0.9263234 0.09146972
## Balcia 36.622915 0.0000007127725482058977 264 0.5953345 0.07661383
## Balcib 14.475398 0.0128555988944794030715 105 0.7827929 0.075189842.1.2.2 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
## 0.7969849 0.8003590 0.6446502 0.5195315 0.6987064
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0018861508 0.0004099329 0.0004707938 0.0001950756 0.0002623528
## L2 0.0004099329 0.0018834415 0.0004673686 0.0001959015 0.0002634636
## L3 0.0004707938 0.0004673686 0.0020258499 0.0001577891 0.0002122070
## L4 0.0001950756 0.0001959015 0.0001577891 0.0031343648 -0.0003250442
## L5 0.0002623528 0.0002634636 0.0002122070 -0.0003250442 0.0039772879
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 18 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 477
##
## Model Test User Model:
##
## Test statistic 57.687
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.8684909 0.8753378 0.6396407 0.4880936 0.9608786
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.00206802892 0.00069584126 0.00071243600 0.00009368257 0.0001844270
## L2 0.00069584126 0.00205814308 0.00070152449 0.00009442116 0.0001858810
## L3 0.00071243600 0.00070152449 0.00238115270 0.00006899694 0.0001358299
## L4 0.00009368257 0.00009442116 0.00006899694 0.00543615561 -0.0053004314
## L5 0.00018442700 0.00018588101 0.00013582993 -0.00530043142 0.0134203654
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 21 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 375
##
## Model Test User Model:
##
## Test statistic 33.092
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## 0.5895150 0.9156545 0.3050138 0.8405801 0.3806894
##
## [[3]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0453756427 -0.016991967 0.0092965831 0.0018551323 0.0008401689
## L2 -0.0169919669 0.062985668 -0.0068274011 0.0028814532 0.0013049783
## L3 0.0092965831 -0.006827401 0.0385664551 0.0009598415 0.0004347016
## L4 0.0018551323 0.002881453 0.0009598415 0.1800957928 -0.0543381624
## L5 0.0008401689 0.001304978 0.0004347016 -0.0543381624 0.0625523360
##
## [[3]]$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
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.2920001 1.0000000 0.1540000 0.6737536 0.4512037
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.00361265564 0.00055093560 0.00008484407 0.00003993787 0.00002674585
## L2 0.00055093560 0.00188676565 0.00029056186 0.00013677351 0.00009159538
## L3 0.00008484407 0.00029056186 0.00372878360 0.00002106312 0.00001410569
## L4 0.00003993787 0.00013677351 0.00002106312 0.02310016732 -0.01024367663
## L5 0.00002674585 0.00009159538 0.00001410569 -0.01024367663 0.01244114141
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 55 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 17.457
## Degrees of freedom 4
## P-value (Chi-square) 0.002
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.8040935 0.5316154 -0.1983872 0.4340951 0.8362217
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0325363543 -0.0126544938 0.00306217860 0.00029116216 0.0005608822
## L2 -0.0126544938 0.0197394588 -0.00243904990 0.00019249800 0.0003708198
## L3 0.0030621786 -0.0024390499 0.01364481519 -0.00007183599 -0.0001383817
## L4 0.0002911622 0.0001924980 -0.00007183599 0.02442133368 -0.0257014945
## L5 0.0005608822 0.0003708198 -0.00013838175 -0.02570149452 0.0650521958
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 105
##
## Model Test User Model:
##
## Test statistic 5.016
## Degrees of freedom 4
## P-value (Chi-square) 0.286## 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
## Acar 57.6867 0.0000 477 0.9189 0.0565
## Acaretal 33.0925 0.0000 375 0.9558 0.0507
## Auth 3.8267 0.4300 30 1.0000 0.0672
## Balcia 17.4574 0.0016 264 0.8278 0.0569
## Balcib 5.0161 0.2856 105 0.9767 0.0468
## 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_a 5.1019 0.2770 24 0.9829 0.0709
## Carter_b 2.0598 0.7248 24 1.0000 0.0336
## Chi 114.0734 0.0000 203 0.5952 0.1638
## Cho_F 11.5357 0.0212 24 0.8333 0.0795
## Cho_M 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
## Gao 5.3692 0.2515 319 0.9937 0.0243
## 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_2a 144.5767 0.0000 1000 0.9456 0.0508
## Kim_2b 52.4440 0.0000 1000 0.9664 0.0483
## Kim_2c 168.1729 0.0000 1000 0.9310 0.0628
## Kim_3a 141.7916 0.0000 125 0.3822 0.2546
## Kim_3b 60.1716 0.0000 137 0.7698 0.1375
## Liu 557.0301 0.0000 1047 0.8578 0.1704
## Miranda 0.9114 0.9229 12 1.0000 0.0521
## Nguyen 3.0839 0.5439 187 1.0000 0.0252
## Rose 5.1725 0.2700 12 0.9416 0.0939
## Rose_b 9.5764 0.0482 19 0.7485 0.1636
## Roskos_Y 8.8310 0.0655 39 0.8507 0.0857
## Roskos_O 1.9012 0.7539 31 1.0000 0.0603
## Rubenstein_a 51.4485 0.0000 371 0.9496 0.0513
## Rubenstein_b 25.1730 0.0000 371 0.9544 0.0524
## 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_a 18.5349 0.0010 43 0.8513 0.0939
## Storer_b 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
## Wan 7.7500 0.1012 95 0.8952 0.0581
## Warne 52.9054 0.0000 432 0.9396 0.0496
## Yoon 121.9903 0.0000 163 0.6124 0.2126
## Zbarskaya 27.6169 0.0000 125 0.8204 0.1117
## Zhang 19.0140 0.0008 1067 0.9939 0.0208## 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
## Acar 57.686705 0.000000000008878454 477 0.9188750 0.05648029
## Acaretal 33.092492 0.000001143512293966 375 0.9557518 0.05067900
## Auth 3.826686 0.429969118942402750 30 1.0000000 0.06722991
## Balcia 17.457364 0.001574836742134322 264 0.8277916 0.05693066
## Balcib 5.016106 0.285648861730992576 105 0.9767075 0.04683203## 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 Acar 477 0.79342944 0.016278481 0.76152421 0.8253347
## 2 Acaretal 375 0.84145745 0.014069535 0.81388167 0.8690332
## 3 Auth 30 0.65564386 0.104524431 0.45077974 0.8605080
## 4 Balcia 264 0.52510048 0.039484520 0.44771224 0.6024887
## 5 Balcib 105 0.38902715 0.099196619 0.19460535 0.5834490
## 6 Barkul 599 0.87684294 0.009058061 0.85908947 0.8945964
## 7 Berman 13 0.21016567 0.195514311 -0.17303533 0.5933667
## 8 Callans 60 0.82486789 0.038333729 0.74973516 0.9000006
## 9 Carter_a 24 0.92550812 0.026368277 0.87382725 0.9771890
## 10 Carter_b 24 0.87840114 0.041440901 0.79717846 0.9596238
## 11 Chi 203 0.67031672 0.034570247 0.60256028 0.7380732
## 12 Cho_F 24 0.78113939 0.075683560 0.63280234 0.9294764
## 13 Cho_M 35 0.88259986 0.033779342 0.81639357 0.9488062
## 14 Cockcroft 36 0.51583279 0.135877965 0.24951687 0.7821487
## 15 Conway 25 0.83865184 0.055255865 0.73035233 0.9469513
## 16 Crawford 21 0.92207022 0.030206796 0.86286599 0.9812745
## 17 Digranes 17 0.91767077 0.034578505 0.84989815 0.9854434
## 18 Fishkin 116 0.67543999 0.052009003 0.57350422 0.7773758
## 19 Forsyth 45 0.94055748 0.015555705 0.91006886 0.9710461
## 20 Gao 319 0.50809497 0.047486027 0.41502407 0.6011659
## 21 Garcia 95 0.77668460 0.039474752 0.69931551 0.8540537
## 22 Gollmar 128 0.69572184 0.041101217 0.61516494 0.7762787
## 23 Hokanson 1758 0.82110347 0.007243849 0.80690579 0.8353012
## 24 Houtz 42 0.75289536 0.063984429 0.62748818 0.8783025
## 25 Humble 125 0.79567253 0.030606303 0.73568528 0.8556598
## 26 Ibrahim 99 0.75192054 0.039023666 0.67543556 0.8284055
## 27 Kim_1 500 0.88283380 0.008954717 0.86528287 0.9003847
## 28 Kim_2a 1000 0.88851515 0.006118823 0.87652248 0.9005078
## 29 Kim_2b 1000 0.82563158 0.009412889 0.80718266 0.8440805
## 30 Kim_2c 1000 0.88656108 0.006190075 0.87442875 0.8986934
## 31 Kim_3a 125 0.58458079 0.052557496 0.48156999 0.6875916
## 32 Kim_3b 137 0.23957472 0.093681148 0.05596305 0.4231864
## 33 Liu 1047 0.85566281 0.007922086 0.84013581 0.8711898
## 34 Miranda 12 0.66708273 0.162981604 0.34764466 0.9865208
## 35 Nguyen 187 0.77821059 0.026939478 0.72541019 0.8310110
## 36 Rose 12 0.68572562 0.143683681 0.40411078 0.9673405
## 37 Rose_b 19 0.73783593 0.093877348 0.55383971 0.9218322
## 38 Roskos_Y 39 0.66456878 0.089855121 0.48845598 0.8406816
## 39 Roskos_O 31 0.51431965 0.194303603 0.13349158 0.8951477
## 40 Rubenstein_a 371 0.88973463 0.009920206 0.87029138 0.9091779
## 41 Rubenstein_b 371 0.73558217 0.022951589 0.69059788 0.7805665
## 42 Samuels 51 0.64164977 0.074671111 0.49529708 0.7880025
## 43 Shore 18 0.04879865 0.194405932 -0.33222998 0.4298273
## 44 Stephens 84 0.88711473 0.021369179 0.84523191 0.9289976
## 45 Storer_a 43 0.68572584 0.075903808 0.53695711 0.8344946
## 46 Storer_b 46 0.82236445 0.044859980 0.73444050 0.9102884
## 47 Tannehill 199 0.80535849 0.023291147 0.75970868 0.8510083
## 48 Tisone 24 0.74438242 0.081760886 0.58413403 0.9046308
## 49 Trigani 107 0.85280675 0.023974059 0.80581846 0.8997950
## 50 Voss 120 0.88620094 0.017965305 0.85098959 0.9214123
## 51 Wan 95 0.43441825 0.100123344 0.23818011 0.6306564
## 52 Warne 432 0.84503235 0.012736174 0.82006991 0.8699948
## 53 Yoon 163 0.74419778 0.031567220 0.68232716 0.8060684
## 54 Zbarskaya 125 0.65602250 0.050572601 0.55690203 0.7551430
## 55 Zhang 1067 0.91182228 0.004665094 0.90267886 0.9209657
## Omega Factor 2 SE Lower 95% CI Upper 95% CI Composite reliability
## 1 0.54442539 0.04311695 0.459917724 0.6289331 0.7995981
## 2 0.71460948 0.05953533 0.597922378 0.8312966 0.8473549
## 3 0.56496187 0.25729832 0.060666434 1.0692573 0.7062665
## 4 0.48524883 0.07529410 0.337675104 0.6328226 0.5777127
## 5 0.59196819 0.13406183 0.329211825 0.8547245 0.5673408
## 6 0.76734112 0.01859382 0.730897899 0.8037843 0.9067247
## 7 0.13125388 0.63906542 -1.121291339 1.3837991 0.3792193
## 8 0.57080369 0.37412291 -0.162463739 1.3040711 0.7960050
## 9 0.77000008 0.08239435 0.608510111 0.9314900 0.9062086
## 10 0.44168307 0.22914851 -0.007439755 0.8908059 0.8502797
## 11 0.59393298 0.05735172 0.481525674 0.7063403 0.7389661
## 12 0.74362049 0.10602301 0.535819218 0.9514218 0.8521182
## 13 0.52951075 0.15915172 0.217579111 0.8414424 0.8288963
## 14 0.57158106 0.16899674 0.240353530 0.9028086 0.7019128
## 15 0.81823414 0.07401261 0.673172080 0.9632962 0.8918299
## 16 0.55176587 0.19595122 0.167708530 0.9358232 0.8802762
## 17 0.19431940 0.44525652 -0.678367348 1.0670062 0.8539556
## 18 0.55499998 0.06156126 0.434342125 0.6756578 0.6332173
## 19 0.69824220 0.09756896 0.507010559 0.8894739 0.9148728
## 20 0.40557490 0.06722093 0.273824291 0.5373255 0.6626395
## 21 0.66395267 0.06913231 0.528455821 0.7994495 0.8312741
## 22 0.61601475 0.14217430 0.337358237 0.8946713 0.5904046
## 23 0.68896747 0.01872603 0.652265130 0.7256698 0.8376745
## 24 0.37844715 0.19970361 -0.012964733 0.7698590 0.7544145
## 25 0.12418332 0.17032751 -0.209652468 0.4580191 0.7245921
## 26 0.49703327 0.12591109 0.250252063 0.7438145 0.7632648
## 27 0.64133584 0.04348908 0.556098816 0.7265729 0.8553685
## 28 0.66067493 0.02159081 0.618357717 0.7029921 0.8796064
## 29 0.46688762 0.03601213 0.396305141 0.5374701 0.7621709
## 30 0.59277500 0.02756163 0.538755195 0.6467948 0.8475895
## 31 0.72052879 0.07125025 0.580880865 0.8601767 0.7188807
## 32 0.66982318 0.05641769 0.559246536 0.7803998 0.6533906
## 33 0.82925737 0.01403242 0.801754324 0.8567604 0.8909234
## 34 0.34500000 0.22212131 -0.090349758 0.7803498 0.5295116
## 35 0.26798772 0.11342589 0.045677058 0.4902984 0.6832934
## 36 0.78499954 0.10997994 0.569442830 1.0005563 0.8199744
## 37 0.34999823 0.17644147 0.004179309 0.6958171 0.7224723
## 38 0.33423467 0.21365718 -0.084525713 0.7529950 0.7051059
## 39 0.07834996 0.33674747 -0.581662952 0.7383629 0.5443966
## 40 0.64601509 0.03877220 0.570022975 0.7220072 0.8790599
## 41 0.56722532 0.04629451 0.476489758 0.6579609 0.7846358
## 42 0.74000003 0.06263745 0.617232885 0.8627672 0.6581952
## 43 0.47991626 0.24917184 -0.008451577 0.9682841 0.5015645
## 44 0.23396191 0.18273740 -0.124196812 0.5921206 0.7925324
## 45 0.78499986 0.05809909 0.671127741 0.8988720 0.8199745
## 46 0.49852653 0.16718496 0.170850040 0.8262030 0.8118961
## 47 0.55369507 0.06374239 0.428762276 0.6786279 0.8048860
## 48 0.64999988 0.11519913 0.424213735 0.8757860 0.6900959
## 49 0.57668943 0.10559243 0.369732059 0.7836468 0.8213932
## 50 0.70101044 0.05527658 0.592670348 0.8093505 0.8902267
## 51 0.42685868 0.11811324 0.195360980 0.6583564 0.5986157
## 52 0.60592141 0.03833412 0.530787909 0.6810549 0.8427107
## 53 0.73499994 0.03558982 0.665245164 0.8047547 0.7849945
## 54 0.75199998 0.03847119 0.676597836 0.8274021 0.7536246
## 55 0.62011383 0.08280858 0.457811995 0.7824157 0.8619198
## SE Lower 95% CI Upper 95% CI Factor correlation
## 1 0.015202535 0.7698017 0.8293946 0.67112035
## 2 0.016050724 0.8158961 0.8788138 0.40766720
## 3 0.092312134 0.5253380 0.8871949 0.48204516
## 4 0.038109666 0.5030191 0.6524063 0.32801331
## 5 0.071227956 0.4277366 0.7069451 0.42054214
## 6 0.006367321 0.8942449 0.9192044 0.90362658
## 7 0.292905012 -0.1948640 0.9533026 -1.99997082
## 8 0.084711215 0.6299741 0.9620360 0.33847042
## 9 0.030774514 0.8458916 0.9665255 0.34618970
## 10 0.051826648 0.7487013 0.9518581 1.06267836
## 11 0.028113255 0.6838652 0.7940671 0.60827484
## 12 0.049000598 0.7560788 0.9481577 0.78415097
## 13 0.048676434 0.7334922 0.9243004 0.41362514
## 14 0.081491839 0.5421917 0.8616339 1.05894673
## 15 0.035242566 0.8227557 0.9609040 0.70916554
## 16 0.045274721 0.7915393 0.9690130 0.74551392
## 17 0.068403324 0.7198875 0.9880236 1.86818896
## 18 0.047527859 0.5400644 0.7263702 -0.02750476
## 19 0.022620103 0.8705382 0.9592074 0.65616223
## 20 0.030946022 0.6019864 0.7232925 1.30264630
## 21 0.028347792 0.7757135 0.8868348 0.80388201
## 22 0.084898049 0.4240075 0.7568017 -0.29942308
## 23 0.006533163 0.8248697 0.8504793 0.51334010
## 24 0.062922580 0.6310885 0.8777404 0.92952069
## 25 0.042791799 0.6407217 0.8084624 1.38626219
## 26 0.039552275 0.6857437 0.8407858 0.67185316
## 27 0.011844659 0.8321534 0.8785836 0.42054700
## 28 0.006389031 0.8670841 0.8921287 0.68298986
## 29 0.012648486 0.7373803 0.7869614 0.29332002
## 30 0.008232262 0.8314545 0.8637244 0.43867231
## 31 0.038151808 0.6441045 0.7936568 0.43386323
## 32 0.047508286 0.5602760 0.7465051 1.51035460
## 33 0.005719269 0.8797138 0.9021329 0.50836078
## 34 0.183120296 0.1706024 0.8884208 0.39013455
## 35 0.038323521 0.6081807 0.7584062 0.36799956
## 36 0.080796026 0.6616171 0.9783317 0.71164958
## 37 0.090955429 0.5442030 0.9007417 -0.56000128
## 38 0.077116973 0.5539595 0.8562524 1.11841425
## 39 0.133724762 0.2823009 0.8064923 2.07692958
## 40 0.010666716 0.8581535 0.8999663 0.70681067
## 41 0.018205624 0.7489534 0.8203182 0.79647720
## 42 0.060411229 0.5397913 0.7765990 -0.10999984
## 43 0.161694096 0.1846499 0.8184791 3.33168108
## 44 0.040502569 0.7131489 0.8719160 0.74456919
## 45 0.042682138 0.7363191 0.9036300 0.71164801
## 46 0.047358438 0.7190753 0.9047170 0.74711475
## 47 0.022718967 0.7603577 0.8494144 0.64817413
## 48 0.082728027 0.5279519 0.8522398 -0.11999999
## 49 0.030549877 0.7615165 0.8812698 0.41817045
## 50 0.016719483 0.8574572 0.9229963 0.74367211
## 51 0.067252572 0.4668031 0.7304283 0.99740453
## 52 0.012553997 0.8181054 0.8673161 0.66580678
## 53 0.024549751 0.7368779 0.8331111 0.29000060
## 54 0.033105707 0.6887387 0.8185106 0.36486522
## 55 0.017322974 0.8279674 0.8958722 0.28115578## 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]]$coefs
## L1 L2 L3 L4 L5
## 0.8131975 0.7993139 0.4172651 0.5956043 0.6094648
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0019904044 0.0002967262 0.0002107058 0.00019608301 0.00020064613
