More Data on Piagetian and Psychometric Intelligence
Setup
library(pacman); p_load(lavaan, psych, semPlot, dynamic, DT)
CONGO <- function(F1, F2) {
PHI = sum(F1*F2) / sqrt(sum(F1^2)*sum(F2^2))
return(PHI)}
CRITR <- function(n, alpha = .05) {
df <- n - 2; CRITT <- qt(alpha/2, df, lower.tail = T)
CRITR <- sqrt((CRITT^2)/((CRITT^2) + df ))
return(CRITR)}
NP <- function(N, S = 2) {
NP = 1-pnorm(qnorm(1-(N^(-6/5))/S))
return(NP)}
FITM <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "aic", "bic", "srmr")
NP(c(47, 50, 79, 56, 39, 35, 41, 76, 459))## [1] 0.0049255255 0.0045730505 0.0026412986 0.0039915757 0.0061615855
## [6] 0.0070159801 0.0058026901 0.0027669015 0.0003197384CRITR(c(47, 50, 79, 56, 39, 35, 41, 76, 459))## [1] 0.28756298 0.27871059 0.22129818 0.26320921 0.31603193 0.33384462 0.30813060
## [8] 0.22565419 0.09154074CRITR(c(47, 50, 79, 56, 39, 35, 41, 76, 459), c(0.0049, 0.0046, 0.0026, 0.0040, 0.0062, 0.0070, 0.0058, 0.0028, 0.00032))## [1] 0.4036447 0.3943510 0.3343366 0.3787136 0.4306888 0.4477047 0.4234795
## [8] 0.3382857 0.1672374#DeVries & Kohlberg (1977); n = 47
lowerDK77 <- '
1
0.45 1
0.1 0.11 1
0.18 0.32 -0.02 1
0.22 0.25 0.11 0.2 1
0.17 0.4 0.22 0.38 0.21 1
0.3 0.35 0.17 0.26 0.15 0.34 1
0.19 0.21 0.01 0.45 -0.15 0.23 0 1
0.32 0.45 0.14 0.38 0.1 0.51 0.3 0.48 1
0.13 0.06 0.05 0.05 0.06 0.32 0.16 0.05 0.13 1
0.11 0.35 0.29 0.25 0.2 0.34 0.22 0.13 0.32 0.09 1
0.1 0.43 0.05 0.25 0.16 0.45 0.4 0.23 0.45 0.05 0.27 1
0.12 0.12 -0.04 0.11 0.23 0.25 0.21 0.03 0.17 0.26 0.25 0.12 1
0.2 0.15 0.31 0.42 0.32 0.31 0.23 0.13 0.11 0.17 0.48 0.28 0.31 1
0.18 0.44 0.08 0.29 0.45 0.4 0.33 0.16 0.33 0.16 0.32 0.37 0.37 0.33 1'
##LO correlations were reflected because it was reverse-scored; the direction was kept consistently positive, however.
lowerDK77Psy <- '
1
0.45 1
0.1 0.11 1
0.18 0.32 -0.02 1
0.22 0.25 0.11 0.2 1
0.17 0.4 0.22 0.38 0.21 1
0.3 0.35 0.17 0.26 0.15 0.34 1
0.19 0.21 0.01 0.45 -0.15 0.23 0 1
0.32 0.45 0.14 0.38 0.1 0.51 0.3 0.48 1'
lowerDK77Pia <- '
1
0.09 1
0.05 0.27 1
0.26 0.25 0.12 1
0.17 0.48 0.28 0.31 1
0.16 0.32 0.37 0.37 0.33 1'
nDK77 <- 47
DK77.cor = getCov(lowerDK77, names = c("QT", "IN", "MC", "DS", "CO", "S1", "MT", "LD", "PS", "LO", "AS", "LC", "NC", "S2", "AI"))
DK77Psy.cor = getCov(lowerDK77Psy, names = c("QT", "IN", "MC", "DS", "CO", "S1", "MT", "LD", "PS"))
DK77Pia.cor = getCov(lowerDK77Pia, names = c("LO", "AS", "LC", "NC", "S2", "AI"))
#DeVries (1974) - 1; n = 50
lowerD74A <- '
1
0.56 1
0.62 0.47 1
0.54 0.57 0.58 1
0.32 0.36 0.38 0.38 1
0.42 0.32 0.4 0.32 0.1 1
0.23 0.27 0.02 0.19 0.15 0.24 1
0.33 0.35 0.33 0.33 0.14 0.35 0.24 1
0.36 0.14 0.2 0.26 0.06 0.28 0.07 0.61 1
0.42 0.31 0.36 0.23 0.24 0.35 0.17 0.68 0.47 1
0.21 0.3 0.25 0.29 0.05 0.21 0.22 0.6 0.57 0.4 1
0.58 0.48 0.4 0.47 0.28 0.39 0.33 0.62 0.44 0.54 0.32 1
0.4 0.31 0.39 0.5 0.33 0.37 0.17 0.53 0.39 0.47 0.38 0.46 1
0.43 0.33 0.36 0.45 0.33 0.14 0.2 0.56 0.37 0.4 0.39 0.5 0.75 1
0.31 0.3 0.27 0.23 0.2 0.18 0.2 0.38 0.35 0.33 0.38 0.45 0.26 0.36 1
0.45 0.27 0.12 0.02 0.17 0.34 0.18 0.23 -0.01 0.1 0.02 0.33 0.19 0.15 0.22 1
0.05 0.13 0.06 0.07 -0.16 0.22 0.12 0.46 0.24 0.09 0.24 0.18 0.19 0.27 0.02 0.2 1
-0.12 -0.03 -0.02 0.09 0.07 0.17 -0.08 -0.03 0.23 -0.01 0.01 0 0.17 0.1 0.1 0 0.15 1
0.55 0.28 0.36 0.26 0.23 0.55 0.2 0.21 0.29 0.39 0.28 0.28 0.37 0.37 0.42 0.34 -0.06 0.22 1
0.43 0.27 0.33 0.22 0.23 0.57 0.16 0.34 0.32 0.33 0.27 0.31 0.41 0.4 0.32 0.23 0.06 0.1 0.7 1
0.34 0.39 0.34 0.22 0.29 0.54 0.36 0.2 0.34 0.07 0.21 0.07 0.28 0.17 0.26 0.22 0.1 0.28 0.51 0.51 1
0.29 0.24 0.3 0.16 0.15 0.25 0.07 0.08 0.07 0.07 0.16 0.1 0.22 0.14 0.05 0.2 0.02 0.14 0.55 0.61 0.4 1'
lowerD74PsyA <- '
1
0.56 1
0.62 0.47 1
0.55 0.28 0.36 1
0.43 0.27 0.33 0.7 1
0.34 0.39 0.34 0.51 0.51 1
0.29 0.24 0.3 0.55 0.61 0.4 1'
lowerD74PiaA <- '
1
0.38 1
0.32 0.1 1
0.19 0.15 0.24 1
0.33 0.14 0.35 0.24 1
0.26 0.06 0.28 0.07 0.61 1
0.23 0.24 0.35 0.17 0.68 0.47 1
0.29 0.05 0.21 0.22 0.6 0.57 0.4 1
0.47 0.28 0.39 0.33 0.62 0.44 0.54 0.32 1
0.5 0.33 0.37 0.17 0.53 0.39 0.47 0.38 0.46 1
0.45 0.33 0.14 0.2 0.56 0.37 0.4 0.39 0.5 0.75 1
0.23 0.2 0.18 0.2 0.38 0.35 0.33 0.38 0.45 0.26 0.36 1
0.02 0.17 0.34 0.18 0.23 -0.01 0.1 0.02 0.33 0.19 0.15 0.22 1
0.07 -0.16 0.22 0.12 0.46 0.24 0.09 0.24 0.18 0.19 0.27 0.02 0.2 1
0.09 0.07 0.17 -0.08 -0.03 0.23 -0.01 0.01 0 0.17 0.1 0.1 0 0.15 1'
nD74A <- 50
D74A.cor = getCov(lowerD74A, names = c("SB", "CL", "CN", "PM", "PC", "PD", "PL", "PN", "PI", "PE", "PA", "PR", "PG", "PS", "PSI", "PT", "PGG", "POS", "MW", "MK", "MA", "MR"))
D74PsyA.cor = getCov(lowerD74PsyA, names = c("SB", "CL", "CN", "MW", "MK", "MA", "MR"))
D74PiaA.cor = getCov(lowerD74PiaA, names = c("PM", "PC", "PD", "PL", "PN", "PI", "PE", "PA", "PR", "PG", "PS", "PSI", "PT", "PGG", "POS"))
#DeVries (1974) - 2; n = 79
lowerD74B <- '
1
0.58 1
0.65 0.55 1
0.42 0.51 0.45 1
0.38 0.36 0.34 0.41 1
0.51 0.43 0.44 0.28 0.12 1
0.25 0.16 0.11 0.12 0.15 0.1 1
0.31 0.31 0.33 0.23 0.1 0.38 0.06 1
0.31 0.19 0.22 0.19 0 0.24 -0.01 0.59 1
0.29 0.27 0.26 0.17 0.05 0.33 -0.06 0.67 0.55 1
0.21 0.32 0.28 0.18 0 0.12 0.07 0.56 0.58 0.46 1
0.54 0.47 0.46 0.35 0.2 0.38 0.18 0.58 0.51 0.58 0.37 1
0.45 0.31 0.39 0.4 0.28 0.39 0.06 0.42 0.35 0.42 0.33 0.47 1
0.42 0.31 0.34 0.44 0.3 0.22 0.07 0.37 0.3 0.35 0.3 0.43 0.8 1
0.26 0.24 0.25 0.19 0.17 0.1 0.17 0.22 0.34 0.18 0.31 0.42 0.2 0.22 1
0.39 0.18 0.07 0.06 0.22 0.16 0.22 0.24 0.01 0.05 0.05 0.17 0.17 0.18 0.02 1
0.15 0.15 0.14 0.11 -0.02 0.2 0.18 0.33 0.2 0.09 0.06 0.17 0.2 0.25 -0.01 0.28 1
-0.13 -0.06 -0.03 0 -0.02 -0.02 0 0 0.16 -0.05 0.07 -0.08 0.08 0.05 0.04 0.15 0.21 1'
lowerD74PsyB <- '
1
0.58 1
0.65 0.55 1'
lowerD74PiaB <- '
1
0.41 1
0.28 0.12 1
0.12 0.15 0.1 1
0.23 0.1 0.38 0.06 1
0.19 0 0.24 -0.01 0.59 1
0.17 0.05 0.33 -0.06 0.67 0.55 1
0.18 0 0.12 0.07 0.56 0.58 0.46 1
0.35 0.2 0.38 0.18 0.58 0.51 0.58 0.37 1
0.4 0.28 0.39 0.06 0.42 0.35 0.42 0.33 0.47 1
0.44 0.3 0.22 0.07 0.37 0.3 0.35 0.3 0.43 0.8 1
0.19 0.17 0.1 0.17 0.22 0.34 0.18 0.31 0.42 0.2 0.22 1
0.06 0.22 0.16 0.22 0.24 0.01 0.05 0.05 0.17 0.17 0.18 0.02 1
0.11 -0.02 0.2 0.18 0.33 0.2 0.09 0.06 0.17 0.2 0.25 -0.01 0.28 1
0 -0.02 -0.02 0 0 0.16 -0.05 0.07 -0.08 0.08 0.05 0.04 0.15 0.21 1'
nD74B <- 79
D74B.cor = getCov(lowerD74B, names = c("SB", "CL", "CN", "PM", "PC", "PD", "PL", "PN", "PI", "PE", "PA", "PR", "PG", "PS", "PSI", "PT", "PGG", "POS"))
D74PsyB.cor = getCov(lowerD74PsyB, names = c("SB", "CL", "CN"))
D74PiaB.cor = getCov(lowerD74PiaB, names = c("PM", "PC", "PD", "PL", "PN", "PI", "PE", "PA", "PR", "PG", "PS", "PSI", "PT", "PGG", "POS"))
#DeVries (1974) - 3; n = 126
lowerD74C <- '
1
0.53 1
0.55 0.44 1
0.55 0.41 0.34 1
0.44 0.23 0.3 0.26 1
0.36 0.3 0.23 0.46 0.06 1
0.42 0.27 0.17 0.39 0.06 0.63 1
0.36 0.25 0.18 0.44 0.07 0.64 0.53 1
0.29 0.22 0.08 0.2 0.07 0.57 0.61 0.43 1
0.6 0.42 0.3 0.46 0.31 0.56 0.56 0.57 0.4 1
0.4 0.35 0.26 0.36 0.06 0.34 0.35 0.33 0.22 0.44 1
0.32 0.38 0.23 0.31 0.15 0.32 0.27 0.32 0.2 0.43 0.7 1
0.29 0.18 0.1 0.15 0.11 0.11 0.25 0.12 0.19 0.26 0.21 0.19 1
0.33 0.15 0.23 0.16 0.22 0.2 0.08 0.07 0 0.25 0.16 0.17 -0.07 1
0.45 0.25 0.26 0.35 0.31 0.34 0.3 0.25 0.15 0.28 0.2 0.16 0.11 0.26 1
0.04 0.04 0.03 0.05 -0.05 0.03 0.13 -0.03 0.01 -0.02 0.09 0.03 0.09 0.19 0.18 1'
D74C.cor = getCov(lowerD74C, names = c("SB", "PM", "PC", "PD", "PL", "PN", "PI", "PE", "PA", "PR", "PG", "PS", "PSI", "PT", "PGG", "POS"))
nD74C <- 126
#Hathaway (1972) - Kindergarten; n = 56
lowerH72K <- '
1
0.11 1
0.2 -0.08 1
0.35 0.2 0.28 1
0.36 0.27 -0.03 0.28 1
0.2 0.05 0.01 0.27 0.3 1
0.32 0.07 0.17 0.44 0.4 0.33 1
0.32 0.14 0.09 0.41 0.28 0.11 0.4 1
0.12 0.11 0.05 0.26 0.24 0.14 0.18 0.35 1
0.05 -0.22 0.1 0.14 0.28 0.25 0.35 0.24 0.24 1
0.32 0.03 0.05 0.24 0.4 0.1 0.31 0.55 0.44 0.43 1
0.22 0.03 0.12 0.27 0.18 0.07 0.37 0.53 0.26 0.23 0.42 1
0 -0.06 0.02 0.14 0.25 0.2 0.2 0.4 0.4 0.3 0.54 0.53 1
0.16 -0.01 0.08 0.1 0.05 0 0.1 0.27 0.21 0.22 0.44 0.23 0.26 1
0.32 0.11 0.2 0.25 0.24 0.1 0.38 0.42 0.28 0.11 0.27 0.17 0.23 0.26 1
0.31 0.08 0.12 0.34 0.29 0.13 0.34 0.41 0.16 0.32 0.42 0.34 0.14 0.35 0.3 1
0.25 0.03 -0.02 0.36 0.35 0.22 0.13 0.35 0.32 0.13 0.36 0.37 0.35 0.09 0.34 0.19 1
0.15 0.37 -0.11 0.26 0.28 0.26 0.17 0.1 0.35 0.15 0.11 0.2 0.27 0.15 0.25 0.31 0.31 1
0.09 0.08 0.17 0.32 0.08 -0.1 0.22 0.07 -0.01 0.02 0.12 0.12 0.11 0.25 0.32 0.32 0.23 0.33 1
0.06 0.12 0.1 0.24 0.02 0.04 -0.04 -0.03 0.1 -0.17 -0.01 0.1 -0.1 0.19 0.08 0.28 0.29 0.17 0.4 1
0.21 0.19 -0.08 0.24 0.19 0.03 0.08 0.27 0.43 0.02 0.32 0.23 0.26 0.06 0.37 0.05 0.32 0.15 0 0.01 1
0.26 0 0.13 -0.07 0.02 0.17 0.23 0.07 0.09 0.13 0.19 0.1 0.04 0.09 0.28 0.37 0.03 0.25 0.22 0.15 -0.1 1
0.24 0.12 0.13 0.46 0.12 0.16 0.31 0.24 0.22 0.1 0.3 0.36 0.34 0.2 0.38 0.29 0.35 0.27 0.4 0.3 0.56 0.11 1'
lowerH72KPsy <- '
1
0.11 1
0.2 -0.08 1
0.35 0.2 0.28 1
0.36 0.27 -0.03 0.28 1
0.2 0.05 0.01 0.27 0.3 1
0.32 0.07 0.17 0.44 0.4 0.33 1
0.32 0.14 0.09 0.41 0.28 0.11 0.4 1
0.12 0.11 0.05 0.26 0.24 0.14 0.18 0.35 1
0.05 -0.22 0.1 0.14 0.28 0.25 0.35 0.24 0.24 1
0.32 0.03 0.05 0.24 0.4 0.1 0.31 0.55 0.44 0.43 1
0.22 0.03 0.12 0.27 0.18 0.07 0.37 0.53 0.26 0.23 0.42 1
0 -0.06 0.02 0.14 0.25 0.2 0.2 0.4 0.4 0.3 0.54 0.53 1
0.16 -0.01 0.08 0.1 0.05 0 0.1 0.27 0.21 0.22 0.44 0.23 0.26 1'
lowerH72KPia <- '
1
0.3 1
0.34 0.19 1
0.25 0.31 0.31 1
0.32 0.32 0.23 0.33 1
0.08 0.28 0.29 0.17 0.4 1
0.37 0.05 0.32 0.15 0 0.01 1
0.28 0.37 0.03 0.25 0.22 0.15 -0.1 1
0.38 0.29 0.35 0.27 0.4 0.3 0.56 0.11 1'
H72K.cor = getCov(lowerH72K, names = c("WINF", "WCOM", "WARI", "WSIM", "WVOC", "WPICCO", "WPICAR", "WBD", "WMAZ", "WOA", "LTOV", "LTCO", "LTP", "LOMD", "PS", "PT", "PN", "PD", "PCQ", "PCS", "PI", "PM", "PSE"))
H72KPsy.cor = getCov(lowerH72KPsy, names = c("WINF", "WCOM", "WARI", "WSIM", "WVOC", "WPICCO", "WPICAR", "WBD", "WMAZ", "WOA", "LTOV", "LTCO", "LTP", "LOMD"))
H72KPia.cor = getCov(lowerH72KPia, names = c("PS", "PT", "PN", "PD", "PCQ", "PCS", "PI", "PM", "PSE"))
nH72 <- 56
# Hathaway (1972) - First Grade; n = 56
lowerH72I <- '
1
0.45 1
0.54 0.19 1
0.46 0.30 0.19 1
0.49 0.42 0.29 0.35 1
0.33 0.09 0.23 0.29 0.18 1
0.59 0.26 0.39 0.39 0.33 0.24 1
0.39 0.24 0.27 0.20 0.04 0.23 0.23 1
0.20 0.00 0.08 0.27 0.17 0.44 0.28 0.37 1
-0.02 0.04 -0.02 -0.06 0.21 -0.03 -0.13 -0.05 0.03 1
0.33 0.23 0.15 0.38 0.45 0.22 0.16 0.16 0.16 0.11 1
0.40 0.18 0.43 0.26 0.11 0.24 0.41 0.28 0.11 0.05 0.34 1
0.41 0.30 0.29 0.15 0.11 0.01 0.36 0.18 0.10 -0.07 0.25 0.41 1
0.26 0.04 0.20 0.09 0.00 -0.15 0.27 0.08 0.18 0.19 0.14 0.20 0.08 1
0.50 0.30 0.33 0.36 0.13 0.23 0.44 0.40 0.41 -0.12 0.27 0.27 0.23 0.28 1
0.46 0.31 0.40 0.31 0.34 0.43 0.48 0.35 0.20 -0.10 0.46 0.41 0.20 0.06 0.54 1
0.35 0.03 0.33 0.20 0.14 0.36 0.29 0.19 0.13 -0.05 0.37 0.32 0.22 0.10 0.33 0.41 1
0.33 0.24 0.22 0.11 0.21 0.04 0.23 0.30 0.24 -0.30 0.32 0.25 0.24 0.25 0.32 0.30 0.28 1
0.31 0.02 0.23 0.20 0.00 0.16 0.27 0.15 0.20 -0.24 0.29 0.36 0.21 0.22 0.43 0.45 0.29 0.20 1
0.32 0.02 0.28 0.12 -0.05 0.18 0.18 0.36 0.22 -0.30 0.06 0.09 0.06 0.00 0.39 0.40 0.27 0.21 0.47 1
0.34 0.09 0.26 0.42 0.17 0.14 0.37 0.04 0.32 0.00 0.29 0.41 0.27 0.25 0.24 0.14 0.58 0.30 0.35 0.14 1
0.52 0.23 0.40 0.29 0.22 0.30 0.17 0.56 0.39 0.01 0.32 0.32 0.42 0.02 0.49 0.38 0.30 0.21 0.41 0.40 0.20 1
0.45 0.12 0.42 0.25 0.09 0.20 0.36 0.33 0.37 -0.29 0.23 0.29 0.29 0.23 0.50 0.26 0.42 0.32 0.56 0.26 0.45 0.52 1
0.37 0.56 0.56 0.24 0.15 0.11 0.45 0.30 0.30 0.33 0.16 0.42 0.22 0.35 0.38 0.36 0.37 0.38 0.31 0.37 0.36 0.38 0.46 1
0.34 0.29 0.39 0.35 0.24 0.17 0.45 0.25 0.39 0.45 0.11 0.30 0.18 0.22 0.24 0.19 0.28 0.24 0.10 0.13 0.33 0.32 0.26 0.63 1
0.62 0.01 0.01 0.29 0.36 0.29 0.51 0.45 0.35 0.52 0.21 0.43 0.24 0.35 0.34 0.37 0.31 0.40 0.42 0.45 0.42 0.37 0.61 0.75 0.54 1
0.32 0.01 0.01 0.04 -0.06 0.15 0.37 0.28 0.24 0.41 0.00 0.44 0.21 0.33 0.38 0.38 0.27 0.22 0.36 0.45 0.29 0.44 0.41 0.62 0.24 0.66 1
0.51 0.55 0.55 0.43 0.34 0.21 0.44 0.35 0.34 0.45 0.26 0.33 0.25 0.28 0.40 0.40 0.36 0.41 0.35 0.31 0.45 0.41 0.42 0.66 0.57 0.63 0.45 1
0.27 0.49 0.49 0.41 0.08 0.01 0.30 0.28 0.24 0.32 0.08 0.39 0.21 0.48 0.25 0.25 0.20 0.35 0.26 0.20 0.22 0.31 0.41 0.75 0.52 0.67 0.56 0.55 1'
lowerH72IPsy <- '
1
0.45 1
0.54 0.19 1
0.46 0.30 0.19 1
0.49 0.42 0.29 0.35 1
0.33 0.09 0.23 0.29 0.18 1
0.59 0.26 0.39 0.39 0.33 0.24 1
0.39 0.24 0.27 0.20 0.04 0.23 0.23 1
0.20 0.00 0.08 0.27 0.17 0.44 0.28 0.37 1
-0.02 0.04 -0.02 -0.06 0.21 -0.03 -0.13 -0.05 0.03 1
0.33 0.23 0.15 0.38 0.45 0.22 0.16 0.16 0.16 0.11 1
0.40 0.18 0.43 0.26 0.11 0.24 0.41 0.28 0.11 0.05 0.34 1
0.41 0.30 0.29 0.15 0.11 0.01 0.36 0.18 0.10 -0.07 0.25 0.41 1
0.26 0.04 0.20 0.09 0.00 -0.15 0.27 0.08 0.18 0.19 0.14 0.20 0.08 1
0.37 0.56 0.56 0.24 0.15 0.11 0.45 0.30 0.30 0.33 0.16 0.42 0.22 0.35 1
0.34 0.29 0.39 0.35 0.24 0.17 0.45 0.25 0.39 0.45 0.11 0.30 0.18 0.22 0.63 1
0.62 0.01 0.01 0.29 0.36 0.29 0.51 0.45 0.35 0.52 0.21 0.43 0.24 0.35 0.75 0.54 1