## L2 0.0002967262 0.0019938449 0.0002621118 0.00019273530 0.00019722051
## L3 0.0002107058 0.0002621118 0.0051404659 0.00071402718 0.00080502182
## L4 0.0001960830 0.0001927353 0.0007140272 0.00317679530 0.00005871318
## L5 0.0002006461 0.0001972205 0.0008050218 0.00005871318 0.00322786977
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 477
##
## Model Test User Model:
##
## Test statistic 44.785
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.8731001 0.8738977 0.5700938 0.5508761 0.8513708
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0021150725 0.0006428700 0.0006173610 0.0001158732 0.0001790802
## L2 0.0006428700 0.0021140797 0.0006148720 0.0001159791 0.0001792439
## L3 0.0006173610 0.0006148720 0.0030131822 -0.0003233503 0.0008866267
## L4 0.0001158732 0.0001159791 -0.0003233503 0.0046558590 -0.0025418223
## L5 0.0001790802 0.0001792439 0.0008866267 -0.0025418223 0.0074277732
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 18 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 375
##
## Model Test User Model:
##
## Test statistic 27.222
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## 0.5841981 0.9243441 0.2905938 0.8505294 0.3762364
##
## [[3]]$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
##
## [[3]]$fit
## lavaan 0.6.16 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 30
##
## Model Test User Model:
##
## Test statistic 3.824
## Degrees of freedom 3
## P-value (Chi-square) 0.281
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.2920002 1.0000000 0.1488891 0.6714460 0.4527535
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.00361265511 0.0005509357 0.00008202829 0.00003994436 0.00002693432
## L2 0.00055093569 0.0018867655 0.00028091873 0.00013679570 0.00009224080
## L3 0.00008202829 0.0002809187 0.00463717783 0.00021385343 -0.00007048838
## L4 0.00003994436 0.0001367957 0.00021385343 0.02280211045 -0.01012120683
## L5 0.00002693432 0.0000922408 -0.00007048838 -0.01012120683 0.01242535195
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 53 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 17.429
## Degrees of freedom 3
## P-value (Chi-square) 0.001
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.8041868 0.5347016 -0.1506717 0.4541420 0.7993090
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0359874335 -0.0148887075 0.004788094 0.0003165004 0.0005570545
## L2 -0.0148887075 0.0211724338 -0.003191701 0.0002104401 0.0003703837
## L3 0.0047880939 -0.0031917005 0.019901383 0.0017858456 -0.0041118279
## L4 0.0003165004 0.0002104401 0.001785846 0.0230965143 -0.0203239472
## L5 0.0005570545 0.0003703837 -0.004111828 -0.0203239472 0.0517589851
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 26 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
## Number of inequality constraints 5
##
## Number of observations 105
##
## Model Test User Model:
##
## Test statistic 4.643
## Degrees of freedom 3
## P-value (Chi-square) 0.200## Extract relevant model parameters
## FIT INDICES
## Chi-squares and p values of the parameter-based models
tfmc_model_fit <- t(sapply(tfmc.fit.all, function(x) {
fitMeasures(x$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
## Acar 44.7849 0.0000 477 0.9369 0.0470
## Acaretal 27.2219 0.0000 375 0.9632 0.0372
## Auth 3.8239 0.2811 30 0.9432 0.0678
## Balcia 17.4290 0.0006 264 0.8154 0.0568
## Balcib 4.6425 0.1999 105 0.9623 0.0417
## 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_a 0.6436 0.8864 24 1.0000 0.0421
## Carter_b 2.0061 0.5711 24 1.0000 0.0328
## Chi 55.4909 0.0000 203 0.8070 0.1078
## Cho_F 4.5596 0.2070 24 0.9655 0.0536
## Cho_M 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
## Gao 5.0991 0.1647 319 0.9903 0.0240
## 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_2a 117.9371 0.0000 1000 0.9555 0.0404
## Kim_2b 12.0904 0.0071 1000 0.9937 0.0131
## Kim_2c 107.9193 0.0000 1000 0.9559 0.0864
## Kim_3a 43.2068 0.0000 125 0.8197 0.1415
## Kim_3b 36.3656 0.0000 137 0.8633 0.1240
## Liu 36.6686 0.0000 1047 0.9913 0.0300
## Miranda 0.6569 0.8833 12 1.0000 0.0430
## Nguyen 3.0489 0.3841 187 0.9997 0.0239
## Rose 5.0376 0.1691 12 0.8985 0.0878
## Rose_b 11.2871 0.0103 19 0.6262 0.1509
## Roskos_Y 8.8309 0.0316 39 0.8198 0.0855
## Roskos_O 2.1785 0.5362 31 1.0000 0.0618
## Rubenstein_a 25.8150 0.0000 371 0.9757 0.0267
## Rubenstein_b 15.1161 0.0017 371 0.9739 0.0354
## 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_a 18.0516 0.0004 43 0.8460 0.0878
## Storer_b 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
## Wan 7.0116 0.0715 95 0.8878 0.0551
## Warne 28.0935 0.0000 432 0.9690 0.0439
## Yoon 23.1185 0.0000 163 0.9339 0.0907
## Zbarskaya 4.3840 0.2229 125 0.9895 0.0362
## Zhang 17.3737 0.0006 1067 0.9942 0.0187## 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
## Acar 44.784875 0.000000001027982 477 0.9368596 0.04699874
## Acaretal 27.221879 0.000005289304654 375 0.9631597 0.03724663
## Auth 3.823867 0.281122185722077 30 0.9431856 0.06779564
## Balcia 17.429025 0.000576728751025 264 0.8153577 0.05677000
## Balcib 4.642518 0.199924901808852 105 0.9623481 0.04169383## 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 Acar 477 0.768526179 0.019834695 0.7296509 0.8074015
## 2 Acaretal 375 0.835859315 0.014797985 0.8068558 0.8648628
## 3 Auth 30 0.653670574 0.107856677 0.4422754 0.8650658
## 4 Balcia 264 0.523362747 0.040893434 0.4432131 0.6035124
## 5 Balcib 105 0.410740317 0.106384992 0.2022296 0.6192511
## 6 Barkul 599 0.787772957 0.028512584 0.7318893 0.8436566
## 7 Berman 13 0.683443767 0.159833252 0.3701763 0.9967112
## 8 Callans 60 0.856329746 0.040851555 0.7762622 0.9363973
## 9 Carter_a 24 0.927154283 0.025691873 0.8767991 0.9775094
## 10 Carter_b 24 0.847019015 0.227871788 0.4003985 1.2936395
## 11 Chi 203 0.593002702 0.049954691 0.4950933 0.6909121
## 12 Cho_F 24 0.817798140 0.062998939 0.6943225 0.9412738
## 13 Cho_M 35 0.882090358 0.034132973 0.8151910 0.9489898
## 14 Cockcroft 36 0.343777202 0.472594250 -0.5824905 1.2700449
## 15 Conway 25 0.807463911 0.069678278 0.6708970 0.9440308
## 16 Crawford 21 0.933745960 0.031927839 0.8711685 0.9963234
## 17 Digranes 17 0.913968974 0.038167446 0.8391622 0.9887758
## 18 Fishkin 116 0.669786264 0.051302282 0.5692356 0.7703369
## 19 Forsyth 45 0.937871024 0.016425512 0.9056776 0.9700644
## 20 Gao 319 0.544650902 0.086227062 0.3756490 0.7136528
## 21 Garcia 95 0.735378067 0.051965699 0.6335272 0.8372290
## 22 Gollmar 128 0.766058096 0.038435615 0.6907257 0.8413905
## 23 Hokanson 1758 0.804897564 0.008142107 0.7889393 0.8208558
## 24 Houtz 42 0.458329744 1.281344374 -2.0530591 2.9697186
## 25 Humble 125 0.001127804 0.106258653 -0.2071353 0.2093909
## 26 Ibrahim 99 0.758951858 0.043049709 0.6745760 0.8433277
## 27 Kim_1 500 0.889613868 0.008285288 0.8733750 0.9058527
## 28 Kim_2a 1000 0.878281651 0.006987244 0.8645869 0.8919764
## 29 Kim_2b 1000 0.824550915 0.009605933 0.8057236 0.8433782
## 30 Kim_2c 1000 0.888960256 0.005933625 0.8773306 0.9005899
## 31 Kim_3a 125 0.564555188 0.065229490 0.4367077 0.6924026
## 32 Kim_3b 137 0.596009927 0.061019415 0.4764141 0.7156058
## 33 Liu 1047 0.881255175 0.007114774 0.8673105 0.8951999
## 34 Miranda 12 0.664389696 0.166030810 0.3389753 0.9898041
## 35 Nguyen 187 0.776273251 0.028415615 0.7205797 0.8319668
## 36 Rose 12 0.716436389 0.150983978 0.4205132 1.0123595
## 37 Rose_b 19 0.993548228 0.063572049 0.8689493 1.1181472
## 38 Roskos_Y 39 0.658265502 0.504882906 -0.3312868 1.6478178
## 39 Roskos_O 31 0.314200161 0.418032551 -0.5051286 1.1335289
## 40 Rubenstein_a 371 0.875943499 0.011889541 0.8526404 0.8992466
## 41 Rubenstein_b 371 0.663651357 0.042377095 0.5805938 0.7467089
## 42 Samuels 51 0.659250825 0.072295638 0.5175540 0.8009477
## 43 Shore 18 0.105086770 0.441498475 -0.7602343 0.9704079
## 44 Stephens 84 0.871663728 0.051241046 0.7712331 0.9720943
## 45 Storer_a 43 0.716436134 0.079760447 0.5601085 0.8727637
## 46 Storer_b 46 0.835509219 0.049907087 0.7376931 0.9333253
## 47 Tannehill 199 0.772246618 0.031778095 0.7099627 0.8345305
## 48 Tisone 24 0.750704490 0.080076475 0.5937575 0.9076515
## 49 Trigani 107 0.857182140 0.022762679 0.8125681 0.9017962
## 50 Voss 120 0.877239537 0.020103505 0.8378374 0.9166417
## 51 Wan 95 0.149108396 0.583197331 -0.9939374 1.2921542
## 52 Warne 432 0.832182178 0.014113254 0.8045207 0.8598436
## 53 Yoon 163 0.807233506 0.028921209 0.7505490 0.8639180
## 54 Zbarskaya 125 0.648665154 0.047054882 0.5564393 0.7408910
## 55 Zhang 1067 0.912546014 0.004657329 0.9034178 0.9216742
## Omega Factor 2 SE Lower 95% CI Upper 95% CI Composite reliability
## 1 0.5661430 0.037231389 0.49317081 0.6391152 0.8049032
## 2 0.6079821 0.037758518 0.53397676 0.6819874 0.8424830
## 3 0.4304457 0.228896963 -0.01818406 0.8790755 0.7080218
## 4 0.3589215 0.070339441 0.22105873 0.4967843 0.5792982
## 5 0.3911985 0.120940859 0.15415875 0.6282382 0.5543792
## 6 0.8229706 0.020476067 0.78283822 0.8631029 0.9178338
## 7 0.7640589 0.105668421 0.55695259 0.9711652 0.6825554
## 8 0.6209308 0.082703511 0.45883493 0.7830267 0.8126529
## 9 0.7684078 0.076993231 0.61750383 0.9193117 0.9125341
## 10 0.4775192 0.735797596 -0.96461763 1.9196559 0.8488549
## 11 0.7425099 0.033753708 0.67635385 0.8086659 0.8036901
## 12 0.7974172 0.072746606 0.65483647 0.9399979 0.8789835
## 13 0.5326083 0.165911937 0.20742687 0.8577897 0.8283102
## 14 0.6753116 0.195492669 0.29215303 1.0584702 0.7281700
## 15 0.8246381 0.062864877 0.70142522 0.9478510 0.9091115
## 16 0.7211523 0.107084957 0.51126967 0.9310350 0.9031175
## 17 0.1955976 0.452136611 -0.69057391 1.0817690 0.8537584
## 18 0.4145218 0.066743116 0.28370768 0.5453359 0.6674901
## 19 0.7290754 0.074780379 0.58250858 0.8756423 0.9219511
## 20 0.2629411 0.100301499 0.06635377 0.4595284 0.6621673
## 21 0.7041132 0.056422518 0.59352706 0.8146993 0.8415844
## 22 0.6126398 0.059837349 0.49536079 0.7299189 0.6615778
## 23 0.6345411 0.015417964 0.60432247 0.6647598 0.8430808
## 24 0.7879058 0.439812817 -0.07411152 1.6499230 0.8128315
## 25 0.8493042 0.072976087 0.70627367 0.9923347 0.8239503
## 26 0.5848694 0.079054069 0.42992630 0.7398126 0.7830406
## 27 0.7072821 0.020200626 0.66768961 0.7468746 0.8731967
## 28 0.6546655 0.020281307 0.61491491 0.6944162 0.8832819
## 29 0.4826084 0.029316947 0.42514820 0.5400685 0.7778928
## 30 0.6794374 0.015380890 0.64929141 0.7095834 0.8706153
## 31 0.8472008 0.023755036 0.80064182 0.8937598 0.8387767
## 32 0.8589660 0.020294884 0.81918874 0.8987432 0.8404802
## 33 0.8470108 0.008347057 0.83065084 0.8633707 0.9254371
## 34 0.1303795 0.938401194 -1.70885300 1.9696121 0.5333744
## 35 0.2079270 0.102716523 0.00660629 0.4092477 0.6841580
## 36 0.5457923 0.212095395 0.13009299 0.9614917 0.8180478
## 37 0.9882795 0.088600698 0.81462535 1.1619337 0.7823249
## 38 0.3066629 0.903013544 -1.46321117 2.0765369 0.7052351
## 39 0.6699684 0.112883969 0.44871988 0.8912169 0.6355349
## 40 0.6740912 0.031196083 0.61294802 0.7352344 0.8837767
## 41 0.6008464 0.047419291 0.50790633 0.6937865 0.7939180
## 42 0.6433924 0.073962362 0.49842884 0.7883560 0.7680445
## 43 0.9003439 0.052944286 0.79657497 1.0041128 0.8075012
## 44 0.5430463 0.396553821 -0.23418488 1.3202775 0.8198361
## 45 0.5457923 0.112043736 0.32619063 0.7653940 0.8180476
## 46 0.3700022 0.227095886 -0.07509756 0.8151020 0.8158777
## 47 0.6777027 0.044607538 0.59027352 0.7651319 0.8392724
## 48 0.6648445 0.102731710 0.46349403 0.8661949 0.8010826
## 49 0.7005870 0.044817183 0.61274692 0.7884270 0.8574797
## 50 0.7123495 0.049526931 0.61527846 0.8094205 0.8922357
## 51 0.6114699 0.352081875 -0.07859790 1.3015377 0.6171624
## 52 0.6426562 0.030686589 0.58251154 0.7028008 0.8524045
## 53 0.7939201 0.027715595 0.73959848 0.8482416 0.8556028
## 54 0.7088408 0.040217202 0.63001652 0.7876651 0.7958534
## 55 0.5389738 0.068302045 0.40510422 0.6728433 0.8581444
## SE Lower 95% CI Upper 95% CI Factor correlation
## 1 0.014734698 0.77602375 0.8337827 0.6221182
## 2 0.013847621 0.81534219 0.8696239 0.4256405
## 3 0.093818456 0.52414099 0.8919026 0.4756440
## 4 0.039274769 0.50232103 0.6562753 0.3286031
## 5 0.071671866 0.41390493 0.6948535 0.4286476
## 6 0.005606417 0.90684544 0.9288222 0.8964628
## 7 0.116559034 0.45410389 0.9110069 -0.2555810
## 8 0.039229646 0.73576425 0.8895416 0.3046393
## 9 0.028867430 0.85595499 0.9691132 0.3155412
## 10 0.052077286 0.74678534 0.9509245 1.0626498
## 11 0.021633441 0.76128929 0.8460908 0.6051602
## 12 0.039679215 0.80121365 0.9567533 0.4926070
## 13 0.049017303 0.73223802 0.9243823 0.3944023
## 14 0.073562141 0.58399081 0.8723491 0.8396080
## 15 0.029530824 0.85123213 0.9669908 0.6654713
## 16 0.035981513 0.83259500 0.9736399 0.6492101
## 17 0.068628757 0.71924852 0.9882683 1.8872193
## 18 0.044358318 0.58054934 0.7544308 0.1409424
## 19 0.021161247 0.88047580 0.9634264 0.5991126
## 20 0.030943240 0.60151963 0.7228149 1.2698894
## 21 0.026490306 0.78966433 0.8935044 0.6792078
## 22 0.046748235 0.56995292 0.7532026 -0.3256691
## 23 0.006154373 0.83101841 0.8551431 0.5311592
## 24 0.092697734 0.63114733 0.9945158 0.8470350
## 25 0.024863836 0.77521811 0.8726826 0.9188285
## 26 0.037837034 0.70888135 0.8571998 0.4052477
## 27 0.008823746 0.85590243 0.8904909 0.1960032
## 28 0.006193187 0.87114352 0.8954204 0.6547173
## 29 0.011914261 0.75454131 0.8012444 0.2602787
## 30 0.006371707 0.85812695 0.8831036 0.2200003
## 31 0.022318890 0.79503245 0.8825209 0.4653317
## 32 0.020846923 0.79962097 0.8813394 0.4123712
## 33 0.003867541 0.91785681 0.9330173 0.5317694
## 34 0.311078740 -0.07632876 1.1430775 0.3290446
## 35 0.038487946 0.60872302 0.7595930 0.3713846
## 36 0.082036171 0.65725983 0.9788357 0.7106701
## 37 0.075736496 0.63388412 0.9307657 0.9965072
## 38 0.077288864 0.55375168 0.8567185 1.1226288
## 39 0.107921399 0.42401286 0.8470570 0.5035671
## 40 0.010125234 0.86393161 0.9036218 0.6921394
## 41 0.017410296 0.75979442 0.8280415 0.7771981
## 42 0.047824176 0.67431084 0.8617782 0.2400000
## 43 0.068962607 0.67233699 0.9426654 0.8649308
## 44 0.043676233 0.73423222 0.9054399 0.7635129
## 45 0.043337322 0.73310804 0.9029872 0.7106699
## 46 0.047857357 0.72207900 0.9096764 0.7013148
## 47 0.018905308 0.80221867 0.8763261 0.6336887
## 48 0.060289851 0.68291666 0.9192485 0.2600004
## 49 0.021163632 0.81599972 0.8989596 0.2800012
## 50 0.016376975 0.86013739 0.9243339 0.6807858
## 51 0.065714285 0.48836479 0.7459601 0.8782405
## 52 0.011747424 0.82937996 0.8754290 0.5602003
## 53 0.018001022 0.82032143 0.8908841 0.3064697
## 54 0.027128833 0.74268189 0.8490250 0.3270000
## 55 0.014981635 0.82878090 0.8875078 0.2958872## 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
## 0.8002171 0.8122797 0.4981151 0.5156007 0.7470457
##
## [[1]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0020041928 0.0002860722 0.0002688384 0.0002782756 0.0004031892
## L2 0.0002860722 0.0020015283 0.0002728912 0.0002824706 0.0004092673
## L3 0.0002688384 0.0002728912 0.0024895394 0.0002488667 0.0002489445
## L4 0.0002782756 0.0002824706 0.0002488667 0.0024713113 0.0002535638
## L5 0.0004031892 0.0004092673 0.0002489445 0.0002535638 0.0024480658
##
## [[1]]$fit
## lavaan 0.6.16 ended normally after 16 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 477
##
## Model Test User Model:
##
## Test statistic 58.274
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[2]]
## [[2]]$coefs
## L1 L2 L3 L4 L5
## 0.8559405 0.8914171 0.3763517 0.4981037 0.7619132
##
## [[2]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0021812266 0.0005938561 0.0002644743 0.0003500328 0.0005354197
## L2 0.0005938561 0.0021407548 0.0002754362 0.0003645409 0.0005576116
## L3 0.0002644743 0.0002754362 0.0033086306 0.0002395522 0.0002491501
## L4 0.0003500328 0.0003645409 0.0002395522 0.0031568366 0.0003054554
## L5 0.0005354197 0.0005576116 0.0002491501 0.0003054554 0.0033523641
##
## [[2]]$fit
## lavaan 0.6.16 ended normally after 21 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 375
##
## Model Test User Model:
##
## Test statistic 85.235
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[3]]
## [[3]]$coefs
## L1 L2 L3 L4 L5
## 0.5400006 1.0000000 0.7651308 0.3827568 0.2172019
##
## [[3]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0275242359 0.0087000184 0.001834831 0.0009178736 0.0005208637
## L2 0.0087000184 0.0161111333 0.003397832 0.0016997646 0.0009645616
## L3 0.0018348309 0.0033978323 0.098934551 -0.0177614703 -0.0084516627
## L4 0.0009178736 0.0016997646 -0.017761470 0.0517805816 0.0040403316
## L5 0.0005208637 0.0009645616 -0.008451663 0.0040403316 0.0488336913
##
## [[3]]$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
##
##
## [[4]]
## [[4]]$coefs
## L1 L2 L3 L4 L5
## 0.2920004 1.0000000 0.6261702 0.4715271 0.1182645
##
## [[4]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.003612652359 0.00055093578 0.00004356659 0.00003280708 0.000008228402
## L2 0.000550935783 0.00188676440 0.00014920048 0.00011235290 0.000028179429
## L3 0.000043566586 0.00014920048 0.01660434996 -0.00673301463 -0.000752408588
## L4 0.000032807081 0.00011235290 -0.00673301463 0.01114541774 0.000365149631
## L5 0.000008228402 0.00002817943 -0.00075240859 0.00036514963 0.007284998235
##
## [[4]]$fit
## lavaan 0.6.16 ended normally after 72 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 264
##
## Model Test User Model:
##
## Test statistic 22.035
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
##
## [[5]]
## [[5]]$coefs
## L1 L2 L3 L4 L5
## 0.7067616 0.6084091 0.4883365 0.7340460 -0.1865381
##
## [[5]]$vcoefs
## L1 L2 L3 L4 L5
## L1 0.0270488964 -0.0117067518 0.0004066690 0.0006112869 -0.0001553422
## L2 -0.0117067518 0.0224872239 0.0003500772 0.0005262205 -0.0001337249
## L3 0.0004066690 0.0003500772 0.0201440484 -0.0112781006 -0.0017229643
## L4 0.0006112869 0.0005262205 -0.0112781006 0.0328240430 0.0026200213
## L5 -0.0001553422 -0.0001337249 -0.0017229643 0.0026200213 0.0151928792
##
## [[5]]$fit
## lavaan 0.6.16 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
## Number of inequality constraints 5
##
## Number of observations 105
##
## Model Test User Model:
##
## Test statistic 5.338
## Degrees of freedom 4
## P-value (Chi-square) 0.254## 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
## Acar 58.2737 0.0000 477 0.9180 0.0561
## Acaretal 85.2350 0.0000 375 0.8764 0.0887
## Auth 4.9636 0.2911 30 0.9336 0.0983
## Balcia 22.0349 0.0002 264 0.7692 0.0587
## Balcib 5.3376 0.2544 105 0.9693 0.0421
## 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_a 8.5375 0.0738 24 0.9294 0.1234
## Carter_b 2.0228 0.7316 24 1.0000 0.0333
## Chi 56.2894 0.0000 203 0.8077 0.1096
## Cho_F 7.8447 0.0974 24 0.9149 0.0717
## Cho_M 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
## Gao 12.8084 0.0123 319 0.9595 0.0356
## 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_2a 192.5836 0.0000 1000 0.9270 0.0605
## Kim_2b 77.5064 0.0000 1000 0.9491 0.0616
## Kim_2c 236.0753 0.0000 1000 0.9024 0.0848
## Kim_3a 64.7562 0.0000 125 0.7276 0.1798
## Kim_3b 51.0455 0.0000 137 0.8072 0.1601
## Liu 36.6795 0.0000 1047 0.9916 0.0299
## Miranda 1.3888 0.8461 12 1.0000 0.0638
## Nguyen 5.9355 0.2040 187 0.9898 0.0384
## Rose 5.0518 0.2820 12 0.9476 0.0882
## Rose_b 13.9349 0.0075 19 0.5519 0.1686
## Roskos_Y 8.9535 0.0623 39 0.8469 0.0889
## Roskos_O 2.1785 0.7030 31 1.0000 0.0618
## Rubenstein_a 40.5525 0.0000 371 0.9611 0.0427
## Rubenstein_b 15.3233 0.0041 371 0.9756 0.0357
## 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_a 18.1023 0.0012 43 0.8557 0.0882
## Storer_b 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
## Wan 7.2675 0.1224 95 0.9086 0.0558
## Warne 56.1459 0.0000 432 0.9356 0.0552
## Yoon 23.1916 0.0001 163 0.9369 0.0918
## Zbarskaya 4.3965 0.3550 125 0.9970 0.0372
## Zhang 129.4983 0.0000 1067 0.9493 0.0806## 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
## Acar 58.273738 0.000000000006685208 477 0.9179879 0.05611845
## Acaretal 85.235030 0.000000000000000000 375 0.8764455 0.08868591
## Auth 4.963578 0.291055121191334365 30 0.9335511 0.09825559
## Balcia 22.034942 0.000197235994077283 264 0.7692142 0.05869786
## Balcib 5.337602 0.254377491832347369 105 0.9693378 0.04205625## 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 Acar 477 0.7879230 0.019422465 0.74985562 0.8259903
## 2 Acaretal 375 0.8659270 0.013861703 0.83875860 0.8930955
## 3 Auth 30 0.7700003 0.073695681 0.62555945 0.9144412
## 4 Balcia 264 0.6460004 0.035022508 0.57735750 0.7146432
## 5 Balcib 105 0.6047810 0.079138763 0.44967187 0.7598901
## 6 Barkul 599 0.9744939 0.002080806 0.97041555 0.9785722
## 7 Berman 13 0.6949999 0.141042727 0.41856121 0.9714385
## 8 Callans 60 0.8827988 0.031949253 0.82017946 0.9454182
## 9 Carter_a 24 0.9279418 0.029174066 0.87076173 0.9851220
## 10 Carter_b 24 0.9099999 0.035050009 0.84130312 0.9786966
## 11 Chi 203 0.7165000 0.033685510 0.65047763 0.7825224
## 12 Cho_F 24 0.8050006 0.071425899 0.66500843 0.9449928
## 13 Cho_M 35 0.7476911 0.085012742 0.58106919 0.9143130
## 14 Cockcroft 36 0.5554435 0.188006684 0.18695714 0.9239298
## 15 Conway 25 0.9011436 0.039548341 0.82363032 0.9786570
## 16 Crawford 21 0.9700000 0.012895183 0.94472590 0.9952741
## 17 Digranes 17 0.8640321 0.065895715 0.73487891 0.9931854
## 18 Fishkin 116 0.7595687 0.052606411 0.65646200 0.8626753
## 19 Forsyth 45 0.9538664 0.013684640 0.92704499 0.9806878
## 20 Gao 319 0.4732834 0.058981047 0.35768271 0.5888842
## 21 Garcia 95 0.7710162 0.047072858 0.67875512 0.8632773
## 22 Gollmar 128 0.8359994 0.026507783 0.78404511 0.8879537
## 23 Hokanson 1758 0.8949419 0.005770018 0.88363288 0.9062509
## 24 Houtz 42 0.7823017 0.080033070 0.62543972 0.9391636
## 25 Humble 125 0.9132729 0.016844923 0.88025750 0.9462884
## 26 Ibrahim 99 0.7596899 0.048448655 0.66473228 0.8546475
## 27 Kim_1 500 0.9209904 0.007201180 0.90687639 0.9351045
## 28 Kim_2a 1000 0.9130688 0.005498046 0.90229281 0.9238448
## 29 Kim_2b 1000 0.8830057 0.007417871 0.86846695 0.8975445
## 30 Kim_2c 1000 0.9282173 0.004592202 0.91921677 0.9372179
## 31 Kim_3a 125 0.7300000 0.041266747 0.64911862 0.8108813
## 32 Kim_3b 137 0.7000003 0.042888383 0.61594059 0.7840600
## 33 Liu 1047 0.9692173 0.001912591 0.96546866 0.9729659
## 34 Miranda 12 0.6674744 0.201382393 0.27277217 1.0621766
## 35 Nguyen 187 0.8623294 0.021582766 0.82002798 0.9046309
## 36 Rose 12 0.8959024 0.060156839 0.77799720 1.0138077
## 37 Rose_b 19 0.8350002 0.069179887 0.69941013 0.9705903
## 38 Roskos_Y 39 0.4299804 0.188549800 0.06042962 0.7995313
## 39 Roskos_O 31 0.3140816 0.300832780 -0.27553980 0.9037030
## 40 Rubenstein_a 371 0.9059530 0.009765379 0.88681320 0.9250928
## 41 Rubenstein_b 371 0.7861099 0.023131314 0.74077339 0.8314465
## 42 Samuels 51 0.8750002 0.032745994 0.81081927 0.9391812
## 43 Shore 18 0.6299999 0.138441342 0.35865989 0.9013400
## 44 Stephens 84 0.9262282 0.016156380 0.89456231 0.9578942
## 45 Storer_a 43 0.8959024 0.031779111 0.83361644 0.9581883
## 46 Storer_b 46 0.8439369 0.046020784 0.75373784 0.9341360
## 47 Tannehill 199 0.9161898 0.012441007 0.89180584 0.9405737
## 48 Tisone 24 0.8400000 0.059866512 0.72266381 0.9573362
## 49 Trigani 107 0.8600006 0.025102314 0.81080093 0.9092002
## 50 Voss 120 0.8378753 0.029424061 0.78020522 0.8955454
## 51 Wan 95 0.4282581 0.118440347 0.19611924 0.6603969
## 52 Warne 432 0.8564004 0.013961649 0.82903610 0.8837648
## 53 Yoon 163 0.8650001 0.019668799 0.82644992 0.9035502
## 54 Zbarskaya 125 0.8070001 0.031014799 0.74621216 0.8677879
## 55 Zhang 1067 0.8821890 0.007137126 0.86820044 0.8961775
## Omega Factor 2 SE Lower 95% CI Upper 95% CI Composite reliability
## 1 0.61657373 0.029900377 0.55797007 0.6751774 0.7961029
## 2 0.56882295 0.037500185 0.49532393 0.6423220 0.8033699
## 3 0.45624463 0.174095303 0.11502411 0.7974652 0.6874343
## 4 0.38402741 0.063634609 0.25930587 0.5087490 0.5647680
## 5 0.32904400 0.104533434 0.12416223 0.5339258 0.5565458
## 6 0.77863942 0.014326462 0.75056007 0.8067188 0.9172739
## 7 0.76409053 0.105262005 0.55778079 0.9704003 0.6762776
## 8 0.65864387 0.065378406 0.53050455 0.7867832 0.8232824
## 9 0.62746975 0.110753332 0.41039721 0.8445423 0.8533497
## 10 0.60965463 0.137095073 0.34095323 0.8783560 0.8498451
## 11 0.73092237 0.032558180 0.66710951 0.7947352 0.8028454
## 12 0.78704960 0.071398319 0.64711146 0.9269877 0.8653867
## 13 0.53593998 0.122019197 0.29678675 0.7750932 0.7712868
## 14 0.64197605 0.095900723 0.45401408 0.8299380 0.7316390
## 15 0.83260782 0.056803611 0.72127479 0.9439409 0.9084899
## 16 0.75090462 0.088968879 0.57652882 0.9252804 0.9017108
## 17 0.74279966 0.102234527 0.54242367 0.9431757 0.8840397
## 18 0.13501415 0.133848305 -0.12732370 0.3973520 0.5451633
## 19 0.72290929 0.067145839 0.59130587 0.8545127 0.8942712
## 20 0.52320575 0.045809452 0.43342088 0.6129906 0.6757915
## 21 0.73147909 0.047424678 0.63852843 0.8244298 0.8370563
## 22 0.57767217 0.063700177 0.45282212 0.7025222 0.7373011
## 23 0.66848336 0.013636458 0.64175639 0.6952103 0.8356207
## 24 0.63128965 0.097167364 0.44084511 0.8217342 0.7921521
## 25 0.45739326 0.080424792 0.29976356 0.6150230 0.7720023
## 26 0.59575313 0.068000334 0.46247492 0.7290313 0.7734210
## 27 0.60299308 0.028874546 0.54640001 0.6595862 0.8330267
## 28 0.69120730 0.016601296 0.65866936 0.7237452 0.8681365
## 29 0.45982149 0.030343008 0.40035029 0.5192927 0.7583341
## 30 0.57274705 0.022273656 0.52909149 0.6164026 0.8274552
## 31 0.81414657 0.027904399 0.75945495 0.8688382 0.7397523
## 32 0.83913813 0.022590664 0.79486124 0.8834150 0.7616337
## 33 0.84682710 0.008162806 0.83082829 0.8628259 0.9254409
## 34 0.04610459 0.177849064 -0.30247317 0.3946823 0.4571518
## 35 0.22396085 0.102912245 0.02225656 0.4256651 0.6642839
## 36 0.55869990 0.177142545 0.21150689 0.9058929 0.8163590
## 37 0.59599410 0.132096970 0.33708880 0.8548994 0.7568528
## 38 0.64891319 0.093567233 0.46552478 0.8323016 0.7144250
## 39 0.66999465 0.088558872 0.49642245 0.8435668 0.6355428
## 40 0.71959418 0.024493928 0.67158696 0.7676014 0.8753199
## 41 0.61687449 0.034273202 0.54970025 0.6840487 0.7938111
## 42 0.63343611 0.075028329 0.48638329 0.7804889 0.7764478
## 43 0.68826146 0.128942389 0.43553903 0.9409839 0.5965216
## 44 0.55117737 0.081168520 0.39208999 0.7102647 0.8204643
## 45 0.55870048 0.093579106 0.37528880 0.7421122 0.8163591
## 46 0.53121564 0.117131833 0.30164147 0.7607898 0.7952131
## 47 0.65969490 0.041772638 0.57782203 0.7415678 0.8386434
## 48 0.62199784 0.127650613 0.37180724 0.8721884 0.7710646
## 49 0.62354154 0.052907188 0.51984535 0.7272377 0.8171664
## 50 0.74098227 0.039078493 0.66438983 0.8175747 0.8692816
## 51 0.49301658 0.089663433 0.31727948 0.6687537 0.6127855
## 52 0.65742730 0.027808434 0.60292377 0.7119308 0.8352745
## 53 0.79446255 0.027477785 0.74060709 0.8483180 0.8557819
## 54 0.70948778 0.039708236 0.63166107 0.7873145 0.7953206
## 55 0.38759036 0.031732931 0.32539496 0.4497858 0.7712278
## SE Lower 95% CI Upper 95% CI Factor correlation
## 1 0.015185967 0.76633894 0.8258668 0.8029838
## 2 0.016598931 0.77083661 0.8359032 0.7857477
## 3 0.089172197 0.51266000 0.8622086 0.5250131
## 4 0.039675182 0.48700609 0.6425299 0.3553694
## 5 0.067293016 0.42465389 0.6884377 0.4998183
## 6 0.005562633 0.90637138 0.9281765 0.8720216
## 7 0.114536441 0.45179028 0.9007649 -0.2900000
## 8 0.034783979 0.75510706 0.8914578 0.5302387
## 9 0.047287275 0.76066833 0.9460310 0.8234923
## 10 0.050779068 0.75031999 0.9493703 1.0336723
## 11 0.021735104 0.76024536 0.8454454 0.5716607
## 12 0.043172322 0.78077054 0.9500029 0.7090588
## 13 0.061062399 0.65160666 0.8909669 0.9957951
## 14 0.072698823 0.58915192 0.8741261 0.7845056
## 15 0.029817101 0.85004946 0.9669303 0.6827169
## 16 