0.32 0.01 0.01 0.04 -0.06 0.15 0.37 0.28 0.24 0.41 0.00 0.44 0.21 0.33 0.62 0.24 0.66 1
0.51 0.55 0.55 0.43 0.34 0.21 0.44 0.35 0.34 0.45 0.26 0.33 0.25 0.28 0.66 0.57 0.63 0.45 1
0.27 0.49 0.49 0.41 0.08 0.01 0.30 0.28 0.24 0.32 0.08 0.39 0.21 0.48 0.75 0.52 0.67 0.56 0.55 1'
lowerH72IPia <- '
1
0.54 1
0.33 0.41 1
0.32 0.30 0.28 1
0.43 0.45 0.29 0.20 1
0.39 0.40 0.27 0.21 0.47 1
0.24 0.14 0.58 0.30 0.35 0.14 1
0.49 0.38 0.30 0.21 0.41 0.40 0.20 1
0.50 0.26 0.42 0.32 0.56 0.26 0.45 0.52 1'
H72I.cor = getCov(lowerH72I, names = c("WINF", "WCOM", "WARI", "WSIM", "WVOC", "WPICCO", "WPICAR", "WBD", "WMAZ", "WOA", "LTOV", "LTCO", "LTP", "LOMD", "PS", "PT", "PN", "PD", "PCQ", "PCS", "PI", "PM", "PSE", "CATRV", "CATCOM", "CATAR", "CATAF", "CATME", "CATSP"))
H72IPsy.cor = getCov(lowerH72IPsy, names = c("WINF", "WCOM", "WARI", "WSIM", "WVOC", "WPICCO", "WPICAR", "WBD", "WMAZ", "WOA", "LTOV", "LTCO", "LTP", "LOMD", "CATRV", "CATCOM", "CATAR", "CATAF", "CATME", "CATSP"))
H72IPia.cor = getCov(lowerH72IPia, names = c("PS", "PT", "PN", "PD", "PCQ", "PCS", "PI", "PM", "PSE"))
# Hathaway (1972) - Second Grade; n = 56
lowerH72II <- '
1
0.45 1
0.35 0.12 1
0.46 0.33 0.31 1
0.52 0.47 0.36 0.35 1
0.47 0.23 0.27 0.39 0.31 1
0.5 0.27 0.06 0.25 0.44 0.45 1
0.44 0.17 0.34 0.34 0.24 0.36 0.39 1
0.25 0.06 0.39 0.08 0.27 0.22 0.08 0.49 1
0.16 -0.04 -0.01 -0.01 -0.01 0.02 -0.16 0.14 0.32 1
0.4 0.24 0.17 0.3 0.46 0.2 0.34 0.29 0.22 0.17 1
0.49 0.26 0.25 0.12 0.39 0.35 0.49 0.18 0.16 0 0.44 1
0.51 0.25 0.15 0.2 0.25 0.28 0.18 0.26 0.09 0.16 0.23 0.35 1
0.2 0.1 0.13 0 0.29 0.16 0 0.03 0.19 0.45 0.29 0.36 0.22 1
0.33 0.17 0.12 0.25 0.11 0.12 0.15 0.3 0.18 0.27 0.4 0.24 0.34 0.22 1
0.25 0.17 0 0.29 0.01 0.01 0.13 0.23 0.1 0.1 0.45 0.15 0.4 0.03 0.49 1
0.27 0.27 0.15 0.04 0.31 0.24 0.29 0.24 0.06 0.09 0.3 0.21 0.11 0.29 0.19 0.17 1
0.32 0.17 0.24 0.2 0.18 0.37 0.27 0.2 0.17 0.09 0.27 0.43 0.29 0.33 0.38 0.24 0.49 1
0.53 0.1 0.26 0.48 0.29 0.19 0.17 0.28 0.13 0.09 0.4 0.21 0.38 0.1 0.44 0.37 0.32 0.5 1
0.39 0.02 0.41 0.21 0.2 0.31 0.17 0.33 0.18 0.17 0.14 0.01 0.26 0.01 0.21 0.289 0.35 0.24 0.58 1
0.4 0.15 0.24 0.26 0.24 0.1 0.15 0.25 0.27 0.26 0.42 0.31 0.45 0.27 0.32 0.32 0.15 0.34 0.36 0.21 1
0.38 0.29 0.31 0.21 0.29 0.16 0.32 0.4 0.14 0.13 0.39 0.36 0.21 0.14 0.31 0.23 0.33 0.35 0.27 0.33 0.22 1
0.3 0.18 0.35 0.04 0.14 0.18 0.21 0.37 0.35 0.19 0.06 0.33 0.31 0.15 0.39 0.15 0.04 0.26 0.2 0.24 0.26 0.08 1
0.41 0.17 0.3 0.23 0.24 0.26 0.2 0.4 0.3 0.27 0.37 0.36 0.38 0.38 0.5 0.46 0.16 0.31 0.26 0.35 0.23 0.39 0.4 1
0.47 0.21 0.28 0.15 0.25 0.34 0.39 0.39 0.38 0.2 0.46 0.54 0.4 0.33 0.44 0.38 0.3 0.42 0.27 0.3 0.2 0.44 0.37 0.63 1
0.55 0.28 0.32 0.27 0.31 0.38 0.39 0.51 0.43 0.25 0.47 0.49 0.48 0.3 0.55 0.52 0.34 0.43 0.37 0.44 0.35 0.54 0.4 0.75 0.8 1
0.55 0.22 0.37 0.19 0.27 0.27 0.19 0.43 0.44 0.36 0.25 0.42 0.42 0.4 0.49 0.32 0.35 0.37 0.3 0.38 0.37 0.4 0.47 0.62 0.62 0.75 1
0.39 0.12 0.26 0.19 0.22 0.29 0.25 0.28 0.28 0.15 0.32 0.56 0.39 0.2 0.37 0.28 0.12 0.32 0.25 0.24 0.23 0.29 0.4 0.66 0.57 0.58 0.56 1
0.4 0.17 0.15 0.17 0.23 0.22 0.13 0.29 0.28 0.3 0.23 0.37 0.45 0.31 0.38 0.47 0.15 0.25 0.27 0.37 0.15 0.32 0.35 0.75 0.52 0.76 0.64 0.59 1'
lowerH72IIPsy <- '
1
0.45 1
0.35 0.12 1
0.46 0.33 0.31 1
0.52 0.47 0.36 0.35 1
0.47 0.23 0.27 0.39 0.31 1
0.5 0.27 0.06 0.25 0.44 0.45 1
0.44 0.17 0.34 0.34 0.24 0.36 0.39 1
0.25 0.06 0.39 0.08 0.27 0.22 0.08 0.49 1
0.16 -0.04 -0.01 -0.01 -0.01 0.02 -0.16 0.14 0.32 1
0.4 0.24 0.17 0.3 0.46 0.2 0.34 0.29 0.22 0.17 1
0.49 0.26 0.25 0.12 0.39 0.35 0.49 0.18 0.16 0 0.44 1
0.51 0.25 0.15 0.2 0.25 0.28 0.18 0.26 0.09 0.16 0.23 0.35 1
0.2 0.1 0.13 0 0.29 0.16 0 0.03 0.19 0.45 0.29 0.36 0.22 1
0.41 0.17 0.3 0.23 0.24 0.26 0.2 0.4 0.3 0.27 0.37 0.36 0.38 0.38 1
0.47 0.21 0.28 0.15 0.25 0.34 0.39 0.39 0.38 0.2 0.46 0.54 0.4 0.33 0.63 1
0.55 0.28 0.32 0.27 0.31 0.38 0.39 0.51 0.43 0.25 0.47 0.49 0.48 0.3 0.75 0.8 1
0.55 0.22 0.37 0.19 0.27 0.27 0.19 0.43 0.44 0.36 0.25 0.42 0.42 0.4 0.62 0.62 0.75 1
0.39 0.12 0.26 0.19 0.22 0.29 0.25 0.28 0.28 0.15 0.32 0.56 0.39 0.2 0.66 0.57 0.58 0.56 1
0.4 0.17 0.15 0.17 0.23 0.22 0.13 0.29 0.28 0.3 0.23 0.37 0.45 0.31 0.75 0.52 0.76 0.64 0.59 1'
lowerH72IIPia <- '
1
0.49 1
0.19 0.17 1
0.38 0.24 0.49 1
0.44 0.37 0.32 0.5 1
0.21 0.289 0.35 0.24 0.58 1
0.32 0.32 0.15 0.34 0.36 0.21 1
0.31 0.23 0.33 0.35 0.27 0.33 0.22 1
0.39 0.15 0.04 0.26 0.2 0.24 0.26 0.08 1'
H72II.cor = getCov(lowerH72II, names = c("WINF", "WCOM", "WARI", "WSIM", "WVOC", "WPICCO", "WPICAR", "WBD", "WMAZ", "WOA", "LTOV", "LTCO", "LTP", "LOMD", "PS", "PT", "PN", "PD", "PCQ", "PCS", "PI", "PM", "PSE", "CATRV", "CATCOM", "CATAR", "CATAF", "CATME", "CATSP"))
H72IIPsy.cor = getCov(lowerH72IIPsy, names = c("WINF", "WCOM", "WARI", "WSIM", "WVOC", "WPICCO", "WPICAR", "WBD", "WMAZ", "WOA", "LTOV", "LTCO", "LTP", "LOMD", "CATRV", "CATCOM", "CATAR", "CATAF", "CATME", "CATSP"))
H72IIPia.cor = getCov(lowerH72IIPia, names = c("PS", "PT", "PN", "PD", "PCQ", "PCS", "PI", "PM", "PSE"))Analysis
DeVries & Kohlberg (1977); n = 47
fa.parallel(DK77.cor, n.obs = nDK77)
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa77 <- fa(DK77.cor, n.obs = nDK77, nfactors = 1)
faPsy77 <- fa(DK77Psy.cor, n.obs = nDK77, nfactors = 1)
faPia77 <- fa(DK77Pia.cor, n.obs = nDK77, nfactors = 1)
print(fa77$loadings, cutoff = 0.15)##
## Loadings:
## MR1
## QT 0.398
## IN 0.632
## MC 0.232
## DS 0.536
## CO 0.375
## S1 0.683
## MT 0.511
## LD 0.343
## PS 0.637
## LO 0.246
## AS 0.532
## LC 0.574
## NC 0.362
## S2 0.519
## AI 0.632
##
## MR1
## SS loadings 3.765
## Proportion Var 0.251print(faPsy77$loadings, cutoff = 0.15)##
## Loadings:
## MR1
## QT 0.473
## IN 0.664
## MC 0.195
## DS 0.558
## CO 0.262
## S1 0.638
## MT 0.467
## LD 0.419
## PS 0.734
##
## MR1
## SS loadings 2.422
## Proportion Var 0.269print(faPia77$loadings, cutoff = 0.15)##
## Loadings:
## MR1
## LO 0.259
## AS 0.592
## LC 0.438
## NC 0.493
## S2 0.654
## AI 0.618
##
## MR1
## SS loadings 1.662
## Proportion Var 0.277EFATOG77 <- c(0.398, 0.632, 0.232, 0.536, 0.375, 0.683, 0.511, 0.343, 0.637, 0.246, 0.532, 0.574, 0.362, 0.519, 0.632)
EFATOG77Psy <- c(0.398, 0.632, 0.232, 0.536, 0.375, 0.683, 0.511, 0.343, 0.637); EFATOG77Pia <- c(0.246, 0.532, 0.574, 0.362, 0.519, 0.632)
EFASEP77 <- c(0.473, 0.664, 0.195, 0.558, 0.262, 0.638, 0.467, 0.419, 0.734, 0.259, 0.592, 0.438, 0.493, 0.654, 0.618)
EFASEP77Psy <- c(0.473, 0.664, 0.195, 0.558, 0.262, 0.638, 0.467, 0.419, 0.734); EFASEP77Pia <- c(0.259, 0.592, 0.438, 0.493, 0.654, 0.618)
cor(EFATOG77, EFASEP77, method = "pearson"); cor(EFATOG77, EFASEP77, method = "spearman"); CONGO(EFATOG77, EFASEP77)## [1] 0.8641941## [1] 0.8203757## [1] 0.9883043cor(EFATOG77Psy, EFASEP77Psy, method = "pearson"); cor(EFATOG77Psy, EFASEP77Psy, method = "spearman"); CONGO(EFATOG77Psy, EFASEP77Psy)## [1] 0.9227877## [1] 0.9166667## [1] 0.9918101cor(EFATOG77Pia, EFASEP77Pia, method = "pearson"); cor(EFATOG77Pia, EFASEP77Pia, method = "spearman"); CONGO(EFATOG77Pia, EFASEP77Pia)## [1] 0.7557447## [1] 0.4285714## [1] 0.9833407DK771FNo <- '
gPsy =~ QT + IN + MC + DS + CO + S1 + MT + LD + PS
gPia =~ LO + AS + LC + NC + S2 + AI
gPsy ~~ 0*gPia'
DK771F <- '
gPsy =~ QT + IN + MC + DS + CO + S1 + MT + LD + PS
gPia =~ LO + AS + LC + NC + S2 + AI
gPsy ~~ gPia'
DK771FID <- '
gPsy =~ QT + IN + MC + DS + CO + S1 + MT + LD + PS
gPia =~ LO + AS + LC + NC + S2 + AI
gPsy ~~ 1*gPia'
DK77No.fit <- cfa(DK771FNo, sample.cov = DK77.cor, sample.nobs = nDK77, std.lv = T)
DK77.fit <- cfa(DK771F, sample.cov = DK77.cor, sample.nobs = nDK77, std.lv = T)
DK77ID.fit <- cfa(DK771FID, sample.cov = DK77.cor, sample.nobs = nDK77, std.lv = T)
round(cbind("No Relationship" = fitMeasures(DK77No.fit, FITM),
"Free Relationship" = fitMeasures(DK77.fit, FITM),
"Identical" = fitMeasures(DK77ID.fit, FITM)),3)## No Relationship Free Relationship Identical
## chisq 111.578 88.259 90.026
## df 90.000 89.000 90.000
## npar 30.000 31.000 30.000
## cfi 0.805 1.000 1.000
## rmsea 0.071 0.000 0.002
## rmsea.ci.lower 0.000 0.000 0.000
## rmsea.ci.upper 0.111 0.078 0.079
## aic 1941.475 1920.157 1919.923
## bic 1996.980 1977.511 1975.427
## srmr 0.179 0.089 0.089#suppressWarnings(cfaHB(DK77.fit)) <- does not work
1 - pchisq(90.026 - 88.259, 1, lower.tail = T)## [1] 0.1837538summary(DK77.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 16 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 31
##
## Number of observations 47
##
## Model Test User Model:
##
## Test statistic 88.259
## Degrees of freedom 89
## P-value (Chi-square) 0.502
##
## Model Test Baseline Model:
##
## Test statistic 215.644
## Degrees of freedom 105
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.008
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -929.078
## Loglikelihood unrestricted model (H1) -884.949
##
## Akaike (AIC) 1920.157
## Bayesian (BIC) 1977.511
## Sample-size adjusted Bayesian (BIC) 1880.283
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.078
## P-value RMSEA <= 0.05 0.769
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.089
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy =~
## QT 0.417 0.150 2.773 0.006 0.417 0.422
## IN 0.643 0.140 4.603 0.000 0.643 0.650
## MC 0.224 0.156 1.439 0.150 0.224 0.227
## DS 0.545 0.145 3.756 0.000 0.545 0.550
## CO 0.340 0.153 2.225 0.026 0.340 0.344
## S1 0.679 0.138 4.937 0.000 0.679 0.687
## MT 0.500 0.147 3.398 0.001 0.500 0.505
## LD 0.384 0.152 2.536 0.011 0.384 0.389
## PS 0.670 0.138 4.849 0.000 0.670 0.677
## gPia =~
## LO 0.250 0.159 1.573 0.116 0.250 0.252
## AS 0.558 0.148 3.765 0.000 0.558 0.564
## LC 0.576 0.147 3.909 0.000 0.576 0.583
## NC 0.403 0.155 2.606 0.009 0.403 0.407
## S2 0.541 0.149 3.629 0.000 0.541 0.547
## AI 0.647 0.144 4.486 0.000 0.647 0.654
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.876 0.096 9.101 0.000 0.876 0.876
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .QT 0.805 0.173 4.638 0.000 0.805 0.822
## .IN 0.565 0.137 4.130 0.000 0.565 0.577
## .MC 0.928 0.194 4.795 0.000 0.928 0.949
## .DS 0.682 0.154 4.424 0.000 0.682 0.697
## .CO 0.863 0.183 4.718 0.000 0.863 0.882
## .S1 0.517 0.130 3.970 0.000 0.517 0.528
## .MT 0.729 0.161 4.514 0.000 0.729 0.745
## .LD 0.831 0.178 4.675 0.000 0.831 0.849
## .PS 0.530 0.132 4.015 0.000 0.530 0.541
## .LO 0.916 0.192 4.764 0.000 0.916 0.936
## .AS 0.667 0.157 4.261 0.000 0.667 0.682
## .LC 0.647 0.154 4.200 0.000 0.647 0.661
## .NC 0.817 0.177 4.603 0.000 0.817 0.834
## .S2 0.686 0.159 4.314 0.000 0.686 0.701
## .AI 0.561 0.144 3.892 0.000 0.561 0.573
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000resid(DK77.fit, "cor"); sum(abs(resid(DK77.fit, "cor")$cov) > CRITR(47)); sum(abs(resid(DK77.fit, "cor")$cov) > CRITR(47, NP(47)))## $type
## [1] "cor.bollen"
##
## $cov
## QT IN MC DS CO S1 MT LD PS LO AS
## QT 0.000
## IN 0.176 0.000
## MC 0.004 -0.037 0.000
## DS -0.052 -0.038 -0.145 0.000
## CO 0.075 0.026 0.032 0.011 0.000
## S1 -0.120 -0.046 0.064 0.002 -0.026 0.000
## MT 0.087 0.022 0.055 -0.018 -0.024 -0.007 0.000
## LD 0.026 -0.043 -0.078 0.236 -0.284 -0.037 -0.196 0.000
## PS 0.034 0.010 -0.014 0.007 -0.133 0.045 -0.042 0.217 0.000
## LO 0.037 -0.084 0.000 -0.072 -0.016 0.168 0.048 -0.036 -0.020 0.000
## AS -0.098 0.029 0.178 -0.022 0.030 0.001 -0.030 -0.062 -0.015 -0.052 0.000
## LC -0.115 0.098 -0.066 -0.031 -0.016 0.100 0.142 0.032 0.104 -0.097 -0.059
## NC -0.030 -0.112 -0.121 -0.086 0.107 0.005 0.030 -0.109 -0.071 0.157 0.020
## S2 -0.002 -0.161 0.201 0.156 0.155 -0.019 -0.012 -0.056 -0.214 0.032 0.172
## AI -0.061 0.068 -0.050 -0.025 0.253 0.007 0.041 -0.062 -0.058 -0.005 -0.049
## LC NC S2 AI
## QT
## IN
## MC
## DS
## CO
## S1
## MT
## LD
## PS
## LO
## AS
## LC 0.000
## NC -0.117 0.000
## S2 -0.038 0.087 0.000
## AI -0.011 0.104 -0.027 0.000## [1] 0## [1] 0With a critical r of 0.29, there were no violations of local independence.
semPaths(DK77.fit, "std", title = F, residuals = F, bifactor = c("gPsy", "gPia"), pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "tree2", exoCov = T)
DeVries, 1974 (1); n = 50
fa.parallel(D74A.cor, n.obs = nD74A)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa.parallel(D74PsyA.cor, n.obs = nD74A)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa.parallel(D74PiaA.cor, n.obs = nD74A)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa74A1 <- fa(D74A.cor, n.obs = nD74A, nfactors = 1)
fa74A2 <- fa(D74A.cor, n.obs = nD74A, nfactors = 2)## Loading required namespace: GPArotationfaPsy74A1 <- fa(D74PsyA.cor, n.obs = nD74A, nfactors = 1)
faPsy74A2 <- fa(D74PsyA.cor, n.obs = nD74A, nfactors = 2)
faPia74A1 <- fa(D74PiaA.cor, n.obs = nD74A, nfactors = 1)
#faPia74A2 <- fa(D74PiaA.cor, n.obs = nD74A, nfactors = 2) #Model not called for and returns practically useless results - run if you want!
print(fa74A1$loadings, cutoff = 0.10)##
## Loadings:
## MR1
## SB 0.722
## CL 0.598
## CN 0.610
## PM 0.591
## PC 0.395
## PD 0.591
## PL 0.331
## PN 0.687
## PI 0.548
## PE 0.608
## PA 0.523
## PR 0.697
## PG 0.688
## PS 0.657
## PSI 0.506
## PT 0.349
## PGG 0.228
## POS 0.121
## MW 0.647
## MK 0.637
## MA 0.508
## MR 0.375
##
## MR1
## SS loadings 6.690
## Proportion Var 0.304print(fa74A2$loadings, cutoff = 0.10)##
## Loadings:
## MR1 MR2
## SB 0.329 0.523
## CL 0.331 0.369
## CN 0.292 0.426
## PM 0.414 0.270
## PC 0.140 0.328
## PD 0.144 0.571
## PL 0.203 0.183
## PN 0.949 -0.141
## PI 0.607
## PE 0.656
## PA 0.605
## PR 0.705
## PG 0.571 0.225
## PS 0.643 0.115
## PSI 0.389 0.197
## PT 0.349
## PGG 0.376 -0.122
## POS 0.191
## MW 0.826
## MK 0.727
## MA 0.701
## MR -0.197 0.683
##
## MR1 MR2
## SS loadings 4.201 3.606
## Proportion Var 0.191 0.164
## Cumulative Var 0.191 0.355print(faPsy74A1$loadings, cutoff = 0.10)##
## Loadings:
## MR1
## SB 0.702
## CL 0.532
## CN 0.592
## MW 0.786
## MK 0.751
## MA 0.625
## MR 0.611
##
## MR1
## SS loadings 3.072
## Proportion Var 0.439print(faPsy74A2$loadings, cutoff = 0.10)##
## Loadings:
## MR1 MR2
## SB 0.821
## CL 0.698
## CN 0.715
## MW 0.750 0.112
## MK 0.909
## MA 0.477 0.202
## MR 0.706
##
## MR1 MR2
## SS loadings 2.120 1.730
## Proportion Var 0.303 0.247
## Cumulative Var 0.303 0.550print(faPia74A1$loadings, cutoff = 0.10)##
## Loadings:
## MR1
## PM 0.527
## PC 0.316
## PD 0.463
## PL 0.319
## PN 0.843
## PI 0.622
## PE 0.664
## PA 0.594
## PR 0.748
## PG 0.725
## PS 0.708
## PSI 0.499
## PT 0.267
## PGG 0.313
## POS 0.116
##
## MR1
## SS loadings 4.601
## Proportion Var 0.307#print(faPia74A2$loadings, cutoff = 0.10)EFATOG74A <- c(0.722, 0.598, 0.610, 0.591, 0.395, 0.591, 0.331, 0.687, 0.548, 0.608, 0.523, 0.697, 0.688, 0.657, 0.506, 0.349, 0.228, 0.121, 0.647, 0.637, 0.508, 0.375)
EFATOG74APsy <- c(0.722, 0.598, 0.610, 0.647, 0.637, 0.508, 0.375); EFATOG74APia <- c(0.591, 0.395, 0.591, 0.331, 0.687, 0.548, 0.608, 0.523, 0.697, 0.688, 0.657, 0.506, 0.349, 0.228, 0.121)
EFASEP74A <- c(0.702, 0.532, 0.592, 0.527, 0.316, 0.463, 0.319, 0.843, 0.622, 0.664, 0.594, 0.748, 0.725, 0.708, 0.499, 0.267, 0.313, 0.116, 0.786, 0.751, 0.625, 0.611)
EFASEP74APsy <- c(0.702, 0.532, 0.592, 0.786, 0.751, 0.625, 0.611); EFASEP74APia <- c(0.527, 0.316, 0.463, 0.319, 0.843, 0.622, 0.664, 0.594, 0.748, 0.725, 0.708, 0.499, 0.267, 0.313, 0.116)
cor(EFATOG74A, EFASEP74A, method = "pearson"); cor(EFATOG74A, EFASEP74A, method = "spearman"); CONGO(EFATOG74A, EFASEP74A)## [1] 0.8842337## [1] 0.8410054## [1] 0.9889509cor(EFATOG74APsy, EFASEP74APsy, method = "pearson"); cor(EFATOG74APsy, EFASEP74APsy, method = "spearman"); CONGO(EFATOG74APsy, EFASEP74APsy)## [1] 0.4503779## [1] 0.6071429## [1] 0.9864973cor(EFATOG74APia, EFASEP74APia, method = "pearson"); cor(EFATOG74APia, EFASEP74APia, method = "spearman"); CONGO(EFATOG74APia, EFASEP74APia)## [1] 0.9362388## [1] 0.9294016## [1] 0.9912709D74A1FNo <- '
gPsy =~ SB + CL + CN + MW + MK + MA + MR
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG + POS
gPsy ~~ 0*gPia'
D74A1F <- '
gPsy =~ SB + CL + CN + MW + MK + MA + MR
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG + POS
gPsy ~~ gPia'
D74A1FID <- '
gPsy =~ SB + CL + CN + MW + MK + MA + MR
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG + POS
gPsy ~~ 1*gPia'
D74A2FNo <- '
SBF =~ SB + CL + CN + MW
MAT =~ MW + MK + MA + MR
gPsy =~ SBF + MAT
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG + POS
gPsy ~~ 0*gPia'
D74A2F <- '
SBF =~ SB + CL + CN + MW
MAT =~ MW + MK + MA + MR
gPsy =~ SBF + MAT
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG + POS
gPsy ~~ gPia'
D74A2FID <- '
SBF =~ SB + CL + CN + MW
MAT =~ MW + MK + MA + MR
gPsy =~ SBF + MAT
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG + POS
gPsy ~~ 1*gPia'
D74ANo1.fit <- cfa(D74A1FNo, sample.cov = D74A.cor, sample.nobs = nD74A, std.lv = T)
D74A1.fit <- cfa(D74A1F, sample.cov = D74A.cor, sample.nobs = nD74A, std.lv = T)
D74AID1.fit <- cfa(D74A1FID, sample.cov = D74A.cor, sample.nobs = nD74A, std.lv = T)
D74ANo2.fit <- cfa(D74A2FNo, sample.cov = D74A.cor, sample.nobs = nD74A, std.lv = T); "\n" #Leads to severe estimation issues## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"D74A2.fit <- cfa(D74A2F, sample.cov = D74A.cor, sample.nobs = nD74A, std.lv = T)
D74AID2.fit <- cfa(D74A2FID, sample.cov = D74A.cor, sample.nobs = nD74A, std.lv = T)
round(cbind("No Rel - 1" = fitMeasures(D74ANo1.fit, FITM),
"Free Rel- 1" = fitMeasures(D74A1.fit, FITM),
"Identical - 1" = fitMeasures(D74AID1.fit, FITM),
"No Rel - 2" = fitMeasures(D74ANo2.fit, FITM),
"Free Rel - 2" = fitMeasures(D74A2.fit, FITM),
"Identical - 2" = fitMeasures(D74AID2.fit, FITM)), 3)## No Rel - 1 Free Rel- 1 Identical - 1 No Rel - 2 Free Rel - 2
## chisq 403.237 383.919 416.131 377.211 351.978
## df 209.000 208.000 209.000 206.000 205.000
## npar 44.000 45.000 44.000 47.000 48.000
## cfi 0.598 0.636 0.572 0.646 0.696
## rmsea 0.136 0.130 0.141 0.129 0.120
## rmsea.ci.lower 0.116 0.110 0.121 0.108 0.098
## rmsea.ci.upper 0.156 0.150 0.160 0.149 0.141
## aic 2876.084 2858.766 2888.978 2856.058 2832.825
## bic 2960.213 2944.807 2973.107 2945.923 2924.602
## srmr 0.206 0.116 0.112 0.204 0.105
## Identical - 2
## chisq 354.482
## df 206.000
## npar 47.000
## cfi 0.693
## rmsea 0.120
## rmsea.ci.lower 0.099
## rmsea.ci.upper 0.141
## aic 2833.329
## bic 2923.194
## srmr 0.106#cfaHB(D74A1.fit) <- does not work
1 - pchisq(354.482 - 351.978, 1, lower.tail = T)## [1] 0.1135575summary(D74A2.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 32 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 48
##
## Number of observations 50
##
## Model Test User Model:
##
## Test statistic 351.978
## Degrees of freedom 205
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 714.595
## Degrees of freedom 231
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.696
## Tucker-Lewis Index (TLI) 0.658
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1368.412
## Loglikelihood unrestricted model (H1) -1192.424
##
## Akaike (AIC) 2832.825
## Bayesian (BIC) 2924.602
## Sample-size adjusted Bayesian (BIC) 2773.938
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.120
## 90 Percent confidence interval - lower 0.098
## 90 Percent confidence interval - upper 0.141
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.105
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SBF =~
## SB 0.413 0.195 2.121 0.034 0.867 0.876
## CL 0.305 0.147 2.081 0.037 0.641 0.647
## CN 0.333 0.157 2.123 0.034 0.701 0.708
## MW 0.084 0.076 1.105 0.269 0.176 0.178
## MAT =~
## MW 0.537 0.117 4.598 0.000 0.697 0.704
## MK 0.670 0.120 5.595 0.000 0.870 0.879
## MA 0.458 0.114 4.030 0.000 0.595 0.601
## MR 0.517 0.113 4.556 0.000 0.671 0.678
## gPsy =~
## SBF 1.848 1.078 1.714 0.087 0.879 0.879
## MAT 0.829 0.274 3.020 0.003 0.638 0.638
## gPia =~
## PM 0.550 0.134 4.090 0.000 0.550 0.556
## PC 0.337 0.142 2.366 0.018 0.337 0.340
## PD 0.483 0.137 3.511 0.000 0.483 0.488
## PL 0.315 0.143 2.202 0.028 0.315 0.318
## PN 0.796 0.119 6.668 0.000 0.796 0.804
## PI 0.614 0.131 4.681 0.000 0.614 0.620
## PE 0.678 0.127 5.322 0.000 0.678 0.685
## PA 0.578 0.133 4.344 0.000 0.578 0.584
## PR 0.743 0.123 6.024 0.000 0.743 0.750
## PG 0.711 0.125 5.669 0.000 0.711 0.718
## PS 0.704 0.126 5.595 0.000 0.704 0.711
## PSI 0.499 0.137 3.646 0.000 0.499 0.504
## PT 0.293 0.144 2.041 0.041 0.293 0.296
## PGG 0.305 0.143 2.132 0.033 0.305 0.309
## POS 0.087 0.147 0.594 0.553 0.087 0.088
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.812 0.109 7.440 0.000 0.812 0.812
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SB 0.229 0.104 2.200 0.028 0.229 0.233
## .CL 0.570 0.130 4.372 0.000 0.570 0.581
## .CN 0.489 0.120 4.092 0.000 0.489 0.499
## .MW 0.325 0.091 3.577 0.000 0.325 0.332
## .MK 0.222 0.098 2.263 0.024 0.222 0.227
## .MA 0.626 0.137 4.566 0.000 0.626 0.638
## .MR 0.530 0.122 4.332 0.000 0.530 0.541
## .PM 0.677 0.142 4.768 0.000 0.677 0.691
## .PC 0.866 0.176 4.932 0.000 0.866 0.884
## .PD 0.747 0.154 4.838 0.000 0.747 0.762
## .PL 0.881 0.178 4.942 0.000 0.881 0.899
## .PN 0.346 0.086 4.043 0.000 0.346 0.353
## .PI 0.603 0.129 4.675 0.000 0.603 0.615
## .PE 0.520 0.115 4.539 0.000 0.520 0.530
## .PA 0.646 0.136 4.731 0.000 0.646 0.659
## .PR 0.429 0.099 4.329 0.000 0.429 0.437
## .PG 0.475 0.107 4.445 0.000 0.475 0.484
## .PS 0.484 0.108 4.466 0.000 0.484 0.494
## .PSI 0.731 0.152 4.824 0.000 0.731 0.746
## .PT 0.894 0.181 4.950 0.000 0.894 0.912
## .PGG 0.887 0.179 4.946 0.000 0.887 0.905
## .POS 0.972 0.195 4.996 0.000 0.972 0.992
## .SBF 1.000 0.226 0.226
## .MAT 1.000 0.593 0.593
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000resid(D74A2.fit, "cor"); sum(abs(resid(D74A2.fit, "cor")$cov) > CRITR(50)); sum(abs(resid(D74A2.fit, "cor")$cov) > CRITR(50, NP(50)))## $type
## [1] "cor.bollen"
##
## $cov
## SB CL CN MW MK MA MR PM PC PD
## SB 0.000
## CL -0.007 0.000
## CN 0.000 0.012 0.000
## MW 0.048 -0.091 -0.046 0.000
## MK -0.002 -0.049 -0.019 -0.007 0.000
## MA 0.044 0.172 0.101 0.027 -0.019 0.000
## MR -0.043 -0.006 0.031 0.005 0.014 -0.008 0.000
## PM 0.193 0.313 0.299 -0.013 -0.033 0.047 -0.035 0.000
## PC 0.107 0.203 0.208 0.063 0.075 0.184 0.030 0.191 0.000
## PD 0.115 0.095 0.154 0.310 0.348 0.388 0.079 0.049 -0.066 0.000
## PL 0.031 0.123 -0.141 0.043 0.015 0.261 -0.042 0.013 0.042 0.085
## PN -0.173 -0.022 -0.077 -0.186 -0.026 -0.051 -0.203 -0.117 -0.134 -0.042
## PI -0.028 -0.147 -0.114 -0.015 0.037 0.147 -0.148 -0.085 -0.151 -0.022
## PE -0.009 -0.007 0.014 0.053 0.018 -0.144 -0.171 -0.151 0.007 0.016
## PA -0.155 0.030 -0.045 -0.007 0.004 0.028 -0.045 -0.035 -0.149 -0.075
## PR 0.111 0.133 0.021 -0.089 -0.032 -0.164 -0.163 0.053 0.025 0.024
## PG -0.049 -0.022 0.027 0.017 0.083 0.056 -0.032 0.101 0.086 0.020
## PS -0.015 0.001 0.000 0.020 0.076 -0.052 -0.110 0.055 0.088 -0.207
## PSI -0.005 0.067 0.015 0.172 0.090 0.103 -0.127 -0.050 0.028 -0.066
## PT 0.265 0.133 -0.030 0.194 0.095 0.128 0.096 -0.144 0.069 0.196
## PGG -0.143 -0.013 -0.096 -0.212 -0.081 0.004 -0.088 -0.101 -0.265 0.070
## POS -0.175 -0.071 -0.064 0.177 0.060 0.253 0.109 0.041 0.040 0.127
## PL PN PI PE PA PR PG PS PSI PT
## SB
## CL
## CN
## MW
## MK
## MA
## MR
## PM
## PC
## PD
## PL 0.000
## PN -0.016 0.000
## PI -0.127 0.111 0.000
## PE -0.048 0.129 0.045 0.000
## PA 0.034 0.130 0.208 0.000 0.000
## PR 0.091 0.017 -0.025 0.026 -0.118 0.000
## PG -0.059 -0.048 -0.056 -0.022 -0.039 -0.079 0.000
## PS -0.026 -0.012 -0.071 -0.087 -0.025 -0.034 0.239 0.000
## PSI 0.040 -0.025 0.037 -0.015 0.086 0.072 -0.102 0.002 0.000
## PT 0.086 -0.008 -0.194 -0.103 -0.153 0.108 -0.023 -0.061 0.071 0.000
## PGG 0.022 0.212 0.049 -0.121 0.060 -0.051 -0.032 0.051 -0.135 0.109
## POS -0.108 -0.101 0.175 -0.070 -0.041 -0.066 0.107 0.037 0.056 -0.026
## PGG POS
## SB
## CL
## CN
## MW
## MK
## MA
## MR
## PM
## PC
## PD
## PL
## PN
## PI
## PE
## PA
## PR
## PG
## PS
## PSI
## PT
## PGG 0.000
## POS 0.123 0.000## [1] 10## [1] 0With a critical r of 0.28, there were ten violations of local independence; this reduced to zero with scaling.
semPaths(D74A2.fit, "std", title = F, residuals = F, bifactor = c("gPsy", "gPia"), pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)## Warning in semPaths(D74A2.fit, "std", title = F, residuals = F, bifactor =
## c("gPsy", : 'bifactor' argument only supported in layouts 'tree2', 'tree3',
## 'circle2' and 'circle3'
DeVries, 1974 (2); n = 79
fa.parallel(D74B.cor, n.obs = nD74B)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(D74PsyB.cor, n.obs = nD74B)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa.parallel(D74PiaB.cor, n.obs = nD74B)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa74B1 <- fa(D74B.cor, n.obs = nD74B, nfactors = 1)
fa74B2 <- fa(D74B.cor, n.obs = nD74B, nfactors = 2)
faPsy74B1 <- fa(D74PsyB.cor, n.obs = nD74B, nfactors = 1)
faPia74B1 <- fa(D74PiaB.cor, n.obs = nD74B, nfactors = 1)
faPia74B2 <- fa(D74PiaB.cor, n.obs = nD74B, nfactors = 2)
print(fa74B1$loadings, cutoff = 0.05)##
## Loadings:
## MR1
## SB 0.716
## CL 0.628
## CN 0.639
## PM 0.534
## PC 0.350
## PD 0.532
## PL 0.184
## PN 0.681
## PI 0.563
## PE 0.595
## PA 0.514
## PR 0.767
## PG 0.687
## PS 0.636
## PSI 0.387
## PT 0.262
## PGG 0.274
## POS
##
## MR1
## SS loadings 5.197
## Proportion Var 0.289print(fa74B2$loadings, cutoff = 0.10)##
## Loadings:
## MR1 MR2
## SB 0.832
## CL 0.695
## CN 0.684
## PM 0.632
## PC 0.620 -0.236
## PD 0.453 0.153
## PL 0.300 -0.102
## PN 0.780
## PI 0.820
## PE 0.750
## PA 0.666
## PR 0.400 0.496
## PG 0.459 0.331
## PS 0.460 0.268
## PSI 0.202 0.250
## PT 0.319
## PGG 0.146 0.173
## POS 0.107
##
## MR1 MR2
## SS loadings 3.489 2.910
## Proportion Var 0.194 0.162
## Cumulative Var 0.194 0.355print(faPsy74B1$loadings, cutoff = 0.10)##
## Loadings:
## MR1
## SB 0.828
## CL 0.701
## CN 0.785
##
## MR1
## SS loadings 1.793
## Proportion Var 0.598print(faPia74B1$loadings, cutoff = 0.10)##
## Loadings:
## MR1
## PM 0.444
## PC 0.255
## PD 0.453
## PL 0.140
## PN 0.771
## PI 0.654
## PE 0.675
## PA 0.568
## PR 0.757
## PG 0.704
## PS 0.648
## PSI 0.381
## PT 0.225
## PGG 0.287
## POS
##
## MR1
## SS loadings 4.058
## Proportion Var 0.271print(faPia74B2$loadings, cutoff = 0.22)##
## Loadings:
## MR1 MR2
## PM 0.607
## PC -0.254 0.602
## PD 0.314
## PL 0.265
## PN 0.762
## PI 0.821
## PE 0.752
## PA 0.678
## PR 0.519 0.337
## PG 0.700
## PS 0.731
## PSI 0.269
## PT 0.332
## PGG 0.226
## POS
##
## MR1 MR2
## SS loadings 2.788 2.246
## Proportion Var 0.186 0.150
## Cumulative Var 0.186 0.336EFATOG74B <- c(0.716, 0.628, 0.639, 0.534, 0.350, 0.53, 0.184, 0.681, 0.563, 0.595, 0.514, 0.767, 0.687, 0.636, 0.387, 0.262, 0.274)
EFATOG74BPsy <- c(0.716, 0.628, 0.639); EFATOG74BPia <- c(0.534, 0.350, 0.53, 0.184, 0.681, 0.563, 0.595, 0.514, 0.767, 0.687, 0.636, 0.387, 0.262, 0.274)
EFASEP74B <- c(0.828, 0.701, 0.785, 0.444, 0.255, 0.453, 0.140, 0.771, 0.654, 0.675, 0.568, 0.757, 0.704, 0.648, 0.381, 0.225, 0.287)
EFASEP74BPsy <- c(0.828, 0.701, 0.785); EFASEP74BPia <- c(0.444, 0.255, 0.453, 0.140, 0.771, 0.654, 0.675, 0.568, 0.757, 0.704, 0.648, 0.381, 0.225, 0.287)
cor(EFATOG74B, EFASEP74B, method = "pearson"); cor(EFATOG74B, EFASEP74B, method = "spearman"); CONGO(EFATOG74B, EFASEP74B)## [1] 0.9597069## [1] 0.9436275## [1] 0.993405cor(EFATOG74BPsy, EFASEP74BPsy, method = "pearson"); cor(EFATOG74BPsy, EFASEP74BPsy, method = "spearman"); CONGO(EFATOG74BPsy, EFASEP74BPsy)## [1] 0.829317## [1] 1## [1] 0.9992701cor(EFATOG74BPia, EFASEP74BPia, method = "pearson"); cor(EFATOG74BPia, EFASEP74BPia, method = "spearman"); CONGO(EFATOG74BPia, EFASEP74BPia)## [1] 0.9624812## [1] 0.9516484## [1] 0.993586POS is removed in the CFAs for DeVries (1974 - 2) because it fails to load on anything in this sample. Sampling error, range restriction and the lack of power are more than enough to explain this.