0.035560859 0.83201280 0.9714088 0.7643346
## 17 0.045706132 0.79445729 0.9736220 1.0398209
## 18 0.070251030 0.40747384 0.6828528 0.6704365
## 19 0.026008062 0.84329635 0.9452461 0.8915926
## 20 0.029604286 0.61776817 0.7338148 1.0997318
## 21 0.027244187 0.78365869 0.8904539 0.7791342
## 22 0.036354007 0.66604852 0.8085536 0.2946672
## 23 0.006418958 0.82303978 0.8482016 0.6169859
## 24 0.051780409 0.69066433 0.8936398 0.7257213
## 25 0.033500218 0.70634311 0.8376615 0.6891124
## 26 0.036703874 0.70148273 0.8453593 0.7498885
## 27 0.012075119 0.80935995 0.8566935 0.7292714
## 28 0.006883575 0.85464495 0.8816281 0.8568125
## 29 0.012683112 0.73347561 0.7831925 0.6521377
## 30 0.008944629 0.80992409 0.8449864 0.7642222
## 31 0.032991000 0.67509111 0.8044135 -0.2595952
## 32 0.028219152 0.70632520 0.8169422 -0.2178581
## 33 0.003867127 0.91786152 0.9330204 0.5310282
## 34 0.225939266 0.01431894 0.8999846 0.6841114
## 35 0.041725233 0.58250396 0.7460639 0.8047517
## 36 0.081647631 0.65633258 0.9763854 0.7107647
## 37 0.079579629 0.60087957 0.9128260 0.3400015
## 38 0.074331273 0.56873837 0.8601116 0.9707069
## 39 0.105000135 0.42974630 0.8413393 0.5037385
## 40 0.010612929 0.85451889 0.8961208 0.8397992
## 41 0.017417539 0.75967335 0.8279488 0.7905793
## 42 0.045035613 0.68817960 0.8647160 0.2399999
## 43 0.136849912 0.32830071 0.8647425 -0.2906585
## 44 0.032228515 0.75729762 0.8836311 0.7700793
## 45 0.043132015 0.73182188 0.9008963 0.7107627
## 46 0.049547402 0.69810200 0.8923242 0.9521721
## 47 0.018983592 0.80143623 0.8758505 0.6041018
## 48 0.072799427 0.62838038 0.9137489 0.3688393
## 49 0.026912805 0.76441824 0.8699145 0.6899985
## 50 0.019220322 0.83161048 0.9069528 0.9260633
## 51 0.064908872 0.48556644 0.7400045 0.8372834
## 52 0.012890119 0.81001034 0.8605387 0.8128623
## 53 0.017943182 0.82061395 0.8909499 0.3176184
## 54 0.026779849 0.74283304 0.8478081 0.3269999
## 55 0.012018395 0.74767218 0.7947834 1.0418061## 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
## Acar 58.2737384 0.0000000000066852079428 477 0.9179879 0.05611845
## Acaretal 85.2350300 0.0000000000000000000000 375 0.8764455 0.08868591
## Auth 4.9635776 0.2910551211913343649940 30 0.9335511 0.09825559
## Balcia 22.0349422 0.0001972359940772827613 264 0.7692142 0.05869786
## Balcib 5.3376015 0.2543774918323473688275 105 0.9693378 0.04205625
## Barkul 114.0179567 0.0000000000000000000000 599 0.9608442 0.02876380
## Berman 6.7520142 0.1495880010679065952317 13 0.8056406 0.13120067
## Callans 5.7928546 0.2151613150094205950680 60 0.9803705 0.07195184
## Carter_a 8.5374948 0.0737588150888134341798 24 0.9293966 0.12344312
## Carter_b 2.0227827 0.7315683246857485055870 24 1.0000000 0.03325786
## Chi 56.2893634 0.0000000000174372738471 203 0.8077218 0.10964189
## Cho_F 7.8447267 0.0974345320442254747562 24 0.9149484 0.07170580
## Cho_M 10.2295462 0.0367335260865379042983 35 0.9061654 0.09617379
## Cockcroft 8.3021446 0.0811166222855811414050 36 0.8723006 0.09924377
## Conway 0.8889755 0.9261371061244323410477 25 1.0000000 0.01843786
## Crawford 4.1616946 0.3845649220312404859001 21 0.9976996 0.05125261
## Digranes 6.6504236 0.1555558127019329717200 17 0.9506538 0.07473993
## Fishkin 2.0368505 0.7289809937310370857588 116 1.0000000 0.03097716
## Forsyth 10.3381919 0.0351003685949619059770 45 0.9602724 0.06526681
## Gao 12.8083576 0.0122511651009710176297 319 0.9594559 0.03563730
## Garcia 13.5111291 0.0090304420932041384873 95 0.9372565 0.04764523
## Gollmar 43.1791907 0.0000000094987471221941 128 0.7400054 0.12680085
## Hokanson 283.9767705 0.0000000000000000000000 1758 0.9149149 0.07349493
## Houtz 3.4474977 0.4859062122440982456339 42 1.0000000 0.04730142
## Humble 8.2194499 0.0838622784140112820239 125 0.9787311 0.05375296
## Ibrahim 42.7677064 0.0000000115623308705182 99 0.7294550 0.09754886
## Kim_1 167.2993976 0.0000000000000000000000 500 0.8649442 0.09923085
## Kim_2a 192.5835800 0.0000000000000000000000 1000 0.9270304 0.06051507
## Kim_2b 77.5063974 0.0000000000000005551115 1000 0.9490579 0.06163331
## Kim_2c 236.0752688 0.0000000000000000000000 1000 0.9024048 0.08477319
## Kim_3a 64.7562446 0.0000000000002896571871 125 0.7275914 0.17983244
## Kim_3b 51.0455158 0.0000000002183865310812 137 0.8072334 0.16014229
## Liu 36.6794921 0.0000002097008866552841 1047 0.9915996 0.02992908
## Miranda 1.3887585 0.8461464699435627956348 12 1.0000000 0.06378383
## Nguyen 5.9355052 0.2040168367815755612327 187 0.9897562 0.03840829
## Rose 5.0518104 0.2820226174393694051901 12 0.9476006 0.08815172
## Rose_b 13.9348757 0.0075058326841783706840 19 0.5519365 0.16864979
## Roskos_Y 8.9535133 0.0622719885770953718307 39 0.8469183 0.08886656
## Roskos_O 2.1784895 0.7029692688101959463509 31 1.0000000 0.06181563
## Rubenstein_a 40.5525279 0.0000000332679327419427 371 0.9611431 0.04273534
## Rubenstein_b 15.3233317 0.0040755124077527238313 371 0.9756381 0.03565326
## Samuels 4.9266837 0.2949032714816962608140 51 0.9835969 0.08610035
## Shore 17.9607613 0.0012560801072869498540 18 0.2735955 0.22179542
## Stephens 1.8279847 0.7673585947114770489108 84 1.0000000 0.02798716
## Storer_a 18.1023205 0.0011785479448310764994 43 0.8557475 0.08815127
## Storer_b 10.3481802 0.0349537821149170646606 46 0.9109395 0.07096107
## Tannehill 7.1674124 0.1273013297674244759250 199 0.9915642 0.02005184
## Tisone 3.5011952 0.4776966312815904558420 24 1.0000000 0.07522753
## Trigani 21.8629651 0.0002134085734527557676 107 0.9087319 0.09152566
## Voss 16.1637294 0.0028071510715872438624 120 0.9589320 0.05493900
## Wan 7.2675425 0.1224074308794176335624 95 0.9086441 0.05579743
## Warne 56.1459071 0.0000000000186879400843 432 0.9355730 0.05516412
## Yoon 23.1916233 0.0001159388910124681260 163 0.9369490 0.09184230
## Zbarskaya 4.3964860 0.3549986083092668831540 125 0.9969846 0.03721615
## Zhang 129.4982963 0.0000000000000000000000 1067 0.9492744 0.08064859### 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(4,7,11,22,26,27,31,32,37,43,45)
## Data exclusions due to poor model fit
srel.meta <- srel.meta1[-fitexclude,]
## ADD NEW MODERATORS (see Table 1 in the manuscript)
srel.meta$LanguageEnglish <- c(1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,
1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0)
srel.meta$Culture <- c("Mixed","Western","Western","Eastern","Eastern","Western","Western","Western","Western","Western","African","Western","Western","Western","Western","Western","Eastern","Western","Western","Western","African","Western","Western","Western","Eastern","Western","Mixed","Western","Western","Western","Western","Western","Western","Western","Western","Western","Western","Western","Western","Eastern","Western","Eastern","Western","Eastern")
table(srel.meta$Culture)##
## African Eastern Mixed Western
## 2 7 2 33srel.meta$CultureWestern <- c(0,1,1,0,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,
0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0)
srel.meta$PropFemale <- c(69.83,52.94,53,52,62.1,75,54.17,79.17,
100,0,27.8,60,52,47.05,38.79,NA,31.66,NA,50,69.05,54,
51.27,51.27,51.27,47.94,58.33,70.59,75,49,73,48.9,48.9,
94.12,45,50,50,50,100,46,50.59,75,39.9,100,44.7)
## FURTHER EXCLUSIONS DUE TO SMALL SAMPLE SIZE
## Some power analysis to set a criterion
## Source for the size of parameters: Said-Metwaly et al. (2018), https://doi.org/10.1080/10400419.2018.1530534
## Run CFA power analysis
## Source: https://cran.r-project.org/web/packages/semPower/semPower.pdf
powerCFA <- semPower.powerCFA(type = 'a-priori',
Phi = .6,
loadings = list(c(.7, .8, .1),
c(.6, .6, .6)),
alpha = .05,
beta = .05)
summary(powerCFA)##
## semPower: A priori power analysis
##
## F0 0.181217
## RMSEA 0.425696
## Mc 0.913375
##
## df 1
## Required Num Observations 73
##
## Critical Chi-Square 3.841459
## NCP 13.04764
## Alpha 0.050000
## Beta 0.049248
## Power (1 - Beta) 0.950752
## Implied Alpha/Beta Ratio 1.015269
## Criterion: N < 75 for the exclusion
which(srel.meta$N < 75)## [1] 3 6 7 8 9 10 11 12 13 14 16 20 26 28 29 30 33 35 37length(which(srel.meta$N < 75))## [1] 19srel.meta <- srel.meta[!(srel.meta$N < 75),]
## Inspect the data again
head(srel.meta, 5)## ESID STUDID Reference N SREL1 SE.SREL1 SREL2 SE.SREL2
## 1 1 1 Acar 477 0.7879230 0.019422465 0.6165737 0.02990038
## 2 2 2 Acaretal 375 0.8659270 0.013861703 0.5688229 0.03750018
## 5 5 5 Balcib 105 0.6047810 0.079138763 0.3290440 0.10453343
## 6 6 6 Barkul 599 0.9744939 0.002080806 0.7786394 0.01432646
## 18 18 18 Fishkin 116 0.7595687 0.052606411 0.1350142 0.13384830
## SRELCR SE.SRELCR SREL1C SE.SREL1C SREL2C SE.SREL2C SRELCRC
## 1 0.7961029 0.015185967 0.7685262 0.01983469 0.5661430 0.03723139 0.8049032
## 2 0.8033699 0.016598931 0.8358593 0.01479798 0.6079821 0.03775852 0.8424830
## 5 0.5565458 0.067293016 0.4107403 0.10638499 0.3911985 0.12094086 0.5543792
## 6 0.9172739 0.005562633 0.7877730 0.02851258 0.8229706 0.02047607 0.9178338
## 18 0.5451633 0.070251030 0.6697863 0.05130228 0.4145218 0.06674312 0.6674901
## SE.SRELCRC Fcorr FcorrC Adults Forms Scores Validity SREL1.vg
## 1 0.014734698 0.8029838 0.6221182 1 A 0 1 0.000377232156
## 2 0.013847621 0.7857477 0.4256405 0 A 0 1 0.000192146808
## 5 0.071671866 0.4998183 0.4286476 0 Both 0 1 0.006262943736
## 6 0.005606417 0.8720216 0.8964628 1 A 0 0 0.000004329754
## 18 0.044358318 0.6704365 0.1409424 0 A 0 1 0.002767434440
## SREL2.vg SRELCR.vg SREL1C.vg SREL2C.vg SRELCRC.vg
## 1 0.0008940326 0.00023061360 0.0003934151 0.0013861763 0.00021711132
## 2 0.0014062639 0.00027552451 0.0002189803 0.0014257057 0.00019175659
## 5 0.0109272389 0.00452835001 0.0113177664 0.0146266914 0.00513685636
## 6 0.0002052475 0.00003094289 0.0008129674 0.0004192693 0.00003143191
## 18 0.0179153687 0.00493520728 0.0026319241 0.0044546436 0.00196766041
## LanguageEnglish Culture CultureWestern PropFemale
## 1 1 Mixed 0 69.83
## 2 1 Western 1 52.94
## 5 0 Eastern 0 52.00
## 6 0 Eastern 0 62.10
## 18 1 Western 1 38.79View(srel.meta)2.2.2 Description of the Meta-Analytic Data
## Number of effect sizes
length(srel.meta$ESID)## [1] 25## Number of primary studies
length(unique(srel.meta$STUDID))## [1] 25## Proportion adult samples
prop.table(table(srel.meta$Adults))##
## 0 1
## 0.68 0.32## Proportion evidence against validity
prop.table(table(srel.meta$Validity))##
## 0 1
## 0.8 0.2## Distribution of test forms
prop.table(table(srel.meta$Forms))##
## A B Both
## 0.86956522 0.08695652 0.04347826## Distribution of test score types
prop.table(table(srel.meta$Scores))##
## 0 1
## 0.5416667 0.4583333## Distribution of the sample sizes
psych::describe(srel.meta$N)## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 25 453.48 441.71 319 396.81 300.97 84 1758 1674 1.26 0.76
## se
## X1 88.34sum(unique(srel.meta$N))## [1] 8746## Distribution of English language
prop.table(table(srel.meta$LanguageEnglish))##
## 0 1
## 0.32 0.68## Distribution of cultures
prop.table(table(srel.meta$Culture))##
## African Eastern Mixed Western
## 0.04 0.28 0.08 0.60prop.table(table(srel.meta$CultureWestern))##
## 0 1
## 0.4 0.6## Distribution of the proportion of women in the samples
psych::describe(srel.meta$PropFemale)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 24 55.53 16.85 50.93 53.11 5.93 31.66 100 68.34 1.42 1.43 3.44The 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 17.0172 -34.0345 -28.0345 -24.5003 -26.8345
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0048 0.0690 25 no STUDID
## sigma^2.2 0.0048 0.0690 25 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 24) = 1020.7004, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.8460 0.0204 41.3845 24 <.0001 0.8038 0.8882 ***
##
## ---
## 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 0.0048 0.0000 0.0212
## sigma.1 0.0690 0.0000 0.1457
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0048 0.0000 0.0212
## sigma.2 0.0690 0.0000 0.1457## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfm.srel1))## % of total variance I2
## Level 1 0.4905075 ---
## Level 2 49.7547462 49.75
## Level 3 49.7547462 49.75
## Total I2: 99.51%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 0.846 0.0204 23.4 0.804 0.888# 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 9.3566 -18.7131 -12.7131 -9.1790 -11.5131
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0104 0.1019 25 no STUDID
## sigma^2.2 0.0104 0.1019 25 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 24) = 652.7154, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.6017 0.0306 19.6647 24 <.0001 0.5386 0.6649 ***
##
## ---
## 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 0.0104 0.0000 0.0435
## sigma.1 0.1019 0.0000 0.2085
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0104 0.0000 0.0435
## sigma.2 0.1019 0.0000 0.2085## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfm.srel2))## % of total variance I2
## Level 1 3.052523 ---
## Level 2 48.473739 48.47
## Level 3 48.473738 48.47
## Total I2: 96.95%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 0.602 0.0305 23.5 0.539 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 23.2586 -46.5173 -40.5173 -36.9831 -39.3173
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0030 0.0551 25 no STUDID
## sigma^2.2 0.0030 0.0551 25 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 24) = 693.1757, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.7997 0.0165 48.4817 24 <.0001 0.7657 0.8337 ***
##
## ---
## 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 0.0030 0.0000 0.0132
## sigma.1 0.0551 0.0000 0.1149
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0030 0.0000 0.0132
## sigma.2 0.0551 0.0000 0.1149## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfm.srelcr))## % of total variance I2
## Level 1 2.141714 ---
## Level 2 48.929143 48.93
## Level 3 48.929143 48.93
## Total I2: 97.86%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 0.8 0.0164 23.5 0.766 0.834# 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 17.1451 -34.2901 -26.2901 -21.7482 -24.0679
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0045 0.0671 25 no STUDID
## sigma^2.2 0.0045 0.0671 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 927.3901, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.0163, p-val = 0.0958
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8694 0.0238 36.4585 23 <.0001 0.8200 0.9187 ***