D74B1FNo <- '
gPsy =~ SB + CL + CN
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG
gPsy ~~ 0*gPia'
D74B1F <- '
gPsy =~ SB + CL + CN
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG
gPsy ~~ gPia'
D74B1FID <- '
gPsy =~ SB + CL + CN
gPia =~ PM + PC + PD + PL + PN + PI + PE + PA + PR + PG + PS + PSI + PT + PGG
gPsy ~~ 1*gPia'
D74B2FNo <- '
Pia1 =~ PN + PI + PE + PA + PR + PSI
Pia2 =~ PM + PC + PD + PL + PG + PS + PT + PGG + PR
gPsy =~ SB + CL + CN
gPia =~ Pia1 + Pia2
gPsy ~~ 0*gPia'
D74B2F <- '
Pia1 =~ PN + PI + PE + PA + PR + PSI
Pia2 =~ PM + PC + PD + PL + PG + PS + PT + PGG + PR
gPsy =~ SB + CL + CN
gPia =~ Pia1 + Pia2
gPsy ~~ gPia'
D74B2FID <- '
Pia1 =~ PN + PI + PE + PA + PR + PSI
Pia2 =~ PM + PC + PD + PL + PG + PS + PT + PGG + PR
gPsy =~ SB + CL + CN
gPia =~ Pia1 + Pia2
gPsy ~~ 1*gPia'
D74BNo1.fit <- cfa(D74B1FNo, sample.cov = D74B.cor, sample.nobs = nD74B, std.lv = T)
D74B1.fit <- cfa(D74B1F, sample.cov = D74B.cor, sample.nobs = nD74B, std.lv = T)
D74BID1.fit <- cfa(D74B1FID, sample.cov = D74B.cor, sample.nobs = nD74B, std.lv = T)
D74BNo2.fit <- cfa(D74B2FNo, sample.cov = D74B.cor, sample.nobs = nD74B, std.lv = T); "\n" #Leads to severe estimation issues## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"D74B2.fit <- cfa(D74B2F, sample.cov = D74B.cor, sample.nobs = nD74B, std.lv = T)
D74BID2.fit <- cfa(D74B2FID, sample.cov = D74B.cor, sample.nobs = nD74B, std.lv = T)
round(cbind("No Rel - 1" = fitMeasures(D74BNo1.fit, FITM),
"Free Rel- 1" = fitMeasures(D74B1.fit, FITM),
"Identical - 1" = fitMeasures(D74BID1.fit, FITM),
"No Rel - 2" = fitMeasures(D74BNo2.fit, FITM),
"Free Rel - 2" = fitMeasures(D74B2.fit, FITM),
"Identical - 2" = fitMeasures(D74BID2.fit, FITM)),3)## No Rel - 1 Free Rel- 1 Identical - 1 No Rel - 2 Free Rel - 2
## chisq 278.164 242.787 271.287 208.949 175.633
## df 119.000 118.000 119.000 116.000 115.000
## npar 34.000 35.000 34.000 37.000 38.000
## cfi 0.669 0.741 0.684 0.807 0.874
## rmsea 0.130 0.116 0.127 0.101 0.082
## rmsea.ci.lower 0.110 0.095 0.107 0.078 0.056
## rmsea.ci.upper 0.150 0.136 0.147 0.122 0.105
## aic 3522.862 3489.485 3515.984 3459.647 3428.330
## bic 3603.423 3572.415 3596.545 3547.316 3518.369
## srmr 0.194 0.103 0.104 0.188 0.091
## Identical - 2
## chisq 180.338
## df 116.000
## npar 37.000
## cfi 0.866
## rmsea 0.084
## rmsea.ci.lower 0.059
## rmsea.ci.upper 0.107
## aic 3431.036
## bic 3518.705
## srmr 0.095#cfaHB(D74B1.fit) <- does not work
1 - pchisq(180.338-175.633, 1, lower.tail = T)## [1] 0.030075summary(D74B2.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
##
## Number of observations 79
##
## Model Test User Model:
##
## Test statistic 175.633
## Degrees of freedom 115
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 617.463
## Degrees of freedom 136
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.874
## Tucker-Lewis Index (TLI) 0.851
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1676.165
## Loglikelihood unrestricted model (H1) -1588.349
##
## Akaike (AIC) 3428.330
## Bayesian (BIC) 3518.369
## Sample-size adjusted Bayesian (BIC) 3398.553
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.056
## 90 Percent confidence interval - upper 0.105
## P-value RMSEA <= 0.05 0.023
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.091
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Pia1 =~
## PN 0.617 0.092 6.706 0.000 0.820 0.825
## PI 0.553 0.091 6.074 0.000 0.734 0.739
## PE 0.573 0.091 6.286 0.000 0.762 0.767
## PA 0.492 0.091 5.427 0.000 0.654 0.658
## PR 0.434 0.093 4.664 0.000 0.577 0.581
## PSI 0.280 0.090 3.105 0.002 0.372 0.374
## Pia2 =~
## PM 0.284 0.094 3.018 0.003 0.527 0.530
## PC 0.202 0.081 2.507 0.012 0.375 0.377
## PD 0.232 0.085 2.719 0.007 0.430 0.432
## PL 0.072 0.066 1.083 0.279 0.133 0.134
## PG 0.471 0.133 3.544 0.000 0.873 0.879
## PS 0.455 0.128 3.541 0.000 0.844 0.849
## PT 0.131 0.071 1.831 0.067 0.243 0.244
## PGG 0.145 0.073 1.981 0.048 0.268 0.270
## PR 0.130 0.069 1.890 0.059 0.242 0.243
## gPsy =~
## SB 0.839 0.099 8.430 0.000 0.839 0.844
## CL 0.693 0.105 6.576 0.000 0.693 0.697
## CN 0.765 0.102 7.473 0.000 0.765 0.770
## gPia =~
## Pia1 0.876 0.233 3.758 0.000 0.659 0.659
## Pia2 1.562 0.604 2.585 0.010 0.842 0.842
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.788 0.096 8.178 0.000 0.788 0.788
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .PN 0.315 0.073 4.284 0.000 0.315 0.319
## .PI 0.448 0.087 5.164 0.000 0.448 0.454
## .PE 0.407 0.082 4.950 0.000 0.407 0.412
## .PA 0.560 0.100 5.583 0.000 0.560 0.567
## .PR 0.441 0.081 5.466 0.000 0.441 0.447
## .PSI 0.849 0.138 6.137 0.000 0.849 0.860
## .PM 0.710 0.119 5.968 0.000 0.710 0.719
## .PC 0.847 0.138 6.152 0.000 0.847 0.858
## .PD 0.803 0.132 6.100 0.000 0.803 0.813
## .PL 0.970 0.155 6.270 0.000 0.970 0.982
## .PG 0.225 0.068 3.319 0.001 0.225 0.228
## .PS 0.275 0.070 3.929 0.000 0.275 0.279
## .PT 0.929 0.149 6.234 0.000 0.929 0.940
## .PGG 0.915 0.147 6.222 0.000 0.915 0.927
## .SB 0.284 0.085 3.331 0.001 0.284 0.287
## .CL 0.507 0.098 5.162 0.000 0.507 0.514
## .CN 0.402 0.090 4.481 0.000 0.402 0.407
## .Pia1 1.000 0.566 0.566
## .Pia2 1.000 0.291 0.291
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000resid(D74B2.fit, "cor"); sum(abs(resid(D74B2.fit, "cor")$cov) > CRITR(79)); sum(abs(resid(D74B2.fit, "cor")$cov) > CRITR(79, NP(79)))## $type
## [1] "cor.bollen"
##
## $cov
## PN PI PE PA PR PSI PM PC PD PL
## PN 0.000
## PI -0.020 0.000
## PE 0.037 -0.017 0.000
## PA 0.017 0.094 -0.044 0.000
## PR -0.011 -0.019 0.031 -0.101 0.000
## PSI -0.089 0.063 -0.107 0.064 0.152 0.000
## PM -0.013 -0.027 -0.056 -0.013 0.050 0.080 0.000
## PC -0.073 -0.155 -0.111 -0.138 -0.013 0.092 0.210 0.000
## PD 0.182 0.063 0.146 -0.038 0.135 0.010 0.051 -0.043 0.000
## PL -0.001 -0.065 -0.117 0.021 0.104 0.142 0.049 0.099 0.042 0.000
## PG 0.018 -0.010 0.046 0.009 -0.027 0.017 -0.066 -0.052 0.010 -0.058
## PS -0.019 -0.048 -0.011 -0.010 -0.050 0.044 -0.010 -0.021 -0.147 -0.044
## PT 0.128 -0.090 -0.054 -0.039 0.032 -0.031 -0.069 0.128 0.054 0.187
## PGG 0.206 0.089 -0.025 -0.038 0.017 -0.066 -0.033 -0.122 0.083 0.144
## SB -0.052 -0.014 -0.046 -0.078 0.149 0.096 0.123 0.169 0.268 0.175
## CL 0.011 -0.077 -0.007 0.082 0.147 0.105 0.265 0.185 0.230 0.098
## CN 0.000 -0.075 -0.046 0.017 0.104 0.100 0.179 0.147 0.219 0.041
## PG PS PT PGG SB CL CN
## PN
## PI
## PE
## PA
## PR
## PSI
## PM
## PC
## PD
## PL
## PG 0.000
## PS 0.054 0.000
## PT -0.045 -0.027 0.000
## PGG -0.037 0.021 0.214 0.000
## SB -0.042 -0.056 0.253 -0.001 0.000
## CL -0.096 -0.083 0.067 0.025 -0.009 0.000
## CN -0.059 -0.094 -0.055 0.002 0.000 0.013 0.000## [1] 8## [1] 0With a critical r of 0.22, there were eight violations of local independence; this reduced to zero with scaling.
semPaths(D74B2.fit, "std", title = F, residuals = F, bifactor = c("gPsy", "gPia"), pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "tree2", exoCov = T)
DeVries, 1974 (3); n = 126
fa.parallel(D74C.cor, n.obs = nD74C)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 3 and the number of components = 2fa74C1 <- fa(D74C.cor, n.obs = nD74C, nfactors = 1)
fa74C2 <- fa(D74C.cor, n.obs = nD74C, nfactors = 2)
fa74C3 <- fa(D74C.cor, n.obs = nD74C, nfactors = 3)
print(fa74C1$loadings)##
## Loadings:
## MR1
## SB 0.756
## PM 0.565
## PC 0.462
## PD 0.643
## PL 0.322
## PN 0.698
## PI 0.669
## PE 0.631
## PA 0.499
## PR 0.786
## PG 0.576
## PS 0.537
## PSI 0.291
## PT 0.284
## PGG 0.464
## POS
##
## MR1
## SS loadings 4.828
## Proportion Var 0.302print(fa74C2$loadings, cutoff = 0.30)##
## Loadings:
## MR2 MR1
## SB 0.846
## PM 0.572
## PC 0.666
## PD 0.485
## PL 0.577
## PN 0.795
## PI 0.797
## PE 0.698
## PA 0.724
## PR 0.409 0.489
## PG 0.361
## PS 0.361
## PSI
## PT 0.423
## PGG 0.445
## POS
##
## MR2 MR1
## SS loadings 2.914 2.837
## Proportion Var 0.182 0.177
## Cumulative Var 0.182 0.359print(fa74C3$loadings, cutoff = 0.30)##
## Loadings:
## MR1 MR2 MR3
## SB 0.848
## PM 0.457
## PC 0.623
## PD 0.439
## PL 0.635
## PN 0.804
## PI 0.808
## PE 0.672
## PA 0.743
## PR 0.448 0.331
## PG 0.830
## PS 0.842
## PSI
## PT 0.408
## PGG 0.495
## POS
##
## MR1 MR2 MR3
## SS loadings 2.647 2.462 1.536
## Proportion Var 0.165 0.154 0.096
## Cumulative Var 0.165 0.319 0.415EFATOG74A <- c(0.722, 0.591, 0.395, 0.591, 0.331, 0.687, 0.548, 0.608, 0.523, 0.697, 0.688, 0.657, 0.506, 0.349, 0.228)
EFATOG74B <- c(0.716, 0.534, 0.350, 0.532, 0.184, 0.681, 0.563, 0.595, 0.514, 0.767, 0.687, 0.636, 0.387, 0.262, 0.274)
EFATOG74C <- c(0.756, 0.565, 0.462, 0.643, 0.322, 0.698, 0.669, 0.631, 0.499, 0.786, 0.576, 0.537, 0.291, 0.284, 0.464)
cor(EFATOG74A, EFATOG74B, method = "pearson"); cor(EFATOG74A, EFATOG74B, method = "spearman"); CONGO(EFATOG74A, EFATOG74B)## [1] 0.9540999## [1] 0.9740844## [1] 0.9940475cor(EFATOG74A, EFATOG74C, method = "pearson"); cor(EFATOG74A, EFATOG74C, method = "spearman"); CONGO(EFATOG74A, EFATOG74C)## [1] 0.7580764## [1] 0.8275249## [1] 0.9826617cor(EFATOG74C, EFATOG74B, method = "pearson"); cor(EFATOG74C, EFATOG74B, method = "spearman"); CONGO(EFATOG74C, EFATOG74B)## [1] 0.8710679## [1] 0.8642857## [1] 0.9871956Hathaway (1972) - Kindergarten; n = 56
fa.parallel(H72K.cor, n.obs = nH72)
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa72K1 <- fa(H72K.cor, n.obs = nH72, nfactors = 1)
fa72K2 <- fa(H72K.cor, n.obs = nH72, nfactors = 2)
fa72K3 <- fa(H72K.cor, n.obs = nH72, nfactors = 3)
faPsy72K1 <- fa(H72KPsy.cor, n.obs = nH72, nfactors = 1)
faPsy72K2 <- fa(H72KPsy.cor, n.obs = nH72, nfactors = 2)
faPia72K1 <- fa(H72KPia.cor, n.obs = nH72, nfactors = 1)
#faPia72K2 <- fa(H72KPia.cor, n.obs = nH72, nfactors = 2) #produces an ultra-Heywood
print(fa72K1$loadings)##
## Loadings:
## MR1
## WINF 0.457
## WCOM 0.174
## WARI 0.168
## WSIM 0.569
## WVOC 0.492
## WPICCO 0.301
## WPICAR 0.553
## WBD 0.649
## WMAZ 0.506
## WOA 0.377
## LTOV 0.675
## LTCO 0.578
## LTP 0.527
## LOMD 0.381
## PS 0.559
## PT 0.572
## PN 0.551
## PD 0.441
## PCQ 0.349
## PCS 0.203
## PI 0.421
## PM 0.255
## PSE 0.587
##
## MR1
## SS loadings 5.148
## Proportion Var 0.224print(fa72K2$loadings, cutoff = 0.25)##
## Loadings:
## MR1 MR2
## WINF 0.279 0.292
## WCOM 0.274
## WARI
## WSIM 0.276 0.469
## WVOC 0.449
## WPICCO 0.266
## WPICAR 0.440
## WBD 0.676
## WMAZ 0.524
## WOA 0.535
## LTOV 0.797
## LTCO 0.569
## LTP 0.689
## LOMD 0.297
## PS 0.332 0.373
## PT 0.324 0.406
## PN 0.392 0.279
## PD 0.394
## PCQ 0.666
## PCS 0.624
## PI 0.374
## PM 0.273
## PSE 0.279 0.495
##
## MR1 MR2
## SS loadings 3.850 2.274
## Proportion Var 0.167 0.099
## Cumulative Var 0.167 0.266print(fa72K3$loadings, cutoff = 0.25)##
## Loadings:
## MR1 MR2 MR3
## WINF 0.271 0.310
## WCOM 0.264
## WARI
## WSIM 0.448
## WVOC 0.397
## WPICCO 0.271
## WPICAR 0.507 0.264
## WBD 0.604
## WMAZ 0.370 0.372
## WOA 0.677
## LTOV 0.749
## LTCO 0.497
## LTP 0.569 0.276
## LOMD 0.322
## PS 0.259 0.365
## PT 0.429 0.490
## PN 0.385
## PD 0.374
## PCQ 0.672
## PCS -0.268 0.600
## PI 0.743
## PM 0.348 -0.290
## PSE 0.456 0.415
##
## MR1 MR2 MR3
## SS loadings 3.271 2.296 1.580
## Proportion Var 0.142 0.100 0.069
## Cumulative Var 0.142 0.242 0.311print(faPsy72K1$loadings)##
## Loadings:
## MR1
## WINF 0.419
## WCOM 0.110
## WARI 0.169
## WSIM 0.505
## WVOC 0.511
## WPICCO 0.313
## WPICAR 0.580
## WBD 0.706
## WMAZ 0.498
## WOA 0.458
## LTOV 0.750
## LTCO 0.602
## LTP 0.570
## LOMD 0.364
##
## MR1
## SS loadings 3.504
## Proportion Var 0.250print(faPsy72K2$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2
## WINF 0.577
## WCOM 0.326
## WARI 0.225
## WSIM 0.686
## WVOC 0.505
## WPICCO 0.388
## WPICAR 0.614
## WBD 0.480 0.325
## WMAZ 0.455
## WOA 0.440
## LTOV 0.772
## LTCO 0.541
## LTP 0.797
## LOMD 0.463
##
## MR1 MR2
## SS loadings 2.427 1.916
## Proportion Var 0.173 0.137
## Cumulative Var 0.173 0.310print(faPia72K1$loadings)##
## Loadings:
## MR1
## PS 0.580
## PT 0.512
## PN 0.519
## PD 0.500
## PCQ 0.569
## PCS 0.421
## PI 0.382
## PM 0.321
## PSE 0.690
##
## MR1
## SS loadings 2.343
## Proportion Var 0.260#print(faPia72K2$loadings, cutoff = 0.2)EFATOG72HK <- c(.457, .174, .168, .569, .492, .301, .553, .649, .506, .377, .675, .578, .527, .381, .559, .572, .551, .441, .349, .203, .421, .255, .587)
EFATOG72HKPsy <- c(.457, .174, .168, .569, .492, .301, .553, .649, .506, .377, .675, .578, .527, .381); EFATOG72HKPia <- c(.559, .572, .551, .441, .349, .203, .421, .255, .587)
EFASEP72HK <- c(.419, .110, .169, .505, .511, .313, .580, .706, .498, .458, .750, .602, .570, .364, .580, .512, .519, .500, .569, .421, .382, .321, .690)
EFASEP72HKPsy <- c(.419, .110, .169, .505, .511, .313, .580, .706, .498, .458, .750, .602, .570, .364); EFASEP72HKPia <- c(.580, .512, .519, .500, .569, .421, .382, .321, .690)
cor(EFATOG72HK, EFASEP72HK, method = "pearson"); cor(EFATOG72HK, EFASEP72HK, method = "spearman"); CONGO(EFATOG72HK, EFASEP72HK)## [1] 0.8769877## [1] 0.8722511## [1] 0.9883622cor(EFATOG72HKPsy, EFASEP72HKPsy, method = "pearson"); cor(EFATOG72HKPsy, EFASEP72HKPsy, method = "spearman"); CONGO(EFATOG72HKPsy, EFASEP72HKPsy)## [1] 0.9735484## [1] 0.9472527## [1] 0.9963483cor(EFATOG72HKPia, EFASEP72HKPia, method = "pearson"); cor(EFATOG72HKPia, EFASEP72HKPia, method = "spearman"); CONGO(EFATOG72HKPia, EFASEP72HKPia)## [1] 0.69348## [1] 0.7## [1] 0.9771153H72K1FNo <- '
gPsy =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 0*gPia'
H72K1F <- '
gPsy =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ gPia'
H72K1FID <- '
gPsy =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 1*gPia'
H72K2FNo <- '
VER =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR
PERF =~ WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD
gPsy =~ VER + PERF
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 0*gPia'
H72K2F <- '
VER =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR
PERF =~ WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD
gPsy =~ VER + PERF
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ gPia'
H72K2FID <- '
VER =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR
PERF =~ WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD
gPsy =~ VER + PERF
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 1*gPia'
H72KNo1.fit <- cfa(H72K1FNo, sample.cov = H72K.cor, sample.nobs = nH72, std.lv = T)
H72K1.fit <- cfa(H72K1F, sample.cov = H72K.cor, sample.nobs = nH72, std.lv = T)
H72KID1.fit <- cfa(H72K1FID, sample.cov = H72K.cor, sample.nobs = nH72, std.lv = T)
H72KNo2.fit <- cfa(H72K2FNo, sample.cov = H72K.cor, sample.nobs = nH72, std.lv = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"H72K2.fit <- cfa(H72K2F, sample.cov = H72K.cor, sample.nobs = nH72, std.lv = T)
H72KID2.fit <- cfa(H72K2FID, sample.cov = H72K.cor, sample.nobs = nH72, std.lv = T)
round(cbind("No Rel - 1" = fitMeasures(H72KNo1.fit, FITM),
"Free Rel - 1" = fitMeasures(H72K1.fit, FITM),
"Identical - 1" = fitMeasures(H72KID1.fit, FITM),
"No Rel - 2" = fitMeasures(H72KNo2.fit, FITM),
"Free Rel - 2" = fitMeasures(H72K2.fit, FITM),
"Identical - 2" = fitMeasures(H72KID2.fit, FITM)), 3)## No Rel - 1 Free Rel - 1 Identical - 1 No Rel - 2 Free Rel - 2
## chisq 318.306 294.545 307.481 297.623 271.312
## df 230.000 229.000 230.000 228.000 227.000
## npar 46.000 47.000 46.000 48.000 49.000
## cfi 0.683 0.765 0.722 0.750 0.841
## rmsea 0.083 0.071 0.078 0.074 0.059
## rmsea.ci.lower 0.059 0.045 0.053 0.048 0.024
## rmsea.ci.upper 0.104 0.094 0.099 0.096 0.084
## aic 3510.852 3489.091 3500.027 3494.169 3469.858
## bic 3604.018 3584.282 3593.193 3591.386 3569.100
## srmr 0.165 0.103 0.104 0.162 0.096
## Identical - 2
## chisq 272.179
## df 228.000
## npar 48.000
## cfi 0.841
## rmsea 0.059
## rmsea.ci.lower 0.023
## rmsea.ci.upper 0.084
## aic 3468.725
## bic 3565.942
## srmr 0.096#cfaHB(H72K1.fit) <- does not work
1 - pchisq(294.545 - 271.312, 2, lower.tail = T)## [1] 9.016088e-061 - pchisq(272.179 - 271.312, 1, lower.tail = T)## [1] 0.3517872summary(H72K2.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 30 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 49
##
## Number of observations 56
##
## Model Test User Model:
##
## Test statistic 271.312
## Degrees of freedom 227
## P-value (Chi-square) 0.023
##
## Model Test Baseline Model:
##
## Test statistic 531.432
## Degrees of freedom 253
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.841
## Tucker-Lewis Index (TLI) 0.823
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1685.929
## Loglikelihood unrestricted model (H1) -1550.273
##
## Akaike (AIC) 3469.858
## Bayesian (BIC) 3569.100
## Sample-size adjusted Bayesian (BIC) 3415.095
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.059
## 90 Percent confidence interval - lower 0.024
## 90 Percent confidence interval - upper 0.084
## P-value RMSEA <= 0.05 0.294
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.096
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VER =~
## WINF 0.308 0.116 2.662 0.008 0.539 0.544
## WCOM 0.132 0.092 1.439 0.150 0.230 0.233
## WARI 0.130 0.091 1.419 0.156 0.227 0.229
## WSIM 0.380 0.130 2.919 0.004 0.665 0.671
## WVOC 0.317 0.117 2.702 0.007 0.555 0.560
## WPICCO 0.229 0.103 2.221 0.026 0.400 0.404
## WPICAR 0.372 0.128 2.897 0.004 0.650 0.656
## PERF =~
## WBD 0.467 0.109 4.266 0.000 0.689 0.695
## WMAZ 0.360 0.104 3.449 0.001 0.532 0.537
## WOA 0.300 0.102 2.930 0.003 0.442 0.446
## LTOV 0.532 0.114 4.674 0.000 0.786 0.793
## LTCO 0.425 0.107 3.962 0.000 0.627 0.633
## LTP 0.446 0.108 4.118 0.000 0.658 0.664
## LOMD 0.301 0.102 2.946 0.003 0.445 0.449
## gPsy =~
## VER 1.436 0.611 2.349 0.019 0.821 0.821
## PERF 1.086 0.353 3.074 0.002 0.736 0.736
## gPia =~
## PS 0.599 0.132 4.536 0.000 0.599 0.605
## PT 0.543 0.135 4.030 0.000 0.543 0.548
## PN 0.555 0.134 4.135 0.000 0.555 0.560
## PD 0.477 0.137 3.475 0.001 0.477 0.482
## PCQ 0.479 0.137 3.487 0.000 0.479 0.483
## PCS 0.328 0.142 2.304 0.021 0.328 0.331
## PI 0.455 0.138 3.290 0.001 0.455 0.459
## PM 0.291 0.143 2.029 0.042 0.291 0.293
## PSE 0.675 0.128 5.256 0.000 0.675 0.681
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.892 0.109 8.155 0.000 0.892 0.892
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .WINF 0.692 0.148 4.677 0.000 0.692 0.705
## .WCOM 0.929 0.178 5.209 0.000 0.929 0.946
## .WARI 0.931 0.179 5.212 0.000 0.931 0.948
## .WSIM 0.540 0.132 4.078 0.000 0.540 0.550
## .WVOC 0.675 0.146 4.623 0.000 0.675 0.687
## .WPICCO 0.822 0.164 5.009 0.000 0.822 0.837
## .WPICAR 0.559 0.134 4.172 0.000 0.559 0.570
## .WBD 0.508 0.116 4.393 0.000 0.508 0.517
## .WMAZ 0.699 0.142 4.908 0.000 0.699 0.712
## .WOA 0.786 0.156 5.057 0.000 0.786 0.801
## .LTOV 0.364 0.099 3.662 0.000 0.364 0.371
## .LTCO 0.589 0.127 4.654 0.000 0.589 0.600
## .LTP 0.549 0.121 4.536 0.000 0.549 0.559
## .LOMD 0.784 0.155 5.053 0.000 0.784 0.798
## .PS 0.623 0.135 4.599 0.000 0.623 0.634
## .PT 0.687 0.144 4.778 0.000 0.687 0.700
## .PN 0.674 0.142 4.744 0.000 0.674 0.687
## .PD 0.754 0.153 4.930 0.000 0.754 0.768
## .PCQ 0.753 0.153 4.927 0.000 0.753 0.766
## .PCS 0.875 0.170 5.145 0.000 0.875 0.891
## .PI 0.775 0.156 4.973 0.000 0.775 0.789
## .PM 0.898 0.173 5.180 0.000 0.898 0.914
## .PSE 0.527 0.124 4.249 0.000 0.527 0.537
## .VER 1.000 0.327 0.327
## .PERF 1.000 0.459 0.459
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000resid(H72K2.fit, "cor"); sum(abs(resid(H72K2.fit, "cor")$cov > CRITR(56))); sum(abs(resid(H72K2.fit, "cor")$cov > CRITR(56, NP(56))))## $type
## [1] "cor.bollen"
##
## $cov
## WINF WCOM WARI WSIM WVOC WPICCO WPICAR WBD WMAZ WOA
## WINF 0.000
## WCOM -0.016 0.000
## WARI 0.076 -0.133 0.000
## WSIM -0.015 0.044 0.126 0.000
## WVOC 0.056 0.140 -0.158 -0.095 0.000
## WPICCO -0.019 -0.044 -0.082 -0.001 0.074 0.000
## WPICAR -0.037 -0.083 0.020 0.000 0.033 0.065 0.000
## WBD 0.092 0.042 -0.006 0.128 0.045 -0.059 0.125 0.000
## WMAZ -0.056 0.035 -0.024 0.043 0.059 0.009 -0.033 -0.023 0.000
## WOA -0.096 -0.283 0.038 -0.041 0.129 0.141 0.173 -0.070 0.001 0.000
## LTOV 0.060 -0.081 -0.060 -0.081 0.132 -0.093 -0.004 -0.001 0.014 0.076
## LTCO 0.012 -0.059 0.033 0.014 -0.034 -0.084 0.119 0.090 -0.080 -0.052
## LTP -0.218 -0.153 -0.072 -0.129 0.026 0.038 -0.063 -0.062 0.044 0.004
## LOMD 0.013 -0.073 0.018 -0.082 -0.102 -0.109 -0.078 -0.042 -0.031 0.020
## PS 0.080 0.007 0.099 -0.047 -0.008 -0.079 0.090 0.144 0.067 -0.067
## PT 0.092 -0.013 0.028 0.071 0.066 -0.032 0.077 0.160 -0.033 0.160
## PN 0.027 -0.065 -0.114 0.085 0.121 0.055 -0.139 0.095 0.123 -0.034
## PD -0.042 0.288 -0.191 0.024 0.083 0.118 -0.061 -0.120 0.180 0.009
## PCQ -0.102 -0.002 0.089 0.083 -0.118 -0.243 -0.012 -0.150 -0.180 -0.122
## PCS -0.072 0.064 0.045 0.078 -0.115 -0.058 -0.199 -0.181 -0.016 -0.267
## PI 0.027 0.112 -0.157 0.015 0.002 -0.106 -0.140 0.061 0.268 -0.114
## PM 0.143 -0.050 0.081 -0.214 -0.100 0.083 0.089 -0.064 -0.013 0.044
## PSE -0.031 0.004 0.016 0.126 -0.159 -0.041 -0.017 -0.070 -0.020 -0.099
## LTOV LTCO LTP LOMD PS PT PN PD PCQ PCS
## WINF
## WCOM
## WARI
## WSIM
## WVOC
## WPICCO
## WPICAR
## WBD
## WMAZ
## WOA
## LTOV 0.000
## LTCO -0.082 0.000
## LTP 0.013 0.110 0.000
## LOMD 0.084 -0.054 -0.038 0.000
## PS -0.045 -0.081 -0.033 0.082 0.000
## PT 0.135 0.113 -0.099 0.189 -0.031 0.000
## PN 0.069 0.138 0.106 -0.075 0.001 -0.117 0.000
## PD -0.141 0.000 0.060 0.008 -0.041 0.046 0.040 0.000
## PCQ -0.132 -0.081 -0.101 0.108 0.028 0.055 -0.041 0.097 0.000
## PCS -0.182 -0.037 -0.244 0.093 -0.120 0.099 0.105 0.011 0.240 0.000
## PI 0.081 0.039 0.060 -0.075 0.092 -0.201 0.063 -0.071 -0.222 -0.142
## PM 0.037 -0.022 -0.088 0.004 0.103 0.209 -0.134 0.109 0.078 0.053
## PSE -0.054 0.077 0.043 -0.001 -0.032 -0.083 -0.031 -0.058 0.071 0.075
## PI PM PSE
## WINF
## WCOM
## WARI
## WSIM
## WVOC
## WPICCO
## WPICAR
## WBD
## WMAZ
## WOA
## LTOV
## LTCO
## LTP
## LOMD
## PS
## PT
## PN
## PD
## PCQ
## PCS
## PI 0.000
## PM -0.235 0.000
## PSE 0.248 -0.090 0.000## [1] 4## [1] 0There were four local independence violations but this reduced to zero with scaling.
semPaths(H72K2.fit, "std", title = F, residuals = F, pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)
Hathaway (1972) - First Grade; n = 56
fa.parallel(H72I.cor, n.obs = nH72)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 3 and the number of components = 1fa.parallel(H72IPsy.cor, n.obs = nH72)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(H72IPia.cor, n.obs = nH72)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa72K1 <- fa(H72I.cor, n.obs = nH72, nfactors = 1)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.fa72K2 <- fa(H72I.cor, n.obs = nH72, nfactors = 2)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect. Try a different factor score estimation method.fa72K3 <- fa(H72I.cor, n.obs = nH72, nfactors = 3)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done
## Warning in cor.smooth(r): The estimated weights for the factor scores are
## probably incorrect. Try a different factor score estimation method.faPsy72K1 <- fa(H72IPsy.cor, n.obs = nH72, nfactors = 1)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.faPsy72K2 <- fa(H72IPsy.cor, n.obs = nH72, nfactors = 2)## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was done## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.faPia72K1 <- fa(H72IPia.cor, n.obs = nH72, nfactors = 1)
#faPia72K2 <- fa(H72IPia.cor, n.obs = nH72, nfactors = 2) #produces an ultra-Heywood
print(fa72K1$loadings)##
## Loadings:
## MR1
## WINF 0.727
## WCOM 0.409
## WARI 0.553
## WSIM 0.487
## WVOC 0.355
## WPICCO 0.354
## WPICAR 0.623
## WBD 0.493
## WMAZ 0.445
## WOA 0.116
## LTOV 0.408
## LTCO 0.567
## LTP 0.411
## LOMD 0.346
## PS 0.626
## PT 0.609
## PN 0.514
## PD 0.474
## PCQ 0.513
## PCS 0.437
## PI 0.525
## PM 0.622
## PSE 0.647
## CATRV 0.770
## CATCOM 0.578
## CATAR 0.780
## CATAF 0.579
## CATME 0.775
## CATSP 0.645
##
## MR1
## SS loadings 8.784
## Proportion Var 0.303print(fa72K2$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2
## WINF 0.756
## WCOM 0.351
## WARI 0.555
## WSIM 0.496
## WVOC 0.328
## WPICCO 0.428
## WPICAR 0.618
## WBD 0.514
## WMAZ 0.437
## WOA -0.259 0.923
## LTOV 0.460
## LTCO 0.542
## LTP 0.436
## LOMD 0.226 0.303
## PS 0.706
## PT 0.699
## PN 0.562
## PD 0.496
## PCQ 0.603
## PCS 0.512
## PI 0.509
## PM 0.669
## PSE 0.703
## CATRV 0.574 0.526
## CATCOM 0.393 0.482
## CATAR 0.597 0.487
## CATAF 0.441 0.359
## CATME 0.618 0.415
## CATSP 0.438 0.549
##
## MR1 MR2
## SS loadings 8.176 2.523
## Proportion Var 0.282 0.087
## Cumulative Var 0.282 0.369print(fa72K3$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR3 MR2
## WINF 0.679
## WCOM 0.634
## WARI 0.511
## WSIM 0.584
## WVOC -0.297 0.762
## WPICCO 0.332 0.214
## WPICAR 0.253 0.474
## WBD 0.345 0.215
## WMAZ 0.326
## WOA 0.242 -0.876
## LTOV 0.565
## LTCO 0.333 0.325
## LTP 0.340
## LOMD 0.401
## PS 0.369 0.336 0.342
## PT 0.202 0.493 0.305
## PN 0.274 0.308 0.233
## PD 0.255 0.286
## PCQ 0.504 0.429
## PCS 0.522 0.397
## PI 0.303 0.305
## PM 0.377 0.330 0.269
## PSE 0.553 0.361
## CATRV 0.677 0.266 -0.242
## CATCOM 0.339 0.389 -0.332
## CATAR 0.808
## CATAF 0.921 -0.218
## CATME 0.418 0.529 -0.221
## CATSP 0.610 -0.298
##
## MR1 MR3 MR2
## SS loadings 4.802 4.379 2.206
## Proportion Var 0.166 0.151 0.076
## Cumulative Var 0.166 0.317 0.393print(faPsy72K1$loadings, cutoff = 0.2)##
## Loadings:
## MR1
## WINF 0.697
## WCOM 0.465
## WARI 0.525
## WSIM 0.482
## WVOC 0.393
## WPICCO 0.304
## WPICAR 0.627
## WBD 0.447
## WMAZ 0.402
## WOA 0.303
## LTOV 0.340
## LTCO 0.554
## LTP 0.381
## LOMD 0.376
## CATRV 0.824
## CATCOM 0.663
## CATAR 0.801
## CATAF 0.549
## CATME 0.813
## CATSP 0.727
##
## MR1
## SS loadings 6.262
## Proportion Var 0.313print(faPsy72K2$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2
## WINF 0.797
## WCOM 0.494
## WARI 0.529
## WSIM 0.601
## WVOC 0.592
## WPICCO 0.418
## WPICAR 0.557
## WBD 0.209 0.312
## WMAZ 0.227 0.238
## WOA 0.646 -0.310
## LTOV 0.513
## LTCO 0.275 0.371
## LTP 0.405
## LOMD 0.461
## CATRV 0.800
## CATCOM 0.522 0.237
## CATAR 0.815
## CATAF 0.818
## CATME 0.536 0.401
## CATSP 0.770
##
## MR1 MR2
## SS loadings 4.005 3.461
## Proportion Var 0.200 0.173
## Cumulative Var 0.200 0.373print(faPia72K1$loadings, cutoff = 0.2)##
## Loadings:
## MR1
## PS 0.698
## PT 0.607
## PN 0.586
## PD 0.430
## PCQ 0.680
## PCS 0.533
## PI 0.489
## PM 0.626
## PSE 0.708
##
## MR1
## SS loadings 3.262
## Proportion Var 0.362#print(faPia72K2$loadings, cutoff = 0.2)EFATOG72HI <- c(.727, .409, .553, .487, .355, .354, .623, .493, .445, .116, .408, .567, .411, .346, .626, .609, .514, .474, .513, .437, .525, .622, .647, .770, .578, .780, .579, .775, .645)
EFATOG72HIPsy <- c(.727, .409, .553, .487, .355, .354, .623, .493, .445, .116, .408, .567, .411, .346, .770, .578, .780, .579, .775, .645); EFATOG72HIPia <- c(.626, .609, .514, .474, .513, .437, .525, .622, .647)
EFASEP72HI <- c(.697, .465, .525, .482, .393, .304, .627, .447, .402, .303, .340, .554, .381, .376, .698, .607, .586, .430, .680, .533, .489, .626, .708, .824, .663, .801, .549, .813, .727)
EFASEP72HIPsy <- c(.697, .465, .525, .482, .393, .304, .627, .447, .402, .303, .340, .554, .381, .376, .824, .663, .801, .549, .813, .727); EFASEP72HIPia <- c(.698, .607, .586, .430, .680, .533, .489, .626, .708)
cor(EFATOG72HI, EFASEP72HI, method = "pearson"); cor(EFATOG72HI, EFASEP72HI, method = "spearman"); CONGO(EFATOG72HI, EFASEP72HI)## [1] 0.9116304## [1] 0.9374384## [1] 0.9938031cor(EFATOG72HIPsy, EFASEP72HIPsy, method = "pearson"); cor(EFATOG72HIPsy, EFASEP72HIPsy, method = "spearman"); CONGO(EFATOG72HIPsy, EFASEP72HIPsy)## [1] 0.9375847## [1] 0.9609023## [1] 0.9942007cor(EFATOG72HIPia, EFASEP72HIPia, method = "pearson"); cor(EFATOG72HIPia, EFASEP72HIPia, method = "spearman"); CONGO(EFATOG72HIPia, EFASEP72HIPia)## [1] 0.7066751## [1] 0.7333333## [1] 0.9940796NPD makes JCFA impossible with this data unless I selectively remove variables. The result when doing so is always practically identical g factors, but removing so many variables, so selectively, makes the analysis hard to interpret legitimately.
Hathaway (1972) - Second Grade; n = 56
fa.parallel(H72II.cor, n.obs = nH72)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa.parallel(H72IIPsy.cor, n.obs = nH72)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(H72IIPia.cor, n.obs = nH72)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa72K1 <- fa(H72II.cor, n.obs = nH72, nfactors = 1)
fa72K2 <- fa(H72II.cor, n.obs = nH72, nfactors = 2)
fa72K3 <- fa(H72II.cor, n.obs = nH72, nfactors = 3)
faPsy72K1 <- fa(H72IIPsy.cor, n.obs = nH72, nfactors = 1)
faPsy72K2 <- fa(H72IIPsy.cor, n.obs = nH72, nfactors = 2)
faPia72K1 <- fa(H72IIPia.cor, n.obs = nH72, nfactors = 1)
faPia72K2 <- fa(H72IIPia.cor, n.obs = nH72, nfactors = 2)
print(fa72K1$loadings)##
## Loadings:
## MR1
## WINF 0.727
## WCOM 0.360
## WARI 0.431
## WSIM 0.402
## WVOC 0.478
## WPICCO 0.462
## WPICAR 0.444
## WBD 0.559
## WMAZ 0.427
## WOA 0.275
## LTOV 0.560
## LTCO 0.591
## LTP 0.560
## LOMD 0.382
## PS 0.578
## PT 0.479
## PN 0.405
## PD 0.545
## PCQ 0.538
## PCS 0.481
## PI 0.475
## PM 0.545
## PSE 0.478
## CATRV 0.736
## CATCOM 0.756
## CATAR 0.894
## CATAF 0.771
## CATME 0.644
## CATSP 0.668
##
## MR1
## SS loadings 9.001
## Proportion Var 0.310print(fa72K2$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2
## WINF 0.687
## WCOM 0.515
## WARI 0.331
## WSIM 0.559
## WVOC 0.708
## WPICCO 0.537
## WPICAR 0.686
## WBD 0.302 0.344
## WMAZ 0.422
## WOA 0.540 -0.278
## LTOV 0.228 0.434
## LTCO 0.283 0.408
## LTP 0.425 0.204
## LOMD 0.419
## PS 0.589
## PT 0.491
## PN 0.393
## PD 0.282 0.349
## PCQ 0.439
## PCS 0.308 0.240
## PI 0.288 0.256
## PM 0.273 0.361
## PSE 0.499
## CATRV 0.863
## CATCOM 0.666
## CATAR 0.817
## CATAF 0.803
## CATME 0.648
## CATSP 0.848
##
## MR1 MR2
## SS loadings 6.000 3.824
## Proportion Var 0.207 0.132
## Cumulative Var 0.207 0.339print(fa72K3$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2 MR3
## WINF 0.521 0.323
## WCOM 0.465
## WARI 0.254
## WSIM 0.313 0.498
## WVOC 0.664
## WPICCO 0.510
## WPICAR 0.698
## WBD 0.288 0.237 0.209
## WMAZ 0.439
## WOA 0.494 -0.284
## LTOV 0.213 0.300 0.259
## LTCO 0.399 0.547 -0.209
## LTP 0.382 0.237
## LOMD 0.459
## PS 0.505 0.325
## PT 0.383 -0.200 0.425
## PN 0.285 0.207
## PD 0.256 0.229 0.244
## PCQ 0.840
## PCS 0.493
## PI 0.228 0.325
## PM 0.274 0.271
## PSE 0.508
## CATRV 0.849
## CATCOM 0.715 0.213
## CATAR 0.808
## CATAF 0.798
## CATME 0.685
## CATSP 0.823
##
## MR1 MR2 MR3
## SS loadings 5.744 2.754 2.128
## Proportion Var 0.198 0.095 0.073
## Cumulative Var 0.198 0.293 0.366print(faPsy72K1$loadings, cutoff = 0.2)##
## Loadings:
## MR1
## WINF 0.728
## WCOM 0.366
## WARI 0.418
## WSIM 0.381
## WVOC 0.507
## WPICCO 0.491
## WPICAR 0.455
## WBD 0.547
## WMAZ 0.451
## WOA 0.260
## LTOV 0.531
## LTCO 0.621
## LTP 0.536
## LOMD 0.395
## CATRV 0.749
## CATCOM 0.774
## CATAR 0.893
## CATAF 0.768
## CATME 0.671
## CATSP 0.687
##
## MR1
## SS loadings 6.839
## Proportion Var 0.342print(faPsy72K2$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2
## WINF 0.237 0.668
## WCOM 0.533
## WARI 0.208 0.286
## WSIM 0.554
## WVOC 0.672
## WPICCO 0.533
## WPICAR 0.718
## WBD 0.298 0.345
## WMAZ 0.443
## WOA 0.552 -0.322
## LTOV 0.244 0.390
## LTCO 0.323 0.410
## LTP 0.399 0.208
## LOMD 0.490
## CATRV 0.845
## CATCOM 0.685
## CATAR 0.816
## CATAF 0.820
## CATME 0.649
## CATSP 0.844
##
## MR1 MR2
## SS loadings 4.927 3.047
## Proportion Var 0.246 0.152
## Cumulative Var 0.246 0.399print(faPia72K1$loadings, cutoff = 0.2)##
## Loadings:
## MR1
## PS 0.622
## PT 0.520
## PN 0.473
## PD 0.650
## PCQ 0.741
## PCS 0.562
## PI 0.491
## PM 0.480
## PSE 0.363
##
## MR1
## SS loadings 2.772
## Proportion Var 0.308print(faPia72K2$loadings, cutoff = 0.2)##
## Loadings:
## MR1 MR2
## PS 0.785
## PT 0.538
## PN 0.765
## PD 0.250 0.516
## PCQ 0.409 0.438
## PCS 0.201 0.456
## PI 0.453
## PM 0.407
## PSE 0.479
##
## MR1 MR2
## SS loadings 1.656 1.437
## Proportion Var 0.184 0.160
## Cumulative Var 0.184 0.344EFATOG72HII <- c(.727, .360, .431, .402, .478, .462, .444, .559, .427, .275, .560, .591, .560, .382, .578, .479, .405, .545, .538, .481, .475, .545, .478, .736, .756, .894, .771, .644, .668)
EFATOG72HIIPsy <- c(.727, .360, .431, .402, .478, .462, .444, .559, .427, .275, .560, .591, .560, .382, .736, .756, .894, .771, .644, .668); EFATOG72HIIPia <- c(.578, .479, .405, .545, .538, .481, .475, .545, .478)
EFASEP72HII <- c(.728, .366, .418, .381, .507, .491, .455, .547, .451, .260, .531, .621, .536, .395, .622, .520, .473, .650, .741, .562, .491, .480, .363, .749, .774, .893, .768, .671, .687)