## Adults -0.0754 0.0434 -1.7368 23 0.0958 -0.1653 0.0144 .
##
## ---
## 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 0.8694 0.0171 15.8 0.833 0.9056
## Adults -0.0754 0.0561 12.6 -0.197 0.0462## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8694 0.0238 0.8200 0.9187 0.6669 1.0718
## 2 0.7939 0.0363 0.7189 0.8690 0.5837 1.00422.2.3.2.2 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 17.1637 -34.3274 -26.3274 -21.7854 -24.1052
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0040 0.0636 25 no STUDID
## sigma^2.2 0.0040 0.0636 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 851.3590, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.2775, p-val = 0.0833
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8643 0.0210 41.1349 23 <.0001 0.8208 0.9077 ***
## Validity -0.0883 0.0488 -1.8104 23 0.0833 -0.1892 0.0126 .
##
## ---
## 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 0.8643 0.0216 18.50 0.819 0.9095
## Validity -0.0883 0.0411 5.72 -0.190 0.0134## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8643 0.0210 0.8208 0.9077 0.6732 1.0554
## 2 0.7760 0.0440 0.6850 0.8670 0.5688 0.98322.2.3.2.3 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 = 23; method: REML)
##
## logLik Deviance AIC BIC AICc
## 31.0809 -62.1618 -52.1618 -47.1831 -47.8760
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0011 0.0325 23 no STUDID
## sigma^2.2 0.0011 0.0325 23 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 850.5991, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 20) = 7.6967, p-val = 0.0033
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8872 0.0110 80.8489 20 <.0001 0.8643 0.9100 ***
## factor(Forms)B -0.1068 0.0420 -2.5444 20 0.0193 -0.1943 -0.0192 *
## factor(Forms)Both -0.2824 0.0921 -3.0643 20 0.0061 -0.4746 -0.0902 **
##
## ---
## 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 0.887 0.0112 18.52 0.864 0.9105
## factor(Forms)B -0.107 0.0133 1.15 -0.232 0.0181
## factor(Forms)Both -0.282 0.0112 18.52 -0.306 -0.2590## 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 0.8872 0.0110 0.8643 0.9100 0.7887 0.9856
## 2 0.7804 0.0405 0.6959 0.8649 0.6527 0.9081
## 3 0.6048 0.0915 0.4139 0.7956 0.3912 0.81832.2.3.2.4 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 18.5855 -37.1711 -29.1711 -24.8069 -26.8181
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0040 0.0635 24 no STUDID
## sigma^2.2 0.0040 0.0635 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 931.2839, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.1066, p-val = 0.7471
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8605 0.0258 33.3413 22 <.0001 0.8070 0.9140 ***
## Scores -0.0125 0.0384 -0.3265 22 0.7471 -0.0921 0.0670
##
## ---
## 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 0.8605 0.0210 11.8 0.8146 0.9064
## Scores -0.0125 0.0394 21.0 -0.0946 0.0695## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8605 0.0258 0.8070 0.9140 0.6666 1.0544
## 2 0.8480 0.0284 0.7891 0.9068 0.6526 1.04342.2.3.2.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 16.2293 -32.4585 -24.4585 -19.9165 -22.2363
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0052 0.0722 25 no STUDID
## sigma^2.2 0.0052 0.0722 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 465.0746, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.0674, p-val = 0.3123
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8108 0.0394 20.6022 23 <.0001 0.7294 0.8922 ***
## LanguageEnglish 0.0484 0.0468 1.0332 23 0.3123 -0.0485 0.1453
##
## ---
## 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 0.8108 0.0665 6.56 0.6514 0.970
## LanguageEnglish 0.0484 0.0678 12.28 -0.0989 0.196## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8108 0.0394 0.7294 0.8922 0.5844 1.0372
## 2 0.8592 0.0254 0.8067 0.9117 0.6415 1.07692.2.3.2.6 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 16.3265 -32.6530 -24.6530 -20.1110 -22.4308
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0051 0.0713 25 no STUDID
## sigma^2.2 0.0051 0.0713 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 534.3155, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.2869, p-val = 0.2683
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8146 0.0343 23.7516 23 <.0001 0.7436 0.8855 ***
## CultureWestern 0.0493 0.0435 1.1344 23 0.2683 -0.0406 0.1392
##
## ---
## 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 0.8146 0.0510 8.53 0.6983 0.931
## CultureWestern 0.0493 0.0529 17.98 -0.0618 0.160## Predicted subgroup values
predict(MLMEMCSC.tfm.srel1.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8146 0.0343 0.7436 0.8855 0.5944 1.0348
## 2 0.8639 0.0267 0.8086 0.9192 0.6482 1.07962.2.3.2.7 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 14.6934 -29.3868 -21.3868 -17.0226 -19.0339
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0053 0.0727 24 no STUDID
## sigma^2.2 0.0053 0.0727 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 1001.2730, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.1342, p-val = 0.7176
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.8179 0.0840 9.7399 22 <.0001 0.6437
## asin(sqrt(PropFemale/100)) 0.0342 0.0933 0.3663 22 0.7176 -0.1593
## ci.ub
## intrcpt 0.9920 ***
## asin(sqrt(PropFemale/100)) 0.2276
##
## ---
## 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 0.8179 0.0863 3.66 0.569 1.066
## asin(sqrt(PropFemale/100)) 0.0342 0.0831 2.27 -0.286 0.3542.2.3.3 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.4208 -16.8415 -8.8415 -4.2996 -6.6193
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0110 0.1048 25 no STUDID
## sigma^2.2 0.0110 0.1048 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 648.6223, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.0133, p-val = 0.9090
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6034 0.0380 15.8836 23 <.0001 0.5248 0.6820 ***
## Adults -0.0078 0.0675 -0.1155 23 0.9090 -0.1475 0.1319
##
## ---
## 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 0.6034 0.0387 15.7 0.521 0.686
## Adults -0.0078 0.0653 13.5 -0.148 0.133## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6034 0.0380 0.5248 0.6820 0.2868 0.9200
## 2 0.5956 0.0558 0.4802 0.7111 0.2679 0.92332.2.3.3.2 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 9.8000 -19.5999 -11.5999 -7.0579 -9.3777
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0099 0.0997 25 no STUDID
## sigma^2.2 0.0099 0.0997 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 593.6872, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 2.7832, p-val = 0.1088
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6259 0.0332 18.8696 23 <.0001 0.5573 0.6945 ***
## Validity -0.1299 0.0779 -1.6683 23 0.1088 -0.2909 0.0312
##
## ---
## 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 0.626 0.0324 18.76 0.558 0.6937
## Validity -0.130 0.0838 5.57 -0.339 0.0791## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6259 0.0332 0.5573 0.6945 0.3263 0.9255
## 2 0.4960 0.0704 0.3503 0.6417 0.1700 0.82202.2.3.3.3 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 = 23; method: REML)
##
## logLik Deviance AIC BIC AICc
## 7.5300 -15.0600 -5.0600 -0.0814 -0.7743
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0107 0.1034 23 no STUDID
## sigma^2.2 0.0107 0.1034 23 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 604.3319, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 20) = 1.3933, p-val = 0.2713
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6122 0.0344 17.7976 20 <.0001 0.5405 0.6840 ***
## factor(Forms)B 0.0606 0.1128 0.5371 20 0.5972 -0.1748 0.2959
## factor(Forms)Both -0.2832 0.1830 -1.5472 20 0.1375 -0.6650 0.0986
##
## ---
## 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 0.6122 0.0350 18.66 0.539 0.686
## factor(Forms)B 0.0606 0.0671 1.21 -0.507 0.628
## factor(Forms)Both -0.2832 0.0350 18.66 -0.356 -0.210## 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 0.6122 0.0344 0.5405 0.6840 0.2988 0.9257
## 2 0.6728 0.1075 0.4487 0.8970 0.2943 1.0514
## 3 0.3290 0.1798 -0.0460 0.7041 -0.1544 0.81252.2.3.3.4 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.2912 -16.5824 -8.5824 -4.2182 -6.2294
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0106 0.1028 24 no STUDID
## sigma^2.2 0.0106 0.1028 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 405.1244, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 1.0632, p-val = 0.3137
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5759 0.0423 13.6288 22 <.0001 0.4883 0.6636 ***
## Scores 0.0650 0.0631 1.0311 22 0.3137 -0.0658 0.1959
##
## ---
## 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 0.576 0.0409 11.7 0.4865 0.665
## Scores 0.065 0.0632 20.8 -0.0665 0.197## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.5759 0.0423 0.4883 0.6636 0.2619 0.8900
## 2 0.6410 0.0468 0.5439 0.7381 0.3242 0.95782.2.3.3.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.4234 -16.8469 -8.8469 -4.3049 -6.6247
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0110 0.1049 25 no STUDID
## sigma^2.2 0.0110 0.1049 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 408.9066, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.0140, p-val = 0.9069
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5955 0.0561 10.6206 23 <.0001 0.4795 0.7115 ***
## LanguageEnglish 0.0080 0.0677 0.1183 23 0.9069 -0.1320 0.1480
##
## ---
## 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 0.59547 0.0728 6.85 0.423 0.768
## LanguageEnglish 0.00801 0.0794 13.34 -0.163 0.179## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.5955 0.0561 0.4795 0.7115 0.2675 0.9235
## 2 0.6035 0.0379 0.5250 0.6819 0.2868 0.92012.2.3.3.6 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.7507 -17.5014 -9.5014 -4.9594 -7.2792
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0108 0.1038 25 no STUDID
## sigma^2.2 0.0108 0.1038 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 455.1148, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.6709, p-val = 0.4211
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5692 0.0500 11.3830 23 <.0001 0.4657 0.6726 ***
## CultureWestern 0.0523 0.0639 0.8191 23 0.4211 -0.0798 0.1844
##
## ---
## 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 0.5692 0.0661 8.78 0.4191 0.719
## CultureWestern 0.0523 0.0723 18.64 -0.0991 0.204## Predicted subgroup values
predict(MLMEMCSC.tfm.srel2.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.5692 0.0500 0.4657 0.6726 0.2485 0.8898
## 2 0.6215 0.0397 0.5393 0.7037 0.3070 0.93602.2.3.3.7 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.0386 -16.0772 -8.0772 -3.7130 -5.7242
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0111 0.1054 24 no STUDID
## sigma^2.2 0.0111 0.1054 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 644.3099, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.4098, p-val = 0.5287
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.5194 0.1229 4.2278 22 0.0003 0.2646
## asin(sqrt(PropFemale/100)) 0.0875 0.1367 0.6402 22 0.5287 -0.1959
## ci.ub
## intrcpt 0.7742 ***
## asin(sqrt(PropFemale/100)) 0.3709
##
## ---
## 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 0.5194 0.0929 3.61 0.250 0.789
## asin(sqrt(PropFemale/100)) 0.0875 0.0866 2.23 -0.251 0.4262.2.3.4 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 22.1519 -44.3038 -36.3038 -31.7618 -34.0816
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0031 0.0553 25 no STUDID
## sigma^2.2 0.0031 0.0553 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 690.3937, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.9183, p-val = 0.3479
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8103 0.0200 40.5962 23 <.0001 0.7690 0.8516 ***
## Adults -0.0342 0.0357 -0.9583 23 0.3479 -0.1082 0.0397
##
## ---
## 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 0.8103 0.0184 15.6 0.771 0.8494
## Adults -0.0342 0.0388 13.3 -0.118 0.0495## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8103 0.0200 0.7690 0.8516 0.6432 0.9774
## 2 0.7761 0.0296 0.7147 0.8374 0.6029 0.94922.2.3.4.2 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 23.7950 -47.5900 -39.5900 -35.0481 -37.3678
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0028 0.0527 25 no STUDID
## sigma^2.2 0.0028 0.0527 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 607.4349, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 4.2762, p-val = 0.0501
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8157 0.0175 46.7277 23 <.0001 0.7796 0.8518 ***
## Validity -0.0856 0.0414 -2.0679 23 0.0501 -0.1712 0.0000 .
##
## ---
## 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 0.8157 0.0161 18.75 0.782 0.8494
## Validity -0.0856 0.0521 5.43 -0.217 0.0454## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8157 0.0175 0.7796 0.8518 0.6575 0.9739
## 2 0.7301 0.0375 0.6525 0.8078 0.5576 0.90262.2.3.4.3 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 = 23; method: REML)
##
## logLik Deviance AIC BIC AICc
## 24.2827 -48.5655 -38.5655 -33.5868 -34.2798
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0018 0.0419 23 no STUDID
## sigma^2.2 0.0018 0.0419 23 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 589.0590, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 20) = 4.2341, p-val = 0.0293
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8207 0.0141 58.1555 20 <.0001 0.7913 0.8502 ***
## factor(Forms)B -0.0065 0.0470 -0.1379 20 0.8917 -0.1046 0.0916
## factor(Forms)Both -0.2642 0.0908 -2.9100 20 0.0087 -0.4536 -0.0748 **
##
## ---
## 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 0.82074 0.0143 18.52 0.791 0.851
## factor(Forms)B -0.00648 0.0259 1.21 -0.228 0.215
## factor(Forms)Both -0.26420 0.0143 18.52 -0.294 -0.234## 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 0.8207 0.0141 0.7913 0.8502 0.6936 0.9479
## 2 0.8143 0.0449 0.7207 0.9078 0.6592 0.9694
## 3 0.5565 0.0897 0.3695 0.7436 0.3323 0.78082.2.3.4.4 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 22.1055 -44.2109 -36.2109 -31.8468 -33.8580
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0029 0.0534 24 no STUDID
## sigma^2.2 0.0029 0.0534 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 535.7287, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.0965, p-val = 0.7590
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8006 0.0220 36.4337 22 <.0001 0.7550 0.8462 ***
## Scores 0.0101 0.0326 0.3106 22 0.7590 -0.0576 0.0778
##
## ---
## 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 0.8006 0.0225 11.6 0.751 0.8498
## Scores 0.0101 0.0323 21.0 -0.057 0.0772## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8006 0.0220 0.7550 0.8462 0.6374 0.9638
## 2 0.8108 0.0241 0.7607 0.8608 0.6462 0.97532.2.3.4.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 21.9336 -43.8672 -35.8672 -31.3252 -33.6449
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0032 0.0569 25 no STUDID
## sigma^2.2 0.0032 0.0569 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 417.2232, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.4465, p-val = 0.5106
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7821 0.0307 25.4514 23 <.0001 0.7185 0.8456 ***
## LanguageEnglish 0.0246 0.0369 0.6682 23 0.5106 -0.0516 0.1009
##
## ---
## 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 0.7821 0.0443 6.74 0.6766 0.888
## LanguageEnglish 0.0246 0.0468 12.90 -0.0765 0.126## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7821 0.0307 0.7185 0.8456 0.6040 0.9601
## 2 0.8067 0.0204 0.7646 0.8488 0.6351 0.97832.2.3.4.6 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 22.4612 -44.9224 -36.9224 -32.3804 -34.7001
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0031 0.0555 25 no STUDID
## sigma^2.2 0.0031 0.0555 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 476.6963, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.5317, p-val = 0.2283
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7735 0.0268 28.8471 23 <.0001 0.7180 0.8290 ***
## CultureWestern 0.0422 0.0341 1.2376 23 0.2283 -0.0284 0.1128
##
## ---
## 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 0.7735 0.0368 8.7 0.6898 0.857
## CultureWestern 0.0422 0.0395 18.4 -0.0406 0.125## Predicted subgroup values
predict(MLMEMCSC.tfm.srelcr.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7735 0.0268 0.7180 0.8290 0.6021 0.9450
## 2 0.8158 0.0211 0.7721 0.8594 0.6478 0.98382.2.3.4.7 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 20.3507 -40.7014 -32.7014 -28.3373 -30.3485
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0034 0.0587 24 no STUDID
## sigma^2.2 0.0034 0.0587 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 685.9332, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.1632, p-val = 0.6901
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.7704 0.0684 11.2614 22 <.0001 0.6285
## asin(sqrt(PropFemale/100)) 0.0308 0.0761 0.4040 22 0.6901 -0.1271
## ci.ub
## intrcpt 0.9122 ***
## asin(sqrt(PropFemale/100)) 0.1887
##
## ---
## 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 0.7704 0.0517 3.64 0.621 0.920
## asin(sqrt(PropFemale/100)) 0.0308 0.0461 2.26 -0.147 0.2092.2.3.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 39.1954 -78.3907 -70.3907 -65.8487 -68.1685
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0005 0.0220 25 no STUDID
## sigma^2.2 0.0005 0.0220 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 288.5573, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 83.6521, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.9499 0.0111 85.9372 23 <.0001 0.9270 0.9728 ***
## sqrt(SREL1.vg) -4.8102 0.5259 -9.1462 23 <.0001 -5.8982 -3.7223 ***
##
## ---
## 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 0.95 0.011 86.12 13.28 <0.001 ***
## sqrt(SREL1.vg) -4.81 0.674 -7.14 8.45 <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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 17.5793 -35.1586 -27.1586 -22.6167 -24.9364
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0042 0.0649 25 no STUDID
## sigma^2.2 0.0042 0.0649 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 1015.0106, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 4.0950, p-val = 0.0548
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8045 0.0287 28.0528 23 <.0001 0.7452 0.8638 ***
## N 0.0001 0.0000 2.0236 23 0.0548 -0.0000 0.0002 .
##
## ---
## 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 0.8045152 0.0306352 26.26 16.13 <0.001 ***
## N 0.0000885 0.0000372 2.38 5.41 0.0593 .## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 31.7384 -63.4768 -55.4768 -50.9349 -53.2546
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0011 0.0325 25 no STUDID
## sigma^2.2 0.0011 0.0325 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 733.1016, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 47.1798, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8942 0.0112 79.8019 23 <.0001 0.8710 0.9174 ***
## SREL1.vg -48.9790 7.1307 -6.8688 23 <.0001 -63.7300 -34.2280 ***
##
## ---
## 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 0.894 0.0117 76.39 19.42 <0.001 ***
## SREL1.vg -48.979 16.0820 -3.05 2.13 0.0859 .## 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 -0.5806 -0.1003 0.0105 1.0837 0.0099 949.9482 0.0422 4.2245 -0.1004
## 2 0.2076 0.0850 0.0078 1.1240 0.0103 982.7664 0.0430 4.3050 0.0851
## 3 -2.0606 -0.4219 0.1611 0.8749 0.0080 1001.5586 0.0265 2.6491 -0.4346
## 4 1.3711 0.2698 0.0697 1.0042 0.0091 830.4254 0.0439 4.3899 0.2694
## 5 -0.7889 -0.1424 0.0204 1.0458 0.0096 1007.4539 0.0340 3.4027 -0.1423
## 6 -4.4880 -1.3351 1.0272 0.4654 0.0040 955.0759 0.0322 3.2165 -1.5049 *
## 7 -0.6963 -0.1222 0.0152 1.0585 0.0097 1006.0742 0.0356 3.5626 -0.1220
## 8 0.5027 0.1430 0.0219 1.1139 0.0102 922.1433 0.0438 4.3765 0.1433
## 9 0.6827 0.1722 0.0312 1.0975 0.0100 1015.6630 0.0426 4.2647 0.1723
## 10 0.6894 0.1756 0.0325 1.0992 0.0100 970.7886 0.0438 4.3779 0.1759
## 11 0.3810 0.1201 0.0155 1.1203 0.0103 934.4841 0.0437 4.3666 0.1203
## 12 0.8492 0.2014 0.0421 1.0825 0.0099 994.3384 0.0438 4.3821 0.2016
## 13 1.3083 0.2629 0.0669 1.0153 0.0092 871.8229 0.0439 4.3902 0.2626
## 14 0.1694 0.0758 0.0062 1.1212 0.0103 1003.7755 0.0419 4.1870 0.0758
## 15 0.6137 0.1621 0.0279 1.1052 0.0101 999.1130 0.0435 4.3483 0.1624
## 16 -0.5950 -0.1035 0.0111 1.0807 0.0099 969.7595 0.0416 4.1582 -0.1035
## 17 0.8177 0.1941 0.0392 1.0843 0.0099 1018.3396 0.0427 4.2746 0.1942
## 18 0.7173 0.1791 0.0337 1.0955 0.0100 1012.8056 0.0432 4.3216 0.1793
## 19 0.1452 0.0701 0.0053 1.1195 0.0103 1007.5334 0.0412 4.1192 0.0701
## 20 -0.0710 0.0234 0.0006 1.1143 0.0102 1005.8988 0.0403 4.0257 0.0234
## 21 -2.8836 -0.4781 0.2096 0.8208 0.0076 1001.2202 0.0178 1.7756 -0.5094
## 22 0.1126 0.0652 0.0046 1.1247 0.0103 974.4674 0.0430 4.3037 0.0654
## 23 0.1965 0.0817 0.0072 1.1218 0.0103 1001.5186 0.0422 4.2204 0.0818
## 24 -0.3728 -0.0461 0.0022 1.0977 0.0101 999.1161 0.0399 3.9888 -0.0460
## 25 0.3729 0.1185 0.0151 1.1207 0.0103 925.1126 0.0437 4.3685 0.1188## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 18.3446 -36.6892 -28.6892 -24.1472 -26.4670
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0050 0.0706 25 no STUDID
## sigma^2.2 0.0050 0.0706 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 327.0981, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 24.8624, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7775 0.0398 19.5277 23 <.0001 0.6951 0.8599 ***
## sqrt(SREL2.vg) -4.1215 0.8266 -4.9862 23 <.0001 -5.8314 -2.4116 ***
##
## ---
## 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 0.778 0.0363 21.43 14.2 <0.001 ***
## sqrt(SREL2.vg) -4.121 0.6029 -6.84 7.8 <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.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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.5900 -17.1800 -9.1800 -4.6380 -6.9578
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0110 0.1048 25 no STUDID
## sigma^2.2 0.0110 0.1048 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 647.7970, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.3989, p-val = 0.5339
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.5792 0.0466 12.4271 23 <.0001 0.4828 0.6756 ***
## N 0.0000 0.0001 0.6316 23 0.5339 -0.0001 0.0002
##
## ---
## 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 0.5792180 0.0459125 12.616 16.45 <0.001 ***
## N 0.0000449 0.0000657 0.683 5.36 0.523## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 18.3353 -36.6705 -28.6705 -24.1286 -26.4483
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0052 0.0719 25 no STUDID
## sigma^2.2 0.0052 0.0719 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 461.1976, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 24.2103, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6882 0.0273 25.1864 23 <.0001 0.6316 0.7447 ***
## SREL2.vg -32.5633 6.6180 -4.9204 23 <.0001 -46.2537 -18.8729 ***
##
## ---
## 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 0.688 0.0285 24.19 18.11 < 0.001 ***
## SREL2.vg -32.563 4.0114 -8.12 4.21 0.00101 **## 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 0.1056 0.0482 0.0025 1.1058 0.0221 639.0781 0.0432 4.3250 0.0482
## 2 -0.2152 -0.0221 0.0005 1.0976 0.0219 634.9549 0.0423 4.2250 -0.0222
## 3 -1.5995 -0.3080 0.0903 0.9613 0.0192 638.2960 0.0296 2.9554 -0.3110
## 4 1.2623 0.2636 0.0679 1.0256 0.0203 637.2752 0.0447 4.4671 0.2633
## 5 -2.5287 -0.4562 0.1896 0.8690 0.0173 633.2235 0.0242 2.4213 -0.4724
## 6 -0.5182 -0.0915 0.0087 1.0782 0.0215 632.9858 0.0410 4.0971 -0.0915
## 7 0.8661 0.1887 0.0364 1.0654 0.0213 652.6997 0.0407 4.0702 0.1887
## 8 0.4642 0.1228 0.0159 1.1001 0.0219 632.7336 0.0447 4.4712 0.1231
## 9 -0.8895 -0.1673 0.0280 1.0371 0.0208 641.5569 0.0344 3.4394 -0.1672
## 10 0.6213 0.1527 0.0244 1.0907 0.0217 648.0432 0.0445 4.4522 0.1530
## 11 -0.9915 -0.2155 0.0460 1.0350 0.0205 574.0571 0.0432 4.3197 -0.2155
## 12 -0.1923 -0.0169 0.0003 1.1026 0.0220 603.3660 0.0441 4.4060 -0.0170
## 13 1.8369 0.3452 0.1053 0.9370 0.0183 316.8720 0.0450 4.4968 0.3431
## 14 -2.3132 -0.4750 0.2002 0.8709 0.0172 628.9066 0.0299 2.9871 -0.4865
## 15 0.8157 0.1870 0.0360 1.0745 0.0214 652.6535 0.0438 4.3845 0.1871
## 16 0.1070 0.0480 0.0024 1.1044 0.0221 642.4575 0.0427 4.2696 0.0481
## 17 -0.3028 -0.0397 0.0016 1.0759 0.0216 648.0831 0.0342 3.4243 -0.0395
## 18 0.3897 0.1039 0.0114 1.0965 0.0219 650.1954 0.0416 4.1614 0.1040
## 19 0.1463 0.0538 0.0030 1.0972 0.0220 648.9658 0.0398 3.9752 0.0537
## 20 0.9473 0.2054 0.0429 1.0598 0.0211 652.5575 0.0420 4.2021 0.2055
## 21 -0.6447 -0.1096 0.0122 1.0538 0.0212 645.9692 0.0325 3.2517 -0.1094
## 22 0.3827 0.1051 0.0117 1.1009 0.0220 646.5277 0.0435 4.3492 0.1053
## 23 1.3643 0.2755 0.0733 1.0117 0.0200 646.2333 0.0435 4.3529 0.2752
## 24 0.7276 0.1673 0.0290 1.0785 0.0215 652.5489 0.0419 4.1928 0.1674
## 25 -1.5719 -0.3847 0.1337 0.9492 0.0187 536.6417 0.0430 4.3025 -0.3837## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 37.2606 -74.5212 -66.5212 -61.9792 -64.2989
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0009 0.0297 25 no STUDID
## sigma^2.2 0.0009 0.0297 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 305.7577, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 43.4582, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8981 0.0163 55.2552 23 <.0001 0.8645 0.9317 ***
## sqrt(SRELCR.vg) -4.5673 0.6928 -6.5923 23 <.0001 -6.0005 -3.1341 ***
##
## ---
## 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 0.898 0.0145 61.99 13.14 <0.001 ***
## sqrt(SRELCR.vg) -4.567 0.5105 -8.95 7.61 <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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 22.9486 -45.8972 -37.8972 -33.3552 -35.6750
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0029 0.0543 25 no STUDID
## sigma^2.2 0.0029 0.0543 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 690.1930, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 2.6099, p-val = 0.1198
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7710 0.0242 31.8378 23 <.0001 0.7209 0.8211 ***
## N 0.0001 0.0000 1.6155 23 0.1198 -0.0000 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 0.7709769 0.0256130 30.10 16.40 <0.001 ***
## N 0.0000594 0.0000333 1.79 5.39 0.13## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 36.3145 -72.6291 -64.6291 -60.0871 -62.4068
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0010 0.0317 25 no STUDID
## sigma^2.2 0.0010 0.0317 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 469.3450, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 38.8556, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8477 0.0118 71.9485 23 <.0001 0.8233 0.8721 ***
## SRELCR.vg -65.4629 10.5019 -6.2334 23 <.0001 -87.1878 -43.7380 ***
##
## ---
## 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 0.848 0.0118 71.9 18.87 <0.001 ***
## SRELCR.vg -65.463 6.2780 -10.4 3.45 0.001 **## 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 -0.0374 0.0264 0.0007 1.1135 0.0065 667.6021 0.0432 4.3158 0.0264
## 2 0.0529 0.0458 0.0022 1.1140 0.0065 675.7268 0.0429 4.2853 0.0459
## 3 -2.5662 -0.5146 0.2335 0.8308 0.0048 671.1618 0.0257 2.5665 -0.5366
## 4 1.5950 0.3015 0.0837 0.9705 0.0056 615.4980 0.0446 4.4569 0.3005
## 5 -2.6293 -0.5155 0.2352 0.8281 0.0048 671.4950 0.0247 2.4717 -0.5391
## 6 -1.6127 -0.3922 0.1382 0.9305 0.0054 648.9615 0.0391 3.9148 -0.3932
## 7 0.4559 0.1221 0.0157 1.0987 0.0064 691.5093 0.0399 3.9919 0.1221
## 8 0.4620 0.1308 0.0182 1.1094 0.0065 656.7034 0.0445 4.4494 0.1312
## 9 -0.3206 -0.0382 0.0015 1.0892 0.0064 684.2077 0.0378 3.7811 -0.0381
## 10 0.8852 0.2051 0.0433 1.0745 0.0063 692.8051 0.0444 4.4449 0.2054
## 11 -0.5197 -0.0889 0.0082 1.0879 0.0063 610.2809 0.0436 4.3640 -0.0890
## 12 0.3571 0.1101 0.0130 1.1135 0.0065 666.6957 0.0442 4.4214 0.1104
## 13 1.7305 0.3156 0.0890 0.9456 0.0054 416.1811 0.0447 4.4686 0.3140
## 14 -1.6402 -0.3692 0.1249 0.9335 0.0054 668.2991 0.0348 3.4818 -0.3722
## 15 0.9765 0.2185 0.0486 1.0635 0.0062 693.0805 0.0440 4.3981 0.2186
## 16 -0.0658 0.0198 0.0004 1.1116 0.0065 672.6476 0.0427 4.2665 0.0198
## 17 0.2507 0.0813 0.0070 1.1011 0.0065 690.5957 0.0383 3.8255 0.0811
## 18 0.4885 0.1321 0.0185 1.1026 0.0064 690.0260 0.0423 4.2287 0.1322
## 19 0.2166 0.0768 0.0063 1.1062 0.0065 688.9800 0.0400 4.0024 0.0768
## 20 0.8768 0.1987 0.0406 1.0721 0.0063 693.1537 0.0422 4.2228 0.1987
## 21 -1.9516 -0.3808 0.1343 0.9087 0.0053 677.1957 0.0265 2.6451 -0.3894
## 22 0.4532 0.1278 0.0174 1.1078 0.0065 684.7705 0.0436 4.3603 0.1280
## 23 0.7062 0.1712 0.0306 1.0884 0.0064 692.3350 0.0425 4.2541 0.1714
## 24 -0.0460 0.0227 0.0005 1.1054 0.0065 684.8985 0.0401 4.0066 0.0227
## 25 -0.3530 -0.0471 0.0023 1.1012 0.0064 620.3470 0.0438 4.3756 -0.04712.2.3.6 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$k,
digits = 3,
level = 95,
cex = .6,
xlab = "Omega Coefficient",
main = "Reliability Factor 1 (Model 4)")
## Reliability of factor 2
forest.rma(MLREMCSC.tfm.srel2,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfm.srel2$k,
digits = 3,
level = 95,
cex = .6,
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 = .6,
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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 5.9701 -11.9402 -5.9402 -2.4061 -4.7402
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0117 0.1080 25 no STUDID
## sigma^2.2 0.0117 0.1080 25 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 24) = 425.6621, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.7630 0.0322 23.6689 24 <.0001 0.6964 0.8295 ***
##
## ---
## 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 0.0117 0.0000 0.0520
## sigma.1 0.1080 0.0000 0.2280
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0117 0.0000 0.0520
## sigma.2 0.1080 0.0000 0.2280## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfmc.srel1))## % of total variance I2
## Level 1 0.6951387 ---
## Level 2 49.6524307 49.65
## Level 3 49.6524307 49.65
## Total I2: 99.3%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 0.763 0.0321 22.9 0.697 0.829# 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 9.2464 -18.4929 -12.4929 -8.9587 -11.2929
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0095 0.0973 25 no STUDID
## sigma^2.2 0.0095 0.0973 25 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 24) = 494.9445, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.6314 0.0304 20.7645 24 <.0001 0.5687 0.6942 ***
##
## ---
## 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 0.0095 0.0000 0.0411
## sigma.1 0.0973 0.0000 0.2028
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0095 0.0000 0.0411
## sigma.2 0.0973 0.0000 0.2028## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfmc.srel2))## % of total variance I2
## Level 1 4.020696 ---
## Level 2 47.989652 47.99
## Level 3 47.989652 47.99
## Total I2: 95.98%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 0.631 0.0303 22.1 0.569 0.694# 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 24.4985 -48.9970 -42.9970 -39.4629 -41.7970
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0028 0.0529 25 no STUDID
## sigma^2.2 0.0028 0.0529 25 no STUDID/ESID
##
## Test for Heterogeneity:
## Q(df = 24) = 522.6646, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.8182 0.0158 51.7398 24 <.0001 0.7855 0.8508 ***
##
## ---
## 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 0.0028 0.0000 0.0120
## sigma.1 0.0529 0.0000 0.1097
##
## estimate ci.lb ci.ub
## sigma^2.2 0.0028 0.0000 0.0120
## sigma.2 0.0529 0.0000 0.1097## Variance distribution
summary(dmetar::var.comp(MLREMCSC.tfmc.srelcr))## % of total variance I2
## Level 1 2.057698 ---
## Level 2 48.971151 48.97
## Level 3 48.971151 48.97
## Total I2: 97.94%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 0.818 0.0158 23.5 0.786 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 5.1516 -10.3032 -2.3032 2.2388 -0.0810
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0125 0.1117 25 no STUDID
## sigma^2.2 0.0125 0.1117 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 366.0896, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.0950, p-val = 0.7607
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7686 0.0396 19.4138 23 <.0001 0.6867 0.8505 ***
## Adults -0.0225 0.0729 -0.3082 23 0.7607 -0.1733 0.1284
##
## ---
## 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 0.7686 0.0437 15.8 0.676 0.861
## Adults -0.0225 0.0580 11.5 -0.149 0.104## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7686 0.0396 0.6867 0.8505 0.4319 1.1054
## 2 0.7462 0.0612 0.6195 0.8728 0.3958 1.09652.2.4.2.2 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 5.7403 -11.4806 -3.4806 1.0613 -1.2584
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0113 0.1065 25 no STUDID
## sigma^2.2 0.0113 0.1065 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 372.2444, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.3813, p-val = 0.2519
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7820 0.0355 22.0076 23 <.0001 0.7085 0.8555 ***
## Validity -0.0936 0.0797 -1.1753 23 0.2519 -0.2584 0.0712
##
## ---
## 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 0.7820 0.0361 17.97 0.706 0.8580
## Validity -0.0936 0.0718 6.02 -0.269 0.0819## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7820 0.0355 0.7085 0.8555 0.4619 1.1022
## 2 0.6884 0.0713 0.5409 0.8359 0.3437 1.03312.2.4.2.3 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 = 23; method: REML)
##
## logLik Deviance AIC BIC AICc
## 7.6493 -15.2985 -5.2985 -0.3198 -1.0128
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0086 0.0926 23 no STUDID
## sigma^2.2 0.0086 0.0926 23 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 361.7420, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 20) = 2.8583, p-val = 0.0809
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7954 0.0301 26.4088 20 <.0001 0.7325 0.8582 ***
## factor(Forms)B -0.0967 0.1030 -0.9390 20 0.3589 -0.3114 0.1181
## factor(Forms)Both -0.3846 0.1714 -2.2442 20 0.0363 -0.7421 -0.0271 *
##
## ---
## 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 0.7954 0.0305 18.8 0.731 0.859
## factor(Forms)B -0.0967 0.0471 1.2 -0.507 0.314
## factor(Forms)Both -0.3846 0.0305 18.8 -0.449 -0.321## 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 0.7954 0.0301 0.7325 0.8582 0.5151 1.0756
## 2 0.6987 0.0985 0.4933 0.9040 0.3569 1.0404
## 3 0.4107 0.1687 0.0588 0.7627 -0.0348 0.85622.2.4.2.4 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 6.4130 -12.8261 -4.8261 -0.4619 -2.4732
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0120 0.1095 24 no STUDID
## sigma^2.2 0.0120 0.1095 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 419.4714, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.8849, p-val = 0.3571
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7920 0.0439 18.0318 22 <.0001 0.7009 0.8831 ***
## Scores -0.0619 0.0658 -0.9407 22 0.3571 -0.1982 0.0745
##
## ---
## 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 0.7920 0.0308 11.9 0.725 0.8592
## Scores -0.0619 0.0692 20.9 -0.206 0.0821## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7920 0.0439 0.7009 0.8831 0.4582 1.1258
## 2 0.7301 0.0489 0.6286 0.8316 0.3934 1.06692.2.4.2.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 6.9770 -13.9541 -5.9541 -1.4121 -3.7319
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0113 0.1063 25 no STUDID
## sigma^2.2 0.0113 0.1063 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 341.4132, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.7666, p-val = 0.0646
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6623 0.0610 10.8581 23 <.0001 0.5362 0.7885 ***