EFASEP72HIIPsy <- c(.728, .366, .418, .381, .507, .491, .455, .547, .451, .260, .531, .621, .536, .395, .749, .774, .893, .768, .671, .687); EFASEP72HIIPia <- c(.622, .520, .473, .650, .741, .562, .491, .480, .363)
cor(EFATOG72HII, EFASEP72HII, method = "pearson"); cor(EFATOG72HII, EFASEP72HII, method = "spearman"); CONGO(EFATOG72HII, EFASEP72HII)## [1] 0.931689## [1] 0.9132578## [1] 0.9955797cor(EFATOG72HIIPsy, EFASEP72HIIPsy, method = "pearson"); cor(EFATOG72HIIPsy, EFASEP72HIIPsy, method = "spearman"); CONGO(EFATOG72HIIPsy, EFASEP72HIIPsy)## [1] 0.9935642## [1] 0.990598## [1] 0.9994974cor(EFATOG72HIIPia, EFASEP72HIIPia, method = "pearson"); cor(EFATOG72HIIPia, EFASEP72HIIPia, method = "spearman"); CONGO(EFATOG72HIIPia, EFASEP72HIIPia)## [1] 0.5787404## [1] 0.6276206## [1] 0.98763H72II1FNo <- '
gPsy =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD + CATRV + CATCOM + CATAR + CATAF + CATME + CATSP
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 0*gPia'
H72II1F <- '
gPsy =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD + CATRV + CATCOM + CATAR + CATAF + CATME + CATSP
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ gPia'
H72II1FID <- '
gPsy =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + WBD + WMAZ + WOA + LTOV + LTCO + LTP + LOMD + CATRV + CATCOM + CATAR + CATAF + CATME + CATSP
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 1*gPia'
H72II2FNo <- '
PERF =~ WMAZ + WOA + LTP + LOMD + CATRV + CATCOM + CATAR + CATAF + CATME + CATSP
VER =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + LTOV + LTCO
gPsy =~ VER + PERF
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 0*gPia'
H72II2F <- '
PERF =~ WMAZ + WOA + LTP + LOMD + CATRV + CATCOM + CATAR + CATAF + CATME + CATSP
VER =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + LTOV + LTCO
gPsy =~ VER + PERF
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ gPia'
H72II2FID <- '
PERF =~ WMAZ + WOA + LTP + LOMD + CATRV + CATCOM + CATAR + CATAF + CATME + CATSP
VER =~ WINF + WCOM + WARI + WSIM + WVOC + WPICCO + WPICAR + LTOV + LTCO
gPsy =~ VER + PERF
gPia =~ PS + PT + PN + PD + PCQ + PCS + PI + PM + PSE
gPsy ~~ 1*gPia'
H72IINo1.fit <- cfa(H72II1FNo, sample.cov = H72II.cor, sample.nobs = nH72, std.lv = T)
H72II1.fit <- cfa(H72II1F, sample.cov = H72II.cor, sample.nobs = nH72, std.lv = T)
H72IIID1.fit <- cfa(H72II1FID, sample.cov = H72II.cor, sample.nobs = nH72, std.lv = T)
H72IINo2.fit <- cfa(H72II2FNo, sample.cov = H72II.cor, sample.nobs = nH72, std.lv = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"H72II2.fit <- cfa(H72II2F, sample.cov = H72II.cor, sample.nobs = nH72, std.lv = T)
H72IIID2.fit <- cfa(H72II2FID, sample.cov = H72II.cor, sample.nobs = nH72, std.lv = T)
round(cbind("No Rel - 1" = fitMeasures(H72IINo1.fit, FITM),
"Free Rel - 1" = fitMeasures(H72II1.fit, FITM),
"Identical - 1" = fitMeasures(H72IIID1.fit, FITM),
"No Rel - 2" = fitMeasures(H72IINo2.fit, FITM),
"Free Rel - 2" = fitMeasures(H72II2.fit, FITM),
"Identical - 2" = fitMeasures(H72IIID2.fit, FITM)), 3)## No Rel - 1 Free Rel - 1 Identical - 1 No Rel - 2 Free Rel - 2
## chisq 593.095 553.396 566.337 506.032 465.462
## df 377.000 376.000 377.000 348.000 347.000
## npar 58.000 59.000 58.000 58.000 59.000
## cfi 0.680 0.737 0.719 0.757 0.818
## rmsea 0.101 0.092 0.095 0.090 0.078
## rmsea.ci.lower 0.085 0.075 0.078 0.072 0.058
## rmsea.ci.upper 0.116 0.108 0.110 0.107 0.096
## aic 4208.212 4170.512 4181.453 4014.375 3975.805
## bic 4325.682 4290.008 4298.924 4131.845 4095.301
## srmr 0.204 0.102 0.103 0.201 0.095
## Identical - 2
## chisq 466.577
## df 348.000
## npar 58.000
## cfi 0.818
## rmsea 0.078
## rmsea.ci.lower 0.058
## rmsea.ci.upper 0.096
## aic 3974.920
## bic 4092.390
## srmr 0.095#cfaHB(H72II1.fit) <- does not work
1 - pchisq(553.396 - 465.462, 376 - 347, lower.tail = T)## [1] 7.544906e-081 - pchisq(466.577 - 465.462, 1, lower.tail = T)## [1] 0.2909976summary(H72II2.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 43 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 59
##
## Number of observations 56
##
## Model Test User Model:
##
## Test statistic 465.462
## Degrees of freedom 347
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1029.195
## Degrees of freedom 378
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.818
## Tucker-Lewis Index (TLI) 0.802
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1928.902
## Loglikelihood unrestricted model (H1) -1696.172
##
## Akaike (AIC) 3975.805
## Bayesian (BIC) 4095.301
## Sample-size adjusted Bayesian (BIC) 3909.866
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.078
## 90 Percent confidence interval - lower 0.058
## 90 Percent confidence interval - upper 0.096
## P-value RMSEA <= 0.05 0.012
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.095
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## PERF =~
## WMAZ 0.221 0.079 2.802 0.005 0.436 0.440
## WOA 0.157 0.074 2.115 0.034 0.309 0.312
## LTP 0.264 0.083 3.184 0.001 0.520 0.525
## LOMD 0.193 0.077 2.510 0.012 0.379 0.383
## CATRV 0.408 0.099 4.120 0.000 0.804 0.811
## CATCOM 0.405 0.099 4.107 0.000 0.798 0.806
## CATAR 0.475 0.108 4.386 0.000 0.935 0.943
## CATAF 0.404 0.098 4.100 0.000 0.796 0.803
## CATME 0.338 0.091 3.728 0.000 0.666 0.672
## CATSP 0.398 0.098 4.073 0.000 0.785 0.792
## VER =~
## WINF 0.510 0.099 5.157 0.000 0.819 0.827
## WCOM 0.308 0.092 3.365 0.001 0.495 0.499
## WARI 0.259 0.091 2.861 0.004 0.416 0.420
## WSIM 0.317 0.092 3.460 0.001 0.510 0.515
## WVOC 0.401 0.094 4.266 0.000 0.644 0.650
## WPICCO 0.343 0.092 3.711 0.000 0.551 0.556
## WPICAR 0.372 0.093 3.990 0.000 0.597 0.603
## LTOV 0.353 0.093 3.809 0.000 0.567 0.572
## LTCO 0.385 0.093 4.114 0.000 0.618 0.624
## gPsy =~
## VER 1.258 0.341 3.692 0.000 0.783 0.783
## PERF 1.698 0.528 3.217 0.001 0.862 0.862
## gPia =~
## PS 0.633 0.127 4.999 0.000 0.633 0.638
## PT 0.538 0.131 4.099 0.000 0.538 0.543
## PN 0.460 0.134 3.422 0.001 0.460 0.464
## PD 0.614 0.128 4.811 0.000 0.614 0.619
## PCQ 0.653 0.126 5.200 0.000 0.653 0.659
## PCS 0.547 0.131 4.180 0.000 0.547 0.552
## PI 0.493 0.133 3.708 0.000 0.493 0.498
## PM 0.540 0.131 4.116 0.000 0.540 0.545
## PSE 0.429 0.136 3.165 0.002 0.429 0.433
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.924 0.073 12.747 0.000 0.924 0.924
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .WMAZ 0.792 0.152 5.222 0.000 0.792 0.806
## .WOA 0.887 0.169 5.260 0.000 0.887 0.903
## .LTP 0.712 0.137 5.182 0.000 0.712 0.725
## .LOMD 0.838 0.160 5.242 0.000 0.838 0.854
## .CATRV 0.336 0.071 4.718 0.000 0.336 0.342
## .CATCOM 0.345 0.073 4.741 0.000 0.345 0.351
## .CATAR 0.108 0.037 2.917 0.004 0.108 0.110
## .CATAF 0.349 0.073 4.753 0.000 0.349 0.356
## .CATME 0.539 0.107 5.051 0.000 0.539 0.549
## .CATSP 0.366 0.076 4.792 0.000 0.366 0.372
## .WINF 0.311 0.086 3.618 0.000 0.311 0.316
## .WCOM 0.737 0.146 5.037 0.000 0.737 0.751
## .WARI 0.809 0.158 5.128 0.000 0.809 0.824
## .WSIM 0.722 0.144 5.015 0.000 0.722 0.735
## .WVOC 0.567 0.120 4.726 0.000 0.567 0.577
## .WPICCO 0.679 0.137 4.949 0.000 0.679 0.691
## .WPICAR 0.626 0.129 4.853 0.000 0.626 0.637
## .LTOV 0.661 0.134 4.918 0.000 0.661 0.673
## .LTCO 0.600 0.125 4.801 0.000 0.600 0.611
## .PS 0.582 0.124 4.690 0.000 0.582 0.592
## .PT 0.693 0.141 4.929 0.000 0.693 0.705
## .PN 0.771 0.152 5.054 0.000 0.771 0.785
## .PD 0.605 0.127 4.748 0.000 0.605 0.616
## .PCQ 0.556 0.120 4.621 0.000 0.556 0.566
## .PCS 0.683 0.139 4.911 0.000 0.683 0.696
## .PI 0.739 0.148 5.006 0.000 0.739 0.752
## .PM 0.691 0.140 4.925 0.000 0.691 0.703
## .PSE 0.798 0.157 5.092 0.000 0.798 0.813
## .PERF 1.000 0.258 0.258
## .VER 1.000 0.387 0.387
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000resid(H72II2.fit, "cor"); sum(abs(resid(H72II2.fit, "cor")$cov > CRITR(56))); sum(abs(resid(H72II2.fit, "cor")$cov > CRITR(56, NP(56))))## $type
## [1] "cor.bollen"
##
## $cov
## WMAZ WOA LTP LOMD CATRV CATCOM CATAR CATAF CATME CATSP
## WMAZ 0.000
## WOA 0.183 0.000
## LTP -0.141 -0.004 0.000
## LOMD 0.022 0.331 0.019 0.000
## CATRV -0.057 0.017 -0.046 0.070 0.000
## CATCOM 0.025 -0.051 -0.023 0.022 -0.024 0.000
## CATAR 0.015 -0.044 -0.015 -0.061 -0.015 0.040 0.000
## CATAF 0.087 0.110 -0.001 0.093 -0.031 -0.027 -0.007 0.000
## CATME -0.016 -0.060 0.038 -0.057 0.115 0.029 -0.054 0.021 0.000
## CATSP -0.069 0.053 0.034 0.007 0.107 -0.118 0.013 0.004 0.058 0.000
## WINF 0.004 -0.014 0.217 -0.013 -0.042 0.021 0.024 0.102 0.015 -0.042
## WCOM -0.088 -0.145 0.073 -0.029 -0.103 -0.061 -0.038 -0.050 -0.106 -0.097
## WARI 0.265 -0.098 0.001 0.022 0.070 0.052 0.053 0.143 0.070 -0.074
## WSIM -0.073 -0.118 0.018 -0.133 -0.052 -0.130 -0.058 -0.089 -0.043 -0.105
## WVOC 0.077 -0.147 0.020 0.122 -0.116 -0.103 -0.104 -0.082 -0.075 -0.117
## WPICCO 0.055 -0.097 0.083 0.017 -0.044 0.038 0.026 -0.031 0.038 -0.077
## WPICAR -0.099 -0.287 -0.033 -0.156 -0.130 0.063 0.007 -0.136 -0.023 -0.192
## LTOV 0.050 0.050 0.028 0.142 0.057 0.149 0.106 -0.060 0.061 -0.076
## LTCO -0.025 -0.131 0.129 0.199 0.019 0.201 0.093 0.082 0.277 0.037
## PS -0.044 0.111 0.073 0.025 0.087 0.030 0.070 0.082 0.028 -0.023
## PT -0.090 -0.035 0.173 -0.135 0.109 0.032 0.112 -0.027 -0.010 0.128
## PN -0.103 -0.025 -0.084 0.149 -0.140 0.002 -0.009 0.053 -0.128 -0.143
## PD -0.047 -0.064 0.031 0.141 -0.090 0.023 -0.035 -0.026 -0.011 -0.141
## PCQ -0.101 -0.074 0.105 -0.101 -0.165 -0.153 -0.125 -0.121 -0.102 -0.146
## PCS -0.013 0.033 0.029 -0.158 -0.006 -0.054 0.025 0.027 -0.055 0.022
## PI 0.095 0.136 0.242 0.118 -0.092 -0.120 -0.024 0.052 -0.036 -0.164
## PM -0.051 -0.005 -0.018 -0.026 0.038 0.091 0.131 0.052 -0.001 -0.024
## PSE 0.198 0.082 0.129 0.018 0.120 0.092 0.075 0.193 0.168 0.077
## WINF WCOM WARI WSIM WVOC WPICCO WPICAR LTOV LTCO PS
## WMAZ
## WOA
## LTP
## LOMD
## CATRV
## CATCOM
## CATAR
## CATAF
## CATME
## CATSP
## WINF 0.000
## WCOM 0.037 0.000
## WARI 0.003 -0.090 0.000
## WSIM 0.034 0.073 0.094 0.000
## WVOC -0.018 0.145 0.087 0.015 0.000
## WPICCO 0.010 -0.048 0.037 0.104 -0.051 0.000
## WPICAR 0.002 -0.031 -0.193 -0.060 0.048 0.115 0.000
## LTOV -0.073 -0.046 -0.070 0.006 0.088 -0.118 -0.005 0.000
## LTCO -0.026 -0.051 -0.012 -0.201 -0.015 0.003 0.114 0.083 0.000
## PS -0.052 -0.061 -0.074 0.012 -0.190 -0.137 -0.128 0.136 -0.048 0.000
## PT -0.075 -0.026 -0.165 0.088 -0.245 -0.208 -0.107 0.225 -0.095 0.144
## PN -0.008 0.102 0.009 -0.133 0.092 0.053 0.088 0.108 0.001 -0.106
## PD -0.051 -0.054 0.052 -0.031 -0.111 0.121 0.000 0.014 0.151 -0.015
## PCQ 0.136 -0.138 0.060 0.235 -0.020 -0.075 -0.117 0.127 -0.087 0.020
## PCS 0.060 -0.179 0.242 0.004 -0.060 0.088 -0.071 -0.088 -0.239 -0.142
## PI 0.102 -0.030 0.089 0.075 0.006 -0.100 -0.067 0.214 0.085 0.002
## PM 0.054 0.093 0.144 0.007 0.034 -0.059 0.083 0.165 0.114 -0.038
## PSE 0.041 0.024 0.218 -0.121 -0.064 0.006 0.021 -0.119 0.135 0.114
## PT PN PD PCQ PCS PI PM PSE
## WMAZ
## WOA
## LTP
## LOMD
## CATRV
## CATCOM
## CATAR
## CATAF
## CATME
## CATSP
## WINF
## WCOM
## WARI
## WSIM
## WVOC
## WPICCO
## WPICAR
## LTOV
## LTCO
## PS
## PT 0.000
## PN -0.082 0.000
## PD -0.096 0.203 0.000
## PCQ 0.013 0.014 0.092 0.000
## PCS -0.010 0.094 -0.102 0.217 0.000
## PI 0.050 -0.081 0.032 0.032 -0.065 0.000
## PM -0.066 0.077 0.013 -0.089 0.030 -0.051 0.000
## PSE -0.085 -0.161 -0.008 -0.085 0.001 0.045 -0.156 0.000## [1] 6## [1] 0There were six local independence violations but this reduced to zero with scaling.
semPaths(H72II2.fit, "std", title = F, residuals = F, pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)
Kiga (4-to-6-Year Olds); n = 39
fa.parallel(Kiga46[, 3:10])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 3 and the number of components = 1fa.parallel(Kiga46[, 3:6])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa.parallel(Kiga46[, 7:10])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 0 and the number of components = 1fak461 <- fa(Kiga46[, 3:10], nfactors = 1)
fak462 <- fa(Kiga46[, 3:10], nfactors = 2)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefullyfak463 <- fa(Kiga46[, 3:10], nfactors = 3)
faPsyk46 <- fa(Kiga46[, 3:6], nfactors = 1)
faPiak46 <- fa(Kiga46[, 7:10], nfactors = 1)
print(fak461$loadings)##
## Loadings:
## MR1
## RAVEN1 0.660
## RAVEN2 0.559
## RAVEN3 0.329
## RAVEN4 0.615
## PIAGET1 0.372
## PIAGET2 0.639
## PIAGET3
## PIAGET4 0.372
##
## MR1
## SS loadings 1.92
## Proportion Var 0.24print(fak462$loadings)##
## Loadings:
## MR1 MR2
## RAVEN1 0.723 0.284
## RAVEN2 0.551 -0.122
## RAVEN3 0.349 0.274
## RAVEN4 0.608 -0.124
## PIAGET1 0.373 -0.267
## PIAGET2 0.630 -0.194
## PIAGET3 1.001
## PIAGET4 0.362
##
## MR1 MR2
## SS loadings 1.983 1.303
## Proportion Var 0.248 0.163
## Cumulative Var 0.248 0.411print(fak463$loadings)##
## Loadings:
## MR1 MR2 MR3
## RAVEN1 0.862 0.227
## RAVEN2 0.615 -0.238
## RAVEN3 0.395 0.432
## RAVEN4 0.645 -0.230
## PIAGET1 -0.216 0.425
## PIAGET2 0.285 -0.169 0.522
## PIAGET3 0.882
## PIAGET4 -0.105 0.710
##
## MR1 MR2 MR3
## SS loadings 1.642 1.171 1.145
## Proportion Var 0.205 0.146 0.143
## Cumulative Var 0.205 0.352 0.495print(faPsyk46$loadings)##
## Loadings:
## MR1
## RAVEN1 0.845
## RAVEN2 0.565
## RAVEN3 0.265
## RAVEN4 0.642
##
## MR1
## SS loadings 1.517
## Proportion Var 0.379print(faPiak46$loadings)##
## Loadings:
## MR1
## PIAGET1 0.470
## PIAGET2 0.749
## PIAGET3 -0.224
## PIAGET4 0.558
##
## MR1
## SS loadings 1.143
## Proportion Var 0.286EFATOGK46 <- c(.660, .559, .329, .615, .372, .639, 0, .372)
EFATOGK46Psy <- c(.660, .559, .329, .615); EFATOGK46Pia <- c(.372, .639, 0, .372)
EFASEPK46 <- c(.845, .565, .265, .642, .470, .749, -.224, .558)
EFASEPK46Psy <- c(.845, .565, .265, .642); EFASEPK46Pia <- c(.470, .749, -.224, .558)
cor(EFATOGK46, EFASEPK46, method = "pearson"); cor(EFATOGK46, EFASEPK46, method = "spearman"); CONGO(EFATOGK46, EFASEPK46)## [1] 0.9579058## [1] 0.9940298## [1] 0.9810874cor(EFATOGK46Psy, EFASEPK46Psy, method = "pearson"); cor(EFATOGK46Psy, EFASEPK46Psy, method = "spearman"); CONGO(EFATOGK46Psy, EFASEPK46Psy)## [1] 0.9671078## [1] 1## [1] 0.9909776cor(EFATOGK46Pia, EFASEPK46Pia, method = "pearson"); cor(EFATOGK46Pia, EFASEPK46Pia, method = "spearman"); CONGO(EFATOGK46Pia, EFASEPK46Pia)## [1] 0.969075## [1] 0.9486833## [1] 0.9728287KigaModNo <- '
gRav =~ RAVEN1 + RAVEN2 + RAVEN3 + RAVEN4
gPia =~ PIAGET1 + PIAGET2 + PIAGET3 + PIAGET4
gRav ~~ 0*gPia
PIAGET3 ~~ RAVEN1 + RAVEN3'
KigaMod <- '
gRav =~ RAVEN1 + RAVEN2 + RAVEN3 + RAVEN4
gPia =~ PIAGET1 + PIAGET2 + PIAGET3 + PIAGET4
gRav ~~ gPia
PIAGET3 ~~ RAVEN1 + RAVEN3'
KigaModID <- '
gRav =~ RAVEN1 + RAVEN2 + RAVEN3 + RAVEN4
gPia =~ PIAGET1 + PIAGET2 + PIAGET3 + PIAGET4
gRav ~~ 1*gPia
PIAGET3 ~~ RAVEN1 + RAVEN3'
KigaNo.fit <- cfa(KigaModNo, data = Kiga46, std.lv = T)
Kiga.fit <- cfa(KigaMod, data = Kiga46, std.lv = T)
KigaID.fit <- cfa(KigaModID, data = Kiga46, std.lv = T)
round(cbind("No Relationship" = fitMeasures(KigaNo.fit, FITM),
"Free Relationship" = fitMeasures(Kiga.fit, FITM),
"Identical" = fitMeasures(KigaID.fit, FITM)),3)## No Relationship Free Relationship Identical
## chisq 22.891 16.380 21.623
## df 18.000 17.000 18.000
## npar 18.000 19.000 18.000
## cfi 0.894 1.000 0.921
## rmsea 0.083 0.000 0.072
## rmsea.ci.lower 0.000 0.000 0.000
## rmsea.ci.upper 0.174 0.140 0.167
## aic 825.545 821.034 824.276
## bic 855.489 852.642 854.220
## srmr 0.148 0.083 0.099#cfaHB(Kiga.fit) #will not converge
1 - pchisq(21.623 - 16.380, 1, lower.tail = T)## [1] 0.02203524resid(Kiga.fit, "cor"); sum(abs(resid(Kiga.fit, "cor")$cov > CRITR(39))); sum(abs(resid(Kiga.fit, "cor")$cov > CRITR(39, NP(39))))## $type
## [1] "cor.bollen"
##
## $cov
## RAVEN1 RAVEN2 RAVEN3 RAVEN4 PIAGET1 PIAGET2 PIAGET3 PIAGET4
## RAVEN1 0.000
## RAVEN2 -0.007 0.000
## RAVEN3 0.099 -0.161 0.000
## RAVEN4 -0.017 0.032 -0.098 0.000
## PIAGET1 -0.095 -0.034 0.160 0.057 0.000
## PIAGET2 0.007 0.084 0.005 0.004 -0.049 0.000
## PIAGET3 0.012 -0.065 0.067 -0.075 -0.208 0.012 0.000
## PIAGET4 -0.110 -0.037 0.194 -0.060 0.077 0.034 0.171 0.000## [1] 0## [1] 0There were two local independence violations that rendered model fit atrocious and they were modeled out with residual covariances. This barely affected the g factor relationship.