## LanguageEnglish 0.1386 0.0714 1.9408 23 0.0646 -0.0091 0.2864 .
##
## ---
## 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 0.662 0.108 5.95 0.397 0.928
## LanguageEnglish 0.139 0.110 10.64 -0.104 0.382## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6623 0.0610 0.5362 0.7885 0.3267 0.9980
## 2 0.8010 0.0372 0.7241 0.8779 0.4806 1.12142.2.4.2.6 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 6.5957 -13.1914 -5.1914 -0.6494 -2.9692
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0114 0.1067 25 no STUDID
## sigma^2.2 0.0114 0.1067 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 372.6575, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.0470, p-val = 0.0942
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6888 0.0533 12.9302 23 <.0001 0.5786 0.7990 ***
## CultureWestern 0.1160 0.0665 1.7456 23 0.0942 -0.0215 0.2536 .
##
## ---
## 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 0.689 0.0809 7.93 0.502 0.876
## CultureWestern 0.116 0.0836 16.35 -0.061 0.293## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel1.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6888 0.0533 0.5786 0.7990 0.3577 1.0199
## 2 0.8048 0.0398 0.7226 0.8871 0.4819 1.12782.2.4.2.7 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 4.2226 -8.4452 -0.4452 3.9190 1.9078
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0135 0.1163 24 no STUDID
## sigma^2.2 0.0135 0.1163 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 369.2496, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.0049, p-val = 0.9446
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.7529 0.1333 5.6489 22 <.0001 0.4765
## asin(sqrt(PropFemale/100)) 0.0104 0.1476 0.0703 22 0.9446 -0.2956
## ci.ub
## intrcpt 1.0293 ***
## asin(sqrt(PropFemale/100)) 0.3164
##
## ---
## 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 0.7529 0.114 3.74 0.426 1.079
## asin(sqrt(PropFemale/100)) 0.0104 0.119 2.28 -0.446 0.4672.2.4.3 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.6756 -17.3512 -9.3512 -4.8093 -7.1290
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0099 0.0996 25 no STUDID
## sigma^2.2 0.0099 0.0996 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 490.4978, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.7239, p-val = 0.4036
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6482 0.0371 17.4756 23 <.0001 0.5715 0.7249 ***
## Adults -0.0577 0.0678 -0.8509 23 0.4036 -0.1980 0.0826
##
## ---
## 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 0.6482 0.0309 15.0 0.582 0.714
## Adults -0.0577 0.0812 11.6 -0.235 0.120## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6482 0.0371 0.5715 0.7249 0.3469 0.9495
## 2 0.5905 0.0568 0.4730 0.7079 0.2763 0.90462.2.4.3.2 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 9.7565 -19.5130 -11.5130 -6.9710 -9.2908
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0082 0.0908 25 no STUDID
## sigma^2.2 0.0082 0.0908 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 428.6923, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.2051, p-val = 0.0866
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6587 0.0320 20.5751 23 <.0001 0.5925 0.7249 ***
## Validity -0.1280 0.0715 -1.7903 23 0.0866 -0.2758 0.0199 .
##
## ---
## 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 0.659 0.0337 17.14 0.588 0.72973
## Validity -0.128 0.0542 5.93 -0.261 0.00514## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6587 0.0320 0.5925 0.7249 0.3849 0.9325
## 2 0.5307 0.0639 0.3985 0.6629 0.2340 0.82752.2.4.3.3 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 = 23; method: REML)
##
## logLik Deviance AIC BIC AICc
## 10.0585 -20.1171 -10.1171 -5.1384 -5.8313
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0077 0.0880 23 no STUDID
## sigma^2.2 0.0077 0.0880 23 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 457.5460, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 20) = 1.1039, p-val = 0.3509
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6527 0.0301 21.6527 20 <.0001 0.5898 0.7156 ***
## factor(Forms)B -0.0015 0.1000 -0.0153 20 0.9880 -0.2102 0.2071
## factor(Forms)Both -0.2615 0.1761 -1.4846 20 0.1532 -0.6289 0.1059
##
## ---
## 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 0.65268 0.0306 17.95 0.588 0.717
## factor(Forms)B -0.00153 0.0600 1.21 -0.513 0.510
## factor(Forms)Both -0.26148 0.0306 17.95 -0.326 -0.197## 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 0.6527 0.0301 0.5898 0.7156 0.3856 0.9198
## 2 0.6512 0.0954 0.4522 0.8501 0.3241 0.9782
## 3 0.3912 0.1735 0.0292 0.7532 -0.0542 0.83662.2.4.3.4 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.7763 -17.5527 -9.5527 -5.1885 -7.1997
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0092 0.0958 24 no STUDID
## sigma^2.2 0.0092 0.0958 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 248.0145, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 1.1842, p-val = 0.2883
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6039 0.0396 15.2449 22 <.0001 0.5217 0.6860 ***
## Scores 0.0663 0.0609 1.0882 22 0.2883 -0.0600 0.1926
##
## ---
## 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 0.6039 0.0302 11.8 0.538 0.670
## Scores 0.0663 0.0652 19.2 -0.070 0.203## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6039 0.0396 0.5217 0.6860 0.3112 0.8966
## 2 0.6702 0.0463 0.5742 0.7661 0.3733 0.96702.2.4.3.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.7982 -17.5965 -9.5965 -5.0545 -7.3742
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0090 0.0950 25 no STUDID
## sigma^2.2 0.0090 0.0950 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 150.2834, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.0279, p-val = 0.3212
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6797 0.0557 12.2090 23 <.0001 0.5645 0.7948 ***
## LanguageEnglish -0.0668 0.0659 -1.0138 23 0.3212 -0.2031 0.0695
##
## ---
## 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 0.6797 0.0795 6.02 0.485 0.874
## LanguageEnglish -0.0668 0.0841 11.10 -0.252 0.118## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6797 0.0557 0.5645 0.7948 0.3789 0.9804
## 2 0.6129 0.0352 0.5400 0.6858 0.3257 0.90012.2.4.3.6 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.3362 -16.6724 -8.6724 -4.1304 -6.4501
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0102 0.1009 25 no STUDID
## sigma^2.2 0.0102 0.1009 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 212.8276, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.0456, p-val = 0.8327
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6218 0.0520 11.9646 23 <.0001 0.5143 0.7293 ***
## CultureWestern 0.0139 0.0652 0.2136 23 0.8327 -0.1210 0.1489
##
## ---
## 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 0.6218 0.0777 8.03 0.443 0.801
## CultureWestern 0.0139 0.0808 16.58 -0.157 0.185## Predicted subgroup values
predict(MLMEMCSC.tfmc.srel2.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.6218 0.0520 0.5143 0.7293 0.3078 0.9358
## 2 0.6357 0.0394 0.5542 0.7172 0.3296 0.94182.2.4.3.7 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 7.7170 -15.4340 -7.4340 -3.0699 -5.0811
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0104 0.1020 24 no STUDID
## sigma^2.2 0.0104 0.1020 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 483.8490, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.5703, p-val = 0.4581
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.5389 0.1213 4.4418 22 0.0002 0.2873
## asin(sqrt(PropFemale/100)) 0.1007 0.1333 0.7552 22 0.4581 -0.1758
## ci.ub
## intrcpt 0.7905 ***
## asin(sqrt(PropFemale/100)) 0.3772
##
## ---
## 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 0.539 0.0927 3.68 0.272 0.805
## asin(sqrt(PropFemale/100)) 0.101 0.0836 2.21 -0.228 0.4302.2.4.4 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 23.7634 -47.5268 -39.5268 -34.9848 -37.3046
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0027 0.0521 25 no STUDID
## sigma^2.2 0.0027 0.0521 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 522.6509, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.7859, p-val = 0.1945
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8324 0.0188 44.3556 23 <.0001 0.7936 0.8712 ***
## Adults -0.0450 0.0337 -1.3364 23 0.1945 -0.1147 0.0247
##
## ---
## 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 0.832 0.0162 15.7 0.798 0.8668
## Adults -0.045 0.0388 13.2 -0.129 0.0387## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.age, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8324 0.0188 0.7936 0.8712 0.6751 0.9897
## 2 0.7874 0.0280 0.7295 0.8453 0.6243 0.95042.2.4.4.2 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 24.7551 -49.5102 -41.5102 -36.9682 -39.2879
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0025 0.0502 25 no STUDID
## sigma^2.2 0.0025 0.0502 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 444.1613, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.8597, p-val = 0.0617
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8331 0.0167 49.9023 23 <.0001 0.7985 0.8676 ***
## Validity -0.0765 0.0389 -1.9646 23 0.0617 -0.1570 0.0041 .
##
## ---
## 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 0.8331 0.0159 18.7 0.800 0.866
## Validity -0.0765 0.0452 5.6 -0.189 0.036## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.validity, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8331 0.0167 0.7985 0.8676 0.6821 0.9840
## 2 0.7566 0.0352 0.6838 0.8293 0.5926 0.92062.2.4.4.3 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 = 23; method: REML)
##
## logLik Deviance AIC BIC AICc
## 27.8527 -55.7053 -45.7053 -40.7267 -41.4196
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0014 0.0368 23 no STUDID
## sigma^2.2 0.0014 0.0368 23 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 20) = 408.6778, p-val < .0001
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 20) = 5.2885, p-val = 0.0143
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8420 0.0124 67.8009 20 <.0001 0.8161 0.8679 ***
## factor(Forms)B -0.0257 0.0419 -0.6145 20 0.5458 -0.1130 0.0616
## factor(Forms)Both -0.2876 0.0894 -3.2163 20 0.0043 -0.4742 -0.1011 **
##
## ---
## 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 0.8420 0.0126 18.6 0.816 0.868
## factor(Forms)B -0.0257 0.0269 1.2 -0.258 0.206
## factor(Forms)Both -0.2876 0.0126 18.6 -0.314 -0.261## 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 0.8420 0.0124 0.8161 0.8679 0.7304 0.9535
## 2 0.8163 0.0400 0.7329 0.8997 0.6794 0.9531
## 3 0.5544 0.0886 0.3696 0.7391 0.3401 0.76862.2.4.4.4 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 23.5969 -47.1938 -39.1938 -34.8296 -36.8409
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0026 0.0507 24 no STUDID
## sigma^2.2 0.0026 0.0507 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 426.8649, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.0088, p-val = 0.9261
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8252 0.0207 39.8103 22 <.0001 0.7822 0.8682 ***
## Scores -0.0029 0.0309 -0.0938 22 0.9261 -0.0671 0.0613
##
## ---
## 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 0.8252 0.0201 11.7 0.7813 0.8692
## Scores -0.0029 0.0310 20.9 -0.0673 0.0615## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.scores, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.8252 0.0207 0.7822 0.8682 0.6705 0.9799
## 2 0.8223 0.0230 0.7747 0.8699 0.6663 0.97842.2.4.4.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 21.9336 -43.8672 -35.8672 -31.3252 -33.6449
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0032 0.0569 25 no STUDID
## sigma^2.2 0.0032 0.0569 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 417.2232, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.4465, p-val = 0.5106
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7821 0.0307 25.4514 23 <.0001 0.7185 0.8456 ***
## LanguageEnglish 0.0246 0.0369 0.6682 23 0.5106 -0.0516 0.1009
##
## ---
## 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 0.7821 0.0443 6.74 0.6766 0.888
## LanguageEnglish 0.0246 0.0468 12.90 -0.0765 0.126## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.lang, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7821 0.0307 0.7185 0.8456 0.6040 0.9601
## 2 0.8067 0.0204 0.7646 0.8488 0.6351 0.97832.2.4.4.6 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 22.4612 -44.9224 -36.9224 -32.3804 -34.7001
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0031 0.0555 25 no STUDID
## sigma^2.2 0.0031 0.0555 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 476.6963, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 1.5317, p-val = 0.2283
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7735 0.0268 28.8471 23 <.0001 0.7180 0.8290 ***
## CultureWestern 0.0422 0.0341 1.2376 23 0.2283 -0.0284 0.1128
##
## ---
## 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 0.7735 0.0368 8.7 0.6898 0.857
## CultureWestern 0.0422 0.0395 18.4 -0.0406 0.125## Predicted subgroup values
predict(MLMEMCSC.tfmc.srelcr.cult, newmods = c(0,1))##
## pred se ci.lb ci.ub pi.lb pi.ub
## 1 0.7735 0.0268 0.7180 0.8290 0.6021 0.9450
## 2 0.8158 0.0211 0.7721 0.8594 0.6478 0.98382.2.4.4.7 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 = 24; method: REML)
##
## logLik Deviance AIC BIC AICc
## 20.3507 -40.7014 -32.7014 -28.3373 -30.3485
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0034 0.0587 24 no STUDID
## sigma^2.2 0.0034 0.0587 24 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 22) = 685.9332, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 22) = 0.1632, p-val = 0.6901
##
## Model Results:
##
## estimate se tval df pval ci.lb
## intrcpt 0.7704 0.0684 11.2614 22 <.0001 0.6285
## asin(sqrt(PropFemale/100)) 0.0308 0.0761 0.4040 22 0.6901 -0.1271
## ci.ub
## intrcpt 0.9122 ***
## asin(sqrt(PropFemale/100)) 0.1887
##
## ---
## 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 0.7704 0.0517 3.64 0.621 0.920
## asin(sqrt(PropFemale/100)) 0.0308 0.0461 2.26 -0.147 0.2092.2.4.5 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 23.6111 -47.2223 -39.2223 -34.6803 -37.0001
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0007 0.0265 25 no STUDID
## sigma^2.2 0.0007 0.0265 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 186.3863, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 76.3920, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.9000 0.0137 65.6949 23 <.0001 0.8717 0.9283 ***
## sqrt(SREL1C.vg) -4.0655 0.4651 -8.7403 23 <.0001 -5.0277 -3.1033 ***
##
## ---
## 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 0.90 0.0206 43.60 12.95 < 0.001 ***
## sqrt(SREL1C.vg) -4.07 1.0480 -3.88 9.29 0.00352 **## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 6.9163 -13.8326 -5.8326 -1.2906 -3.6103
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0103 0.1014 25 no STUDID
## sigma^2.2 0.0103 0.1014 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 418.8469, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.9690, p-val = 0.0583
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6979 0.0453 15.4084 23 <.0001 0.6042 0.7916 ***