summary(Kiga.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 21 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
##
## Used Total
## Number of observations 39 40
##
## Model Test User Model:
##
## Test statistic 16.380
## Degrees of freedom 17
## P-value (Chi-square) 0.497
##
## Model Test Baseline Model:
##
## Test statistic 74.074
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.022
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -391.517
## Loglikelihood unrestricted model (H1) -383.327
##
## Akaike (AIC) 821.034
## Bayesian (BIC) 852.642
## Sample-size adjusted Bayesian (BIC) 793.209
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.140
## P-value RMSEA <= 0.05 0.602
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.083
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav =~
## RAVEN1 0.773 0.159 4.864 0.000 0.773 0.778
## RAVEN2 0.592 0.161 3.675 0.000 0.592 0.600
## RAVEN3 0.313 0.174 1.802 0.072 0.313 0.316
## RAVEN4 0.668 0.159 4.197 0.000 0.668 0.676
## gPia =~
## PIAGET1 0.456 0.185 2.468 0.014 0.456 0.458
## PIAGET2 0.748 0.195 3.831 0.000 0.748 0.785
## PIAGET3 -0.130 0.175 -0.745 0.456 -0.130 -0.135
## PIAGET4 0.276 0.117 2.360 0.018 0.276 0.438
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav ~~
## gPia 0.575 0.189 3.047 0.002 0.575 0.575
## .RAVEN1 ~~
## .PIAGET3 0.330 0.126 2.625 0.009 0.330 0.554
## .RAVEN3 ~~
## .PIAGET3 0.268 0.141 1.899 0.058 0.268 0.299
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 0.390 0.172 2.263 0.024 0.390 0.395
## .RAVEN2 0.624 0.166 3.758 0.000 0.624 0.641
## .RAVEN3 0.881 0.206 4.267 0.000 0.881 0.900
## .RAVEN4 0.529 0.158 3.336 0.001 0.529 0.542
## .PIAGET1 0.785 0.203 3.873 0.000 0.785 0.790
## .PIAGET2 0.349 0.236 1.478 0.139 0.349 0.384
## .PIAGET3 0.911 0.206 4.427 0.000 0.911 0.982
## .PIAGET4 0.321 0.082 3.939 0.000 0.321 0.808
## gRav 1.000 1.000 1.000
## gPia 1.000 1.000 1.000semPaths(Kiga.fit, "std", title = F, residuals = F, pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)
Shul (6-to-8-Year Olds); n = 35
fa.parallel(Shul68[, 3:14])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa.parallel(Shul68[, 3:10])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fa.parallel(Shul68[, 11:14])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 0 and the number of components = 1fas68 <- fa(Shul68[, 3:14], nfactors = 1)
faPsys68 <- fa(Shul68[, 3:10], nfactors = 1)
faPias68 <- fa(Shul68[, 11:14], nfactors = 1)
print(fas68$loadings)##
## Loadings:
## MR1
## ZVT1 0.659
## ZVT2 0.678
## ZVT3 0.860
## ZVT4 0.785
## RAVEN1 0.719
## RAVEN2 0.619
## RAVEN3 0.608
## RAVEN4 0.769
## PIAGET1 0.430
## PIAGET2 0.512
## PIAGET3 0.231
## PIAGET4 0.450
##
## MR1
## SS loadings 4.815
## Proportion Var 0.401print(faPsys68$loadings)##
## Loadings:
## MR1
## ZVT1 0.668
## ZVT2 0.690
## ZVT3 0.893
## ZVT4 0.805
## RAVEN1 0.734
## RAVEN2 0.608
## RAVEN3 0.542
## RAVEN4 0.778
##
## MR1
## SS loadings 4.177
## Proportion Var 0.522print(faPias68$loadings)##
## Loadings:
## MR1
## PIAGET1 0.702
## PIAGET2 0.703
## PIAGET3 0.304
## PIAGET4 0.331
##
## MR1
## SS loadings 1.189
## Proportion Var 0.297EFATOGS68 <- c(.659, .678, .860, .785, .719, .619, .608, .769, .430, .512, .231, .450)
EFATOGS68Psy <- c(.659, .678, .860, .785, .719, .619, .608, .769); EFATOGS68Pia <- c(.430, .512, .231, .450)
EFASEPS68 <- c(.668, .690, .893, .805, .734, .608, .542, .778, .702, .703, .304, .331)
EFASEPS68Psy <- c(.668, .690, .893, .805, .734, .608, .542, .778); EFASEPS68Pia <- c(.702, .703, .304, .331)
cor(EFATOGS68, EFASEPS68, method = "pearson"); cor(EFATOGS68, EFASEPS68, method = "spearman"); CONGO(EFATOGS68, EFASEPS68)## [1] 0.8272534## [1] 0.7972028## [1] 0.9880394cor(EFATOGS68Psy, EFASEPS68Psy, method = "pearson"); cor(EFATOGS68Psy, EFASEPS68Psy, method = "spearman"); CONGO(EFATOGS68Psy, EFASEPS68Psy)## [1] 0.9838514## [1] 1## [1] 0.999246cor(EFATOGS68Pia, EFASEPS68Pia, method = "pearson"); cor(EFATOGS68Pia, EFASEPS68Pia, method = "spearman"); CONGO(EFATOGS68Pia, EFASEPS68Pia)## [1] 0.6556697## [1] 0.8## [1] 0.9636597ShulModNo <- '
gRav =~ RAVEN1 + RAVEN2 + RAVEN3 + RAVEN4
gZVT =~ ZVT1 + ZVT2 + ZVT3 + ZVT4
gPsy =~ gRav + gZVT
gPia =~ PIAGET1 + PIAGET2 + PIAGET3 + PIAGET4
gPsy ~~ 0*gPia'
ShulMod <- '
gRav =~ RAVEN1 + RAVEN2 + RAVEN3 + RAVEN4
gZVT =~ ZVT1 + ZVT2 + ZVT3 + ZVT4
gPsy =~ gRav + gZVT
gPia =~ PIAGET1 + PIAGET2 + PIAGET3 + PIAGET4
gPsy ~~ gPia'
ShulModID <- '
gRav =~ RAVEN1 + RAVEN2 + RAVEN3 + RAVEN4
gZVT =~ ZVT1 + ZVT2 + ZVT3 + ZVT4
gPsy =~ gRav + gZVT
gPia =~ PIAGET1 + PIAGET2 + PIAGET3 + PIAGET4
gPsy ~~ 1*gPia'
ShulNo.fit <- cfa(ShulModNo, data = Shul68, std.lv = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"Shul.fit <- cfa(ShulMod, data = Shul68, std.lv = T)
ShulID.fit <- cfa(ShulModID, data = Shul68, std.lv = T)
round(cbind("No Relationship" = fitMeasures(ShulNo.fit, FITM),
"Free Relationship" = fitMeasures(Shul.fit, FITM),
"Identical" = fitMeasures(ShulID.fit, FITM)), 3)## No Relationship Free Relationship Identical
## chisq 66.708 56.982 63.573
## df 52.000 51.000 52.000
## npar 26.000 27.000 26.000
## cfi 0.916 0.966 0.934
## rmsea 0.090 0.058 0.080
## rmsea.ci.lower 0.000 0.000 0.000
## rmsea.ci.upper 0.148 0.127 0.140
## aic 1022.107 1014.381 1018.973
## bic 1062.546 1056.376 1059.412
## srmr 0.193 0.091 0.082#cfaHB(Shul.fit) #does not converge
1 - pchisq(63.573 - 56.982, 1, lower.tail = T)## [1] 0.01024956resid(Shul.fit, "cor"); sum(abs(resid(Shul.fit, "cor")$cov > CRITR(35))); sum(abs(resid(Shul.fit, "cor")$cov > CRITR(35, NP(35))))## $type
## [1] "cor.bollen"
##
## $cov
## RAVEN1 RAVEN2 RAVEN3 RAVEN4 ZVT1 ZVT2 ZVT3 ZVT4 PIAGET1 PIAGET2
## RAVEN1 0.000
## RAVEN2 0.023 0.000
## RAVEN3 -0.129 -0.031 0.000
## RAVEN4 -0.006 0.009 0.067 0.000
## ZVT1 0.096 -0.139 -0.014 0.003 0.000
## ZVT2 0.053 -0.132 -0.149 -0.094 0.256 0.000
## ZVT3 0.074 0.019 -0.051 0.018 -0.055 -0.012 0.000
## ZVT4 -0.009 -0.067 0.121 -0.034 -0.003 -0.020 0.010 0.000
## PIAGET1 -0.041 0.015 0.219 -0.070 0.020 -0.078 -0.053 -0.079 0.000
## PIAGET2 0.055 0.032 0.114 -0.137 0.025 0.001 0.048 -0.030 0.016 0.000
## PIAGET3 -0.029 0.018 0.117 0.193 0.048 -0.077 0.036 -0.019 0.020 -0.049
## PIAGET4 0.183 0.142 0.297 0.198 0.133 0.155 0.100 0.126 -0.043 -0.046
## PIAGET3 PIAGET4
## RAVEN1
## RAVEN2
## RAVEN3
## RAVEN4
## ZVT1
## ZVT2
## ZVT3
## ZVT4
## PIAGET1
## PIAGET2
## PIAGET3 0.000
## PIAGET4 0.114 0.000## [1] 0## [1] 0There were no violations of local independence.
summary(Shul.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 40 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 27
##
## Used Total
## Number of observations 35 40
##
## Model Test User Model:
##
## Test statistic 56.982
## Degrees of freedom 51
## P-value (Chi-square) 0.262
##
## Model Test Baseline Model:
##
## Test statistic 240.449
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.966
## Tucker-Lewis Index (TLI) 0.956
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -480.191
## Loglikelihood unrestricted model (H1) -451.700
##
## Akaike (AIC) 1014.381
## Bayesian (BIC) 1056.376
## Sample-size adjusted Bayesian (BIC) 972.069
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.058
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.127
## P-value RMSEA <= 0.05 0.420
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.091
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav =~
## RAVEN1 0.298 0.218 1.363 0.173 0.751 0.768
## RAVEN2 0.285 0.211 1.354 0.176 0.720 0.722
## RAVEN3 0.240 0.181 1.327 0.184 0.607 0.616
## RAVEN4 0.335 0.245 1.368 0.171 0.845 0.857
## gZVT =~
## ZVT1 0.335 0.142 2.363 0.018 0.645 0.652
## ZVT2 0.378 0.153 2.479 0.013 0.728 0.741
## ZVT3 0.472 0.180 2.625 0.009 0.909 0.936
## ZVT4 0.445 0.171 2.601 0.009 0.858 0.867
## gPsy =~
## gRav 2.318 1.983 1.169 0.242 0.918 0.918
## gZVT 1.647 0.855 1.926 0.054 0.855 0.855
## gPia =~
## PIAGET1 0.716 0.173 4.125 0.000 0.716 0.731
## PIAGET2 0.763 0.166 4.605 0.000 0.763 0.822
## PIAGET3 0.123 0.164 0.751 0.453 0.123 0.142
## PIAGET4 0.199 0.135 1.477 0.140 0.199 0.275
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.628 0.153 4.105 0.000 0.628 0.628
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 0.393 0.118 3.336 0.001 0.393 0.411
## .RAVEN2 0.477 0.134 3.549 0.000 0.477 0.479
## .RAVEN3 0.603 0.157 3.832 0.000 0.603 0.621
## .RAVEN4 0.258 0.101 2.554 0.011 0.258 0.265
## .ZVT1 0.563 0.143 3.942 0.000 0.563 0.575
## .ZVT2 0.435 0.115 3.774 0.000 0.435 0.450
## .ZVT3 0.116 0.064 1.812 0.070 0.116 0.124
## .ZVT4 0.242 0.080 3.038 0.002 0.242 0.248
## .PIAGET1 0.447 0.179 2.502 0.012 0.447 0.466
## .PIAGET2 0.279 0.175 1.596 0.111 0.279 0.324
## .PIAGET3 0.736 0.177 4.161 0.000 0.736 0.980
## .PIAGET4 0.482 0.118 4.092 0.000 0.482 0.924
## .gRav 1.000 0.157 0.157
## .gZVT 1.000 0.269 0.269
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000semPaths(Shul.fit, "std", title = F, residuals = F, pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)
Shul (9-to-10-Year Olds); n = 41
fa.parallel(Shul910[, 3:14])
## Parallel analysis suggests that the number of factors = 3 and the number of components = 2fa.parallel(Shul910[, 3:10])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(Shul910[, 11:14])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fas9101 <- fa(Shul910[, 3:14], nfactors = 1)
fas9102 <- fa(Shul910[, 3:14], nfactors = 2)
fas9103 <- fa(Shul910[, 3:14], nfactors = 3)
faPsys9101 <- fa(Shul910[, 3:10], nfactors = 1)
faPsys9102 <- fa(Shul910[, 3:10], nfactors = 2)
faPias910 <- fa(Shul910[, 11:14], nfactors = 1)
print(fas9101$loadings)##
## Loadings:
## MR1
## ZVT1 0.614
## ZVT2 0.531
## ZVT3 0.639
## ZVT4 0.672
## RAVEN1 0.577
## RAVEN2 0.696
## RAVEN3 0.572
## RAVEN4 0.660
## PIAGET1 0.569
## PIAGET2 0.186
## PIAGET3 0.605
## PIAGET4 0.666
##
## MR1
## SS loadings 4.266
## Proportion Var 0.355print(fas9102$loadings)##
## Loadings:
## MR1 MR2
## ZVT1 0.900
## ZVT2 0.840
## ZVT3 0.799
## ZVT4 0.114 0.780
## RAVEN1 0.497 0.179
## RAVEN2 0.814
## RAVEN3 0.665
## RAVEN4 0.883
## PIAGET1 0.511 0.149
## PIAGET2 0.362 -0.172
## PIAGET3 0.500 0.205
## PIAGET4 0.703
##
## MR1 MR2
## SS loadings 3.292 2.902
## Proportion Var 0.274 0.242
## Cumulative Var 0.274 0.516print(fas9103$loadings)##
## Loadings:
## MR2 MR1 MR3
## ZVT1 0.879 -0.129 0.157
## ZVT2 0.827
## ZVT3 0.785 0.158
## ZVT4 0.826 0.253 -0.181
## RAVEN1 0.216 0.595
## RAVEN2 0.765 0.128
## RAVEN3 0.644
## RAVEN4 0.963
## PIAGET1 0.106 0.806
## PIAGET2 -0.220 0.557
## PIAGET3 0.200 0.256 0.379
## PIAGET4 0.312 0.632
##
## MR2 MR1 MR3
## SS loadings 2.911 2.529 1.620
## Proportion Var 0.243 0.211 0.135
## Cumulative Var 0.243 0.453 0.588print(faPsys9101$loadings)##
## Loadings:
## MR1
## ZVT1 0.704
## ZVT2 0.667
## ZVT3 0.705
## ZVT4 0.819
## RAVEN1 0.582
## RAVEN2 0.590
## RAVEN3 0.491
## RAVEN4 0.550
##
## MR1
## SS loadings 3.340
## Proportion Var 0.417print(faPsys9102$loadings)##
## Loadings:
## MR1 MR2
## ZVT1 0.908
## ZVT2 0.833
## ZVT3 0.811
## ZVT4 0.759 0.191
## RAVEN1 0.214 0.548
## RAVEN2 0.797
## RAVEN3 0.684
## RAVEN4 0.986
##
## MR1 MR2
## SS loadings 2.809 2.418
## Proportion Var 0.351 0.302
## Cumulative Var 0.351 0.653print(faPias910$loadings)##
## Loadings:
## MR1
## PIAGET1 0.809
## PIAGET2 0.457
## PIAGET3 0.599
## PIAGET4 0.798
##
## MR1
## SS loadings 1.860
## Proportion Var 0.465EFATOGS910 <- c(.614, .531, .639, .672, .577, .696, .572, .660, .569, .186, .605, .666)
EFATOGS910Psy <- c(.614, .531, .639, .672, .577, .696, .572, .660); EFATOGS910Pia <- c(.569, .186, .605, .666)
EFASEPS910 <- c(.704, .667, .705, .719, .582, .590, .491, .550, .809, .457, .599, .798)
EFASEPS910Psy <- c(.704, .667, .705, .719, .582, .590, .491, .550); EFASEPS910Pia <- c(.809, .457, .599, .798)
cor(EFATOGS910, EFASEPS910, method = "pearson"); cor(EFATOGS910, EFASEPS910, method = "spearman"); CONGO(EFATOGS910, EFASEPS910)## [1] 0.4982116## [1] 0.3006993## [1] 0.9806953cor(EFATOGS910Psy, EFASEPS910Psy, method = "pearson"); cor(EFATOGS910Psy, EFASEPS910Psy, method = "spearman"); CONGO(EFATOGS910Psy, EFASEPS910Psy)## [1] 0.1435842## [1] 0.3095238## [1] 0.9900537cor(EFATOGS910Pia, EFASEPS910Pia, method = "pearson"); cor(EFATOGS910Pia, EFASEPS910Pia, method = "spearman"); CONGO(EFATOGS910Pia, EFASEPS910Pia)## [1] 0.8182909## [1] 0.4## [1] 0.9767309ShulNo.fit <- cfa(ShulModNo, data = Shul910, std.lv = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"Shul.fit <- cfa(ShulMod, data = Shul910, std.lv = T)
ShulID.fit <- cfa(ShulModID, data = Shul910, std.lv = T)
round(cbind("No Relationship" = fitMeasures(ShulNo.fit, FITM),
"Free Relationship" = fitMeasures(Shul.fit, FITM),
"Identical" = fitMeasures(ShulID.fit, FITM)), 3)## No Relationship Free Relationship Identical
## chisq 90.574 73.413 73.433
## df 52.000 51.000 52.000
## npar 26.000 27.000 26.000
## cfi 0.846 0.911 0.915
## rmsea 0.135 0.104 0.100
## rmsea.ci.lower 0.087 0.041 0.036
## rmsea.ci.upper 0.180 0.153 0.150
## aic 1209.521 1194.360 1192.380
## bic 1254.073 1240.626 1236.932
## srmr 0.205 0.095 0.096#cfaHB(Shul.fit) #does not converge
1 - pchisq(73.433 - 73.413, 1)## [1] 0.8875371resid(Shul.fit, "cor"); sum(abs(resid(Shul.fit, "cor")$cov > CRITR(41))); sum(abs(resid(Shul.fit, "cor")$cov > CRITR(41, NP(41))))## $type
## [1] "cor.bollen"
##
## $cov
## RAVEN1 RAVEN2 RAVEN3 RAVEN4 ZVT1 ZVT2 ZVT3 ZVT4 PIAGET1 PIAGET2
## RAVEN1 0.000
## RAVEN2 0.055 0.000
## RAVEN3 -0.054 -0.058 0.000
## RAVEN4 -0.012 -0.004 0.035 0.000
## ZVT1 0.098 -0.035 0.015 -0.096 0.000
## ZVT2 0.145 0.029 -0.113 -0.057 0.030 0.000
## ZVT3 0.169 0.117 0.041 -0.119 -0.003 -0.051 0.000
## ZVT4 0.280 0.108 0.181 0.151 -0.035 0.014 0.049 0.000
## PIAGET1 -0.202 -0.047 0.040 -0.093 0.110 -0.079 0.094 0.004 0.000
## PIAGET2 -0.035 -0.047 -0.144 -0.054 -0.150 -0.170 -0.153 -0.329 0.106 0.000
## PIAGET3 0.095 0.034 0.041 0.042 0.070 0.061 0.114 0.178 -0.010 0.004
## PIAGET4 0.025 0.125 0.005 0.001 -0.027 -0.148 0.116 -0.059 0.005 -0.009
## PIAGET3 PIAGET4
## RAVEN1
## RAVEN2
## RAVEN3
## RAVEN4
## ZVT1
## ZVT2
## ZVT3
## ZVT4
## PIAGET1
## PIAGET2
## PIAGET3 0.000
## PIAGET4 -0.026 0.000## [1] 0## [1] 0There were no violations of local independence.
summary(Shul.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 29 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 27
##
## Number of observations 41
##
## Model Test User Model:
##
## Test statistic 73.413
## Degrees of freedom 51
## P-value (Chi-square) 0.022
##
## Model Test Baseline Model:
##
## Test statistic 317.140
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.911
## Tucker-Lewis Index (TLI) 0.885
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -570.180
## Loglikelihood unrestricted model (H1) -533.473
##
## Akaike (AIC) 1194.360
## Bayesian (BIC) 1240.626
## Sample-size adjusted Bayesian (BIC) 1156.105
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.104
## 90 Percent confidence interval - lower 0.041
## 90 Percent confidence interval - upper 0.153
## P-value RMSEA <= 0.05 0.069
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.095
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav =~
## RAVEN1 0.450 0.140 3.213 0.001 0.600 0.608
## RAVEN2 0.627 0.156 4.013 0.000 0.837 0.847
## RAVEN3 0.530 0.147 3.612 0.000 0.707 0.716
## RAVEN4 0.682 0.164 4.156 0.000 0.909 0.921
## gZVT =~
## ZVT1 0.803 0.122 6.577 0.000 0.887 0.898
## ZVT2 0.736 0.126 5.858 0.000 0.813 0.823
## ZVT3 0.728 0.126 5.772 0.000 0.803 0.813
## ZVT4 0.708 0.127 5.566 0.000 0.781 0.791
## gPsy =~
## gRav 0.883 0.447 1.976 0.048 0.662 0.662
## gZVT 0.468 0.230 2.036 0.042 0.424 0.424
## gPia =~
## PIAGET1 0.740 0.143 5.160 0.000 0.740 0.749
## PIAGET2 0.401 0.161 2.495 0.013 0.401 0.405
## PIAGET3 0.623 0.150 4.157 0.000 0.623 0.631
## PIAGET4 0.837 0.138 6.056 0.000 0.837 0.848
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.964 0.239 4.035 0.000 0.964 0.964
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 0.616 0.145 4.258 0.000 0.616 0.631
## .RAVEN2 0.275 0.088 3.133 0.002 0.275 0.282
## .RAVEN3 0.476 0.118 4.026 0.000 0.476 0.488
## .RAVEN4 0.149 0.079 1.885 0.059 0.149 0.153
## .ZVT1 0.188 0.074 2.547 0.011 0.188 0.193
## .ZVT2 0.315 0.090 3.520 0.000 0.315 0.323
## .ZVT3 0.330 0.092 3.592 0.000 0.330 0.338
## .ZVT4 0.365 0.098 3.735 0.000 0.365 0.374
## .PIAGET1 0.428 0.128 3.332 0.001 0.428 0.439
## .PIAGET2 0.815 0.187 4.362 0.000 0.815 0.836
## .PIAGET3 0.587 0.149 3.947 0.000 0.587 0.602
## .PIAGET4 0.274 0.121 2.274 0.023 0.274 0.281
## .gRav 1.000 0.562 0.562
## .gZVT 1.000 0.820 0.820
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000semPaths(Shul.fit, "std", title = F, residuals = F, pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)
6-to-8 versus 9-to-10-Year Olds
ShulAC.fit <- cfa(ShulMod, data = ShulAll, std.lv = T, group = "STUDIE", orthogonal = T)
ShulAM.fit <- cfa(ShulMod, data = ShulAll, std.lv = F, group = "STUDIE", orthogonal = T, group.equal = "loadings"); "\n" #Multigroup sampling error abounds in small multigroup models## Warning in lav_object_post_check(object): lavaan WARNING: some estimated lv
## variances are negative## [1] "\n"ShulAS.fit <- cfa(ShulMod, data = ShulAll, std.lv = F, group = "STUDIE", orthogonal = T, group.equal = c("loadings", "intercepts")); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 3.988161e-16) is close to zero. This may be a symptom that the