## N 0.0001 0.0001 1.9922 23 0.0583 -0.0000 0.0003 .
##
## ---
## 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 0.697914 0.055971 12.47 15.56 <0.001 ***
## N 0.000137 0.000073 1.87 5.39 0.116## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 7.9836 -15.9673 -7.9673 -3.4253 -5.7450
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0098 0.0989 25 no STUDID
## sigma^2.2 0.0098 0.0989 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 390.6398, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.4707, p-val = 0.0753
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7736 0.0300 25.7989 23 <.0001 0.7116 0.8356 ***
## SREL1C.vg -3.2596 1.7497 -1.8630 23 0.0753 -6.8791 0.3599 .
##
## ---
## 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 0.774 0.0313 24.715 22.54 <0.001 ***
## SREL1C.vg -3.260 8.4850 -0.384 1.05 0.764## 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 0.0428 0.0433 0.0020 1.1270 0.0253 399.2283 0.0438 4.3765 0.0434
## 2 0.4758 0.1315 0.0185 1.1157 0.0250 420.2750 0.0441 4.4089 0.1317
## 3 -2.0587 -0.4375 0.1690 0.8610 0.0193 407.0371 0.0300 2.9975 -0.4495
## 4 0.1642 0.0684 0.0050 1.1247 0.0253 417.3371 0.0430 4.3005 0.0684
## 5 -0.5757 -0.0998 0.0103 1.0822 0.0243 410.4367 0.0400 3.9995 -0.0997
## 6 -1.2987 -0.2673 0.0684 0.9794 0.0220 411.4365 0.0338 3.3755 -0.2688
## 7 -0.1631 -0.0036 0.0000 1.1111 0.0250 418.9619 0.0399 3.9890 -0.0036
## 8 0.2768 0.0929 0.0093 1.1259 0.0252 356.1077 0.0444 4.4376 0.0931
## 9 -5.9128 -1.5778 1.2860 0.3218 0.0066 358.8042 0.0300 2.9998 -2.0176 *
## 10 0.7582 0.1829 0.0350 1.0919 0.0244 423.9669 0.0444 4.4409 0.1831
## 11 0.4035 0.1180 0.0150 1.1205 0.0251 402.0327 0.0443 4.4327 0.1182
## 12 0.8308 0.1952 0.0395 1.0836 0.0242 413.0919 0.0444 4.4435 0.1954
## 13 0.7782 0.1863 0.0362 1.0897 0.0244 422.7039 0.0444 4.4406 0.1865
## 14 0.0914 0.0531 0.0030 1.1251 0.0253 414.7629 0.0430 4.3015 0.0532
## 15 0.7410 0.1796 0.0338 1.0934 0.0245 425.3786 0.0442 4.4234 0.1798
## 16 -0.6255 -0.1138 0.0134 1.0796 0.0242 401.9331 0.0413 4.1324 -0.1137
## 17 0.6777 0.1602 0.0268 1.0911 0.0245 425.6607 0.0400 4.0004 0.1601
## 18 0.0656 0.0474 0.0024 1.1240 0.0252 416.1942 0.0427 4.2658 0.0474
## 19 0.6114 0.1555 0.0256 1.1043 0.0248 425.3541 0.0435 4.3536 0.1557
## 20 0.7455 0.1794 0.0337 1.0920 0.0245 425.5211 0.0437 4.3745 0.1796
## 21 -1.0199 -0.0561 0.0032 0.9993 0.0233 424.1353 0.0029 0.2859 -0.0562
## 22 0.4521 0.1270 0.0173 1.1172 0.0250 418.3646 0.0441 4.4126 0.1272
## 23 0.2874 0.0933 0.0094 1.1218 0.0252 420.9575 0.0430 4.2963 0.0934
## 24 -0.7191 -0.1369 0.0192 1.0674 0.0239 403.5294 0.0406 4.0648 -0.1369
## 25 0.9945 0.2214 0.0498 1.0622 0.0237 310.1251 0.0445 4.4461 0.2215## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 11.7491 -23.4982 -15.4982 -10.9562 -13.2760
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0064 0.0797 25 no STUDID
## sigma^2.2 0.0064 0.0797 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 320.6533, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 6.7122, p-val = 0.0163
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7112 0.0386 18.4088 23 <.0001 0.6313 0.7912 ***
## sqrt(SREL2C.vg) -1.6624 0.6416 -2.5908 23 0.0163 -2.9897 -0.3350 *
##
## ---
## 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 0.711 0.0418 17.01 11.83 <0.001 ***
## sqrt(SREL2C.vg) -1.662 0.9334 -1.78 4.34 0.144## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 8.3137 -16.6273 -8.6273 -4.0854 -6.4051
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0101 0.1006 25 no STUDID
## sigma^2.2 0.0101 0.1006 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 494.3038, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.0947, p-val = 0.7610
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6198 0.0473 13.0900 23 <.0001 0.5218 0.7177 ***
## N 0.0000 0.0001 0.3078 23 0.7610 -0.0001 0.0002
##
## ---
## 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 0.6197671 0.0479670 12.921 15.1 <0.001 ***
## N 0.0000216 0.0000573 0.377 5.2 0.721## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 9.6282 -19.2564 -11.2564 -6.7144 -9.0341
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0089 0.0946 25 no STUDID
## sigma^2.2 0.0089 0.0946 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 467.0447, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 0.8934, p-val = 0.3544
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.6398 0.0308 20.7941 23 <.0001 0.5762 0.7035 ***
## SREL2C.vg -1.8922 2.0018 -0.9452 23 0.3544 -6.0332 2.2489
##
## ---
## 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 0.64 0.0291 21.99 21.59 <0.001 ***
## SREL2C.vg -1.89 1.5272 -1.24 1.23 0.402## 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 -0.4546 -0.0817 0.0070 1.0938 0.0199 473.8330 0.0455 4.5523 -0.0818
## 2 -0.1583 -0.0117 0.0001 1.1092 0.0202 483.3117 0.0454 4.5434 -0.0117
## 3 -1.3485 -0.2400 0.0562 0.9895 0.0181 486.8228 0.0276 2.7559 -0.2417
## 4 1.4482 0.3034 0.0868 0.9963 0.0178 475.4692 0.0478 4.7798 0.3025
## 5 -1.5066 -0.3378 0.1063 0.9625 0.0173 471.6695 0.0395 3.9549 -0.3391
## 6 -2.3690 -0.4958 0.2145 0.8520 0.0152 472.6836 0.0319 3.1900 -0.5095
## 7 0.4920 0.1218 0.0155 1.0940 0.0200 494.6315 0.0418 4.1822 0.1217
## 8 0.0278 0.0314 0.0011 1.1197 0.0203 446.5656 0.0483 4.8251 0.0315
## 9 1.4476 0.2702 0.0705 0.9997 0.0181 492.5023 0.0381 3.8128 0.2708
## 10 0.1709 0.0629 0.0042 1.1182 0.0203 477.9306 0.0478 4.7817 0.0631
## 11 -1.1009 -0.2549 0.0632 1.0231 0.0184 418.1080 0.0467 4.6734 -0.2547
## 12 0.3491 0.1015 0.0110 1.1146 0.0202 479.9340 0.0483 4.8253 0.1019
## 13 1.6847 0.3423 0.1050 0.9543 0.0170 204.9424 0.0487 4.8677 0.3402
## 14 -2.7553 -0.5805 0.2827 0.7994 0.0142 468.4919 0.0314 3.1370 -0.6034
## 15 0.3051 0.0904 0.0087 1.1120 0.0202 490.9536 0.0465 4.6467 0.0906
## 16 -0.2046 -0.0223 0.0005 1.1034 0.0201 486.7779 0.0437 4.3669 -0.0223
## 17 -0.2109 -0.0128 0.0002 1.0116 0.0191 494.7088 0.0052 0.5249 -0.0128
## 18 0.3228 0.0915 0.0089 1.1063 0.0202 493.2400 0.0442 4.4209 0.0916
## 19 0.4808 0.1232 0.0160 1.0996 0.0200 494.3278 0.0442 4.4169 0.1232
## 20 0.5570 0.1365 0.0195 1.0934 0.0199 494.7227 0.0433 4.3251 0.1365
## 21 -0.0527 -0.0007 0.0000 1.0153 0.0191 494.8203 0.0065 0.6472 -0.0007
## 22 0.0842 0.0430 0.0020 1.1157 0.0203 485.5125 0.0465 4.6541 0.0431
## 23 1.1937 0.2594 0.0663 1.0347 0.0186 490.3481 0.0470 4.6951 0.2592
## 24 0.5432 0.1367 0.0196 1.0978 0.0200 494.4961 0.0450 4.5010 0.1368
## 25 -0.6043 -0.1111 0.0127 1.0701 0.0195 486.6137 0.0392 3.9196 -0.1110## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 38.5774 -77.1549 -69.1549 -64.6129 -66.9326
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0007 0.0262 25 no STUDID
## sigma^2.2 0.0007 0.0262 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 232.1572, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 47.8856, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.9125 0.0145 62.7468 23 <.0001 0.8824 0.9425 ***
## sqrt(SRELCRC.vg) -4.6279 0.6688 -6.9199 23 <.0001 -6.0113 -3.2444 ***
##
## ---
## 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 0.912 0.0126 72.65 12.95 <0.001 ***
## sqrt(SRELCRC.vg) -4.628 0.6472 -7.15 8.06 <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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 24.5762 -49.1524 -41.1524 -36.6104 -38.9301
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0026 0.0508 25 no STUDID
## sigma^2.2 0.0026 0.0508 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 518.9919, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 3.5613, p-val = 0.0718
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.7872 0.0227 34.7324 23 <.0001 0.7403 0.8340 ***
## N 0.0001 0.0000 1.8871 23 0.0718 -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 0.787152 0.0248723 31.65 16.41 <0.001 ***
## N 0.000065 0.0000341 1.91 5.38 0.111## 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 = 25; method: REML)
##
## logLik Deviance AIC BIC AICc
## 36.4251 -72.8502 -64.8502 -60.3083 -62.6280
##
## Variance Components:
##
## estim sqrt nlvls fixed factor
## sigma^2.1 0.0009 0.0296 25 no STUDID
## sigma^2.2 0.0009 0.0296 25 no STUDID/ESID
##
## Test for Residual Heterogeneity:
## QE(df = 23) = 331.1155, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 23) = 37.9578, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.8633 0.0110 78.1818 23 <.0001 0.8405 0.8862 ***
## SRELCRC.vg -68.5051 11.1192 -6.1610 23 <.0001 -91.5068 -45.5033 ***
##
## ---
## 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 0.863 0.0101 85.67 18.21 < 0.001 ***
## SRELCRC.vg -68.505 10.1813 -6.73 3.05 0.00637 **## 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 -0.1663 -0.0056 0.0000 1.1071 0.0060 495.4587 0.0430 4.2976 -0.0056
## 2 0.3227 0.0986 0.0103 1.1090 0.0060 514.7507 0.0432 4.3164 0.0987
## 3 -2.7417 -0.5080 0.2305 0.8294 0.0045 501.8788 0.0233 2.3292 -0.5328
## 4 1.3824 0.2778 0.0740 1.0069 0.0054 472.8212 0.0444 4.4392 0.2773
## 5 -1.8689 -0.4123 0.1531 0.9062 0.0049 499.4453 0.0330 3.3040 -0.4178
## 6 -2.2029 -0.5695 0.2641 0.8319 0.0044 472.4256 0.0381 3.8127 -0.5743
## 7 0.2985 0.0893 0.0084 1.1012 0.0060 520.4364 0.0397 3.9673 0.0893
## 8 0.3347 0.1025 0.0112 1.1114 0.0060 479.9229 0.0443 4.4341 0.1027
## 9 0.0787 0.0461 0.0022 1.1050 0.0060 517.3624 0.0402 4.0206 0.0461
## 10 0.8772 0.2019 0.0419 1.0734 0.0058 522.5130 0.0443 4.4338 0.2021
## 11 -0.5283 -0.0928 0.0090 1.0859 0.0058 445.4642 0.0435 4.3538 -0.0929
## 12 0.7028 0.1718 0.0309 1.0897 0.0059 519.6958 0.0443 4.4320 0.1721
## 13 1.5047 0.2939 0.0810 0.9872 0.0053 338.7830 0.0445 4.4522 0.2931
## 14 -1.7136 -0.3875 0.1363 0.9251 0.0049 496.4310 0.0353 3.5308 -0.3907
## 15 0.8789 0.2010 0.0415 1.0725 0.0058 522.5865 0.0438 4.3839 0.2012
## 16 -0.3086 -0.0386 0.0016 1.0990 0.0059 497.2894 0.0424 4.2350 -0.0386
## 17 0.0238 0.0298 0.0009 1.0868 0.0059 520.6986 0.0333 3.3304 0.0296
## 18 0.2770 0.0880 0.0082 1.1074 0.0060 517.7329 0.0420 4.1965 0.0881
## 19 0.5083 0.1313 0.0181 1.0969 0.0059 521.4169 0.0413 4.1337 0.1313
## 20 0.9818 0.2146 0.0468 1.0598 0.0057 522.1870 0.0426 4.2602 0.2147
## 21 -2.1406 -0.4041 0.1504 0.8937 0.0048 506.5283 0.0252 2.5213 -0.4152
## 22 0.4544 0.1248 0.0165 1.1047 0.0060 516.5492 0.0436 4.3568 0.1250
## 23 0.4890 0.1291 0.0176 1.0998 0.0059 520.6466 0.0422 4.2201 0.1293
## 24 -0.2742 -0.0302 0.0010 1.0939 0.0059 512.7552 0.0395 3.9459 -0.0302
## 25 0.5264 0.1373 0.0199 1.0994 0.0059 520.2911 0.0429 4.2922 0.13752.2.4.6 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 = .6,
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$k,
digits = 3,
level = 95,
cex = .6,
xlab = "Omega Coefficient",
main = "Reliability Factor 2 (Model 3)")
## Composite reliability
forest.rma(MLREMCSC.tfmc.srelcr,
addfit = TRUE,
order = "obs",
header = "Reference",
refline = 0,
rows = 1:MLREMCSC.tfmc.srelcr$k,
digits = 3,
level = 95,
cex = .6,
xlab = "Omega Coefficient",
main = "Composite Reliability (Model 3)")
#dev.off()3 R session info
sessionInfo()## R version 4.3.1 (2023-06-16)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Ventura 13.4.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/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: America/Chicago
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] dmetar_0.1.0 semPower_2.0.1 devtools_2.4.5
## [4] usethis_2.2.2 dplyr_1.1.2 lavaan_0.6-16
## [7] clubSandwich_0.5.10 robumeta_2.1 metafor_4.4-0
## [10] numDeriv_2016.8-1.1 metadat_1.2-0 Matrix_1.6-1
## [13] metaSEM_1.3.1 OpenMx_2.21.8 reshape2_1.4.4
## [16] psych_2.3.6 pacman_0.5.1
##
## loaded via a namespace (and not attached):
## [1] mathjaxr_1.6-0 rstudioapi_0.15.0 jsonlite_1.8.7
## [4] magrittr_2.0.3 modeltools_0.2-23 farver_2.1.1
## [7] nloptr_2.0.3 rmarkdown_2.24 fs_1.6.3
## [10] vctrs_0.6.4 memoise_2.0.1 minqa_1.2.6
## [13] CompQuadForm_1.4.3 htmltools_0.5.6 sass_0.4.7
## [16] bslib_0.5.1 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_1.7.5 magic_1.6-1 digest_0.6.33
## [31] colorspace_2.1-0 ps_1.7.5 pkgload_1.3.3
## [34] ellipse_0.5.0 labeling_0.4.3 fansi_1.0.5
## [37] abind_1.4-5 compiler_4.3.1 remotes_2.4.2.1
## [40] withr_2.5.1 meta_6.5-0 pkgbuild_1.4.2
## [43] highr_0.10 MASS_7.3-60 sessioninfo_1.2.2
## [46] tools_4.3.1 pbivnorm_0.6.0 prabclus_2.3-3
## [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_1.2.1 grid_4.3.1 cluster_2.1.4
## [58] generics_0.1.3 gtable_0.3.4 class_7.3-22
## [61] xml2_1.3.5 utf8_1.2.4 flexmix_2.3-19
## [64] ggrepel_0.9.4 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 pbapply_1.7-2
## [73] miniUI_0.1.1.1 knitr_1.43 gridExtra_2.3
## [76] stats4_4.3.1 xfun_0.40 diptest_0.76-0
## [79] DEoptimR_1.1-3 MuMIn_1.47.5 netmeta_2.8-2
## [82] stringi_1.7.12 yaml_2.3.7 boot_1.3-28.1
## [85] evaluate_0.22 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_3.4.4 prettyunits_1.2.0
## [100] mclust_6.0.0 profvis_0.3.8 urlchecker_1.0.1
## [103] lme4_1.1-34 mvtnorm_1.2-3 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