## model is not identified.
## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING: some estimated lv variances are negative## [1] "\n"ShulAF.fit <- cfa(ShulMod, data = ShulAll, std.lv = F, group = "STUDIE", orthogonal = T, group.equal = c("loadings", "intercepts", "residuals")); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= 9.154988e-16) is close to zero. This may be a symptom that the
## model is not identified.## [1] "\n"ShulAV.fit <- cfa(ShulMod, data = ShulAll, std.lv = T, group = "STUDIE", orthogonal = T, group.equal = c("loadings", "intercepts", "residuals", "lv.covariances"))
ShulAME.fit <- cfa(ShulMod, data = ShulAll, std.lv = T, group = "STUDIE", orthogonal = T, group.equal = c("loadings", "intercepts", "residuals", "lv.covariances", "means"))
round(cbind(CONFIGURAL = fitMeasures(ShulAC.fit, FITM),
METRIC = fitMeasures(ShulAM.fit, FITM),
SCALAR = fitMeasures(ShulAS.fit, FITM),
STRICT = fitMeasures(ShulAF.fit, FITM),
LVARS = fitMeasures(ShulAV.fit, FITM),
MEANS = fitMeasures(ShulAME.fit, FITM)),3)## CONFIGURAL METRIC SCALAR STRICT LVARS MEANS
## chisq 130.395 145.830 146.428 158.626 159.147 159.625
## df 102.000 112.000 120.000 132.000 133.000 137.000
## npar 78.000 68.000 60.000 48.000 47.000 43.000
## cfi 0.933 0.921 0.938 0.937 0.939 0.947
## rmsea 0.086 0.089 0.076 0.073 0.072 0.066
## rmsea.ci.lower 0.028 0.040 0.000 0.000 0.000 0.000
## rmsea.ci.upper 0.126 0.127 0.116 0.112 0.111 0.106
## aic 2256.741 2252.176 2236.774 2224.972 2223.493 2215.971
## bic 2438.538 2410.666 2376.618 2336.847 2333.037 2316.192
## srmr 0.087 0.109 0.109 0.107 0.112 0.1121 - pchisq(145.830 - 130.395, 10, lower.tail = T)## [1] 0.1169891 - pchisq(158.626 - 146.428, 12, lower.tail = T)## [1] 0.429912summary(ShulAME.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 91 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
## Number of equality constraints 39
##
## Number of observations per group: Used Total
## 2Schul68 35 40
## 3Schul910 41 41
##
## Model Test User Model:
##
## Test statistic 159.625
## Degrees of freedom 137
## P-value (Chi-square) 0.090
## Test statistic for each group:
## 2Schul68 75.901
## 3Schul910 83.724
##
## Model Test Baseline Model:
##
## Test statistic 557.589
## Degrees of freedom 132
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.947
## Tucker-Lewis Index (TLI) 0.949
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1064.985
## Loglikelihood unrestricted model (H1) -985.173
##
## Akaike (AIC) 2215.971
## Bayesian (BIC) 2316.192
## Sample-size adjusted Bayesian (BIC) 2180.653
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.066
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.106
## P-value RMSEA <= 0.05 0.287
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.112
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [2Schul68]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav =~
## RAVEN1 (.p1.) 0.128 0.383 0.335 0.738 0.684 0.685
## RAVEN2 (.p2.) 0.151 0.450 0.335 0.737 0.803 0.793
## RAVEN3 (.p3.) 0.132 0.393 0.335 0.738 0.701 0.699
## RAVEN4 (.p4.) 0.172 0.514 0.335 0.738 0.916 0.904
## gZVT =~
## ZVT1 (.p5.) 0.522 0.117 4.483 0.000 0.796 0.800
## ZVT2 (.p6.) 0.520 0.116 4.479 0.000 0.792 0.799
## ZVT3 (.p7.) 0.558 0.121 4.619 0.000 0.850 0.862
## ZVT4 (.p8.) 0.546 0.119 4.567 0.000 0.832 0.836
## gPsy =~
## gRav (.p9.) 5.231 16.168 0.324 0.746 0.982 0.982
## gZVT (.10.) 1.150 0.375 3.067 0.002 0.755 0.755
## gPia =~
## PIAGET1 (.11.) 0.492 0.110 4.459 0.000 0.492 0.552
## PIAGET2 (.12.) 0.338 0.102 3.326 0.001 0.338 0.369
## PIAGET3 (.13.) 0.372 0.100 3.707 0.000 0.372 0.423
## PIAGET4 (.14.) 0.488 0.103 4.750 0.000 0.488 0.629
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia (.15.) 0.819 0.143 5.729 0.000 0.819 0.819
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 (.32.) 0.016 0.111 0.142 0.887 0.016 0.016
## .RAVEN2 (.33.) 0.005 0.112 0.045 0.964 0.005 0.005
## .RAVEN3 (.34.) 0.000 0.112 0.000 1.000 0.000 0.000
## .RAVEN4 (.35.) 0.000 0.110 0.001 1.000 0.000 0.000
## .ZVT1 (.36.) 0.031 0.111 0.281 0.779 0.031 0.031
## .ZVT2 (.37.) 0.021 0.111 0.191 0.849 0.021 0.021
## .ZVT3 (.38.) 0.040 0.110 0.368 0.713 0.040 0.041
## .ZVT4 (.39.) 0.015 0.111 0.133 0.894 0.015 0.015
## .PIAGET1 (.40.) 0.020 0.109 0.181 0.857 0.020 0.022
## .PIAGET2 (.41.) 0.053 0.108 0.491 0.623 0.053 0.058
## .PIAGET3 (.42.) 0.063 0.105 0.605 0.545 0.063 0.072
## .PIAGET4 (.43.) 0.085 0.096 0.884 0.377 0.085 0.110
## .gRav 0.000 0.000 0.000
## .gZVT 0.000 0.000 0.000
## gPsy 0.000 0.000 0.000
## gPia 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 (.16.) 0.530 0.096 5.520 0.000 0.530 0.531
## .RAVEN2 (.17.) 0.382 0.079 4.856 0.000 0.382 0.372
## .RAVEN3 (.18.) 0.514 0.094 5.463 0.000 0.514 0.511
## .RAVEN4 (.19.) 0.188 0.064 2.933 0.003 0.188 0.183
## .ZVT1 (.20.) 0.356 0.072 4.938 0.000 0.356 0.360
## .ZVT2 (.21.) 0.356 0.072 4.952 0.000 0.356 0.362
## .ZVT3 (.22.) 0.251 0.060 4.165 0.000 0.251 0.258
## .ZVT4 (.23.) 0.297 0.065 4.548 0.000 0.297 0.301
## .PIAGET1 (.24.) 0.553 0.115 4.830 0.000 0.553 0.695
## .PIAGET2 (.25.) 0.729 0.128 5.699 0.000 0.729 0.864
## .PIAGET3 (.26.) 0.638 0.116 5.518 0.000 0.638 0.821
## .PIAGET4 (.27.) 0.364 0.088 4.152 0.000 0.364 0.605
## .gRav 1.000 0.035 0.035
## .gZVT 1.000 0.431 0.431
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000
##
##
## Group 2 [3Schul910]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav =~
## RAVEN1 (.p1.) 0.128 0.383 0.335 0.738 0.642 0.661
## RAVEN2 (.p2.) 0.151 0.450 0.335 0.737 0.754 0.773
## RAVEN3 (.p3.) 0.132 0.393 0.335 0.738 0.658 0.676
## RAVEN4 (.p4.) 0.172 0.514 0.335 0.738 0.860 0.893
## gZVT =~
## ZVT1 (.p5.) 0.522 0.117 4.483 0.000 0.795 0.800
## ZVT2 (.p6.) 0.520 0.116 4.479 0.000 0.791 0.798
## ZVT3 (.p7.) 0.558 0.121 4.619 0.000 0.850 0.861
## ZVT4 (.p8.) 0.546 0.119 4.567 0.000 0.831 0.836
## gPsy =~
## gRav (.p9.) 5.231 16.168 0.324 0.746 0.650 0.650
## gZVT (.10.) 1.150 0.375 3.067 0.002 0.469 0.469
## gPia =~
## PIAGET1 (.11.) 0.492 0.110 4.459 0.000 0.736 0.703
## PIAGET2 (.12.) 0.338 0.102 3.326 0.001 0.506 0.510
## PIAGET3 (.13.) 0.372 0.100 3.707 0.000 0.556 0.572
## PIAGET4 (.14.) 0.488 0.103 4.750 0.000 0.729 0.770
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia (.15.) 0.819 0.143 5.729 0.000 0.882 0.882
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 (.32.) 0.016 0.111 0.142 0.887 0.016 0.016
## .RAVEN2 (.33.) 0.005 0.112 0.045 0.964 0.005 0.005
## .RAVEN3 (.34.) 0.000 0.112 0.000 1.000 0.000 0.000
## .RAVEN4 (.35.) 0.000 0.110 0.001 1.000 0.000 0.000
## .ZVT1 (.36.) 0.031 0.111 0.281 0.779 0.031 0.031
## .ZVT2 (.37.) 0.021 0.111 0.191 0.849 0.021 0.021
## .ZVT3 (.38.) 0.040 0.110 0.368 0.713 0.040 0.041
## .ZVT4 (.39.) 0.015 0.111 0.133 0.894 0.015 0.015
## .PIAGET1 (.40.) 0.020 0.109 0.181 0.857 0.020 0.019
## .PIAGET2 (.41.) 0.053 0.108 0.491 0.623 0.053 0.054
## .PIAGET3 (.42.) 0.063 0.105 0.605 0.545 0.063 0.065
## .PIAGET4 (.43.) 0.085 0.096 0.884 0.377 0.085 0.090
## .gRav 0.000 0.000 0.000
## .gZVT 0.000 0.000 0.000
## gPsy 0.000 0.000 0.000
## gPia 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 (.16.) 0.530 0.096 5.520 0.000 0.530 0.563
## .RAVEN2 (.17.) 0.382 0.079 4.856 0.000 0.382 0.402
## .RAVEN3 (.18.) 0.514 0.094 5.463 0.000 0.514 0.543
## .RAVEN4 (.19.) 0.188 0.064 2.933 0.003 0.188 0.203
## .ZVT1 (.20.) 0.356 0.072 4.938 0.000 0.356 0.360
## .ZVT2 (.21.) 0.356 0.072 4.952 0.000 0.356 0.362
## .ZVT3 (.22.) 0.251 0.060 4.165 0.000 0.251 0.258
## .ZVT4 (.23.) 0.297 0.065 4.548 0.000 0.297 0.301
## .PIAGET1 (.24.) 0.553 0.115 4.830 0.000 0.553 0.505
## .PIAGET2 (.25.) 0.729 0.128 5.699 0.000 0.729 0.740
## .PIAGET3 (.26.) 0.638 0.116 5.518 0.000 0.638 0.673
## .PIAGET4 (.27.) 0.364 0.088 4.152 0.000 0.364 0.407
## .gRav 14.424 85.560 0.169 0.866 0.577 0.577
## .gZVT 1.808 0.891 2.028 0.043 0.780 0.780
## gPsy 0.386 0.211 1.828 0.068 1.000 1.000
## gPia 2.233 0.817 2.732 0.006 1.000 1.000Combined Groups
fa.parallel(ShulAll[, 3:14])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(ShulAll[, 3:10])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## An ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(ShulAll[, 11:14])## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 2 and the number of components = 1fasAll1 <- fa(ShulAll[, 3:14], nfactors = 1)
fasAll2 <- fa(ShulAll[, 3:14], nfactors = 2)
fasAll3 <- fa(ShulAll[, 3:14], nfactors = 3)
faPsysAll1 <- fa(ShulAll[, 3:10], nfactors = 1)
faPsysAll2 <- fa(ShulAll[, 3:10], nfactors = 2)
faPiasAll1 <- fa(ShulAll[, 11:14], nfactors = 1)
faPiasAll2 <- fa(ShulAll[, 11:14], nfactors = 2)
print(fasAll1$loadings)##
## Loadings:
## MR1
## ZVT1 0.644
## ZVT2 0.609
## ZVT3 0.742
## ZVT4 0.731
## RAVEN1 0.643
## RAVEN2 0.657
## RAVEN3 0.587
## RAVEN4 0.709
## PIAGET1 0.490
## PIAGET2 0.323
## PIAGET3 0.426
## PIAGET4 0.564
##
## MR1
## SS loadings 4.407
## Proportion Var 0.367print(fasAll2$loadings)##
## Loadings:
## MR1 MR2
## ZVT1 0.847
## ZVT2 -0.115 0.905
## ZVT3 0.149 0.749
## ZVT4 0.158 0.724
## RAVEN1 0.488 0.244
## RAVEN2 0.767
## RAVEN3 0.708
## RAVEN4 0.841
## PIAGET1 0.502
## PIAGET2 0.400
## PIAGET3 0.395
## PIAGET4 0.579
##
## MR1 MR2
## SS loadings 3.001 2.698
## Proportion Var 0.250 0.225
## Cumulative Var 0.250 0.475print(fasAll3$loadings)##
## Loadings:
## MR2 MR1 MR3
## ZVT1 0.852 -0.110 0.116
## ZVT2 0.888
## ZVT3 0.747 0.131
## ZVT4 0.728 0.228
## RAVEN1 0.252 0.595 -0.101
## RAVEN2 0.762
## RAVEN3 0.576 0.209
## RAVEN4 0.924
## PIAGET1 0.849
## PIAGET2 0.488
## PIAGET3 0.101 0.194 0.298
## PIAGET4 0.332 0.369
##
## MR2 MR1 MR3
## SS loadings 2.685 2.362 1.265
## Proportion Var 0.224 0.197 0.105
## Cumulative Var 0.224 0.421 0.526print(faPsysAll1$loadings)##
## Loadings:
## MR1
## ZVT1 0.680
## ZVT2 0.673
## ZVT3 0.785
## ZVT4 0.809
## RAVEN1 0.661
## RAVEN2 0.607
## RAVEN3 0.523
## RAVEN4 0.662
##
## MR1
## SS loadings 3.703
## Proportion Var 0.463print(faPsysAll2$loadings)##
## Loadings:
## MR1 MR2
## ZVT1 0.862
## ZVT2 0.892 -0.101
## ZVT3 0.760 0.135
## ZVT4 0.713 0.206
## RAVEN1 0.244 0.546
## RAVEN2 0.773
## RAVEN3 0.653
## RAVEN4 0.941
##
## MR1 MR2
## SS loadings 2.684 2.284
## Proportion Var 0.335 0.285
## Cumulative Var 0.335 0.621print(faPiasAll1$loadings)##
## Loadings:
## MR1
## PIAGET1 0.708
## PIAGET2 0.515
## PIAGET3 0.520
## PIAGET4 0.635
##
## MR1
## SS loadings 1.44
## Proportion Var 0.36print(faPiasAll2$loadings)##
## Loadings:
## MR1 MR2
## PIAGET1 0.134 0.650
## PIAGET2 0.729
## PIAGET3 0.382 0.179
## PIAGET4 0.999
##
## MR1 MR2
## SS loadings 1.170 0.986
## Proportion Var 0.292 0.246
## Cumulative Var 0.292 0.539EFATOGSAll <- c(.644, .609, .742, .731, .643, .657, .587, .709, .490, .323, .426, .564)
EFATOGSAllPsy <- c(.644, .609, .742, .731, .643, .657, .587, .709); EFATOGSAllPia <- c(.490, .323, .426, .564)
EFASEPSAll <- c(.680, .673, .785, .809, .661, .607, .523, .662, .708, .515, .520, .635)
EFASEPSAllPsy <- c(.680, .673, .785, .809, .661, .607, .523, .662); EFASEPSAllPia <- c(.708, .515, .520, .635)
cor(EFATOGSAll, EFASEPSAll, method = "pearson"); cor(EFATOGSAll, EFASEPSAll, method = "spearman"); CONGO(EFATOGSAll, EFASEPSAll)## [1] 0.7202227## [1] 0.6643357## [1] 0.990308cor(EFATOGSAllPsy, EFASEPSAllPsy, method = "pearson"); cor(EFATOGSAllPsy, EFASEPSAllPsy, method = "spearman"); CONGO(EFATOGSAllPsy, EFASEPSAllPsy)## [1] 0.8154537## [1] 0.6666667## [1] 0.9970956cor(EFATOGSAllPia, EFASEPSAllPia, method = "pearson"); cor(EFATOGSAllPia, EFASEPSAllPia, method = "spearman"); CONGO(EFATOGSAllPia, EFASEPSAllPia)## [1] 0.7320973## [1] 0.8## [1] 0.991335ShulNo.fit <- cfa(ShulModNo, data = ShulAll, std.lv = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"Shul.fit <- cfa(ShulMod, data = ShulAll, std.lv = T)
ShulID.fit <- cfa(ShulModID, data = ShulAll, std.lv = T)
round(cbind("No Relationship" = fitMeasures(ShulNo.fit, FITM),
"Free Relationship" = fitMeasures(Shul.fit, FITM),
"Identical" = fitMeasures(ShulID.fit, FITM)), 3)## No Relationship Free Relationship Identical
## chisq 103.291 79.525 83.188
## df 52.000 51.000 52.000
## npar 26.000 27.000 26.000
## cfi 0.874 0.930 0.923
## rmsea 0.114 0.086 0.089
## rmsea.ci.lower 0.081 0.046 0.051
## rmsea.ci.upper 0.146 0.121 0.123
## aic 2215.498 2193.732 2195.395
## bic 2276.097 2256.662 2255.994
## srmr 0.185 0.069 0.083#cfaHB(Shul.fit) #does not converge
1 - pchisq(83.188 - 79.525, df = 1, lower.tail = T)## [1] 0.05563338resid(Shul.fit, "cor"); sum(abs(resid(Shul.fit, "cor")$cov > CRITR(76))); sum(abs(resid(Shul.fit, "cor")$cov > CRITR(76, NP(76))))## $type
## [1] "cor.bollen"
##
## $cov
## RAVEN1 RAVEN2 RAVEN3 RAVEN4 ZVT1 ZVT2 ZVT3 ZVT4 PIAGET1 PIAGET2
## RAVEN1 0.000
## RAVEN2 0.043 0.000
## RAVEN3 -0.095 -0.054 0.000
## RAVEN4 -0.006 0.000 0.037 0.000
## ZVT1 0.089 -0.118 -0.033 -0.086 0.000
## ZVT2 0.110 -0.068 -0.154 -0.094 0.108 0.000
## ZVT3 0.171 0.082 0.002 -0.038 -0.031 -0.036 0.000
## ZVT4 0.177 0.023 0.144 0.068 -0.047 -0.028 0.044 0.000
## PIAGET1 -0.128 -0.019 0.115 -0.086 0.080 -0.064 0.061 -0.012 0.000
## PIAGET2 0.031 0.000 -0.024 -0.075 -0.046 -0.059 -0.001 -0.145 0.143 0.000
## PIAGET3 -0.008 -0.011 0.037 0.057 0.033 -0.034 0.041 0.049 -0.033 -0.072
## PIAGET4 0.034 0.100 0.084 0.032 0.014 -0.065 0.074 -0.030 -0.028 -0.070
## PIAGET3 PIAGET4
## RAVEN1
## RAVEN2
## RAVEN3
## RAVEN4
## ZVT1
## ZVT2
## ZVT3
## ZVT4
## PIAGET1
## PIAGET2
## PIAGET3 0.000
## PIAGET4 0.044 0.000## [1] 0## [1] 0There were two violations of local independence and none with scaling.
summary(Shul.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 27
##
## Used Total
## Number of observations 76 81
##
## Model Test User Model:
##
## Test statistic 79.525
## Degrees of freedom 51
## P-value (Chi-square) 0.006
##
## Model Test Baseline Model:
##
## Test statistic 473.252
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.930
## Tucker-Lewis Index (TLI) 0.909
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1069.866
## Loglikelihood unrestricted model (H1) -1030.104
##
## Akaike (AIC) 2193.732
## Bayesian (BIC) 2256.662
## Sample-size adjusted Bayesian (BIC) 2171.556
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.086
## 90 Percent confidence interval - lower 0.046
## 90 Percent confidence interval - upper 0.121
## P-value RMSEA <= 0.05 0.065
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.069
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gRav =~
## RAVEN1 0.347 0.133 2.612 0.009 0.660 0.671
## RAVEN2 0.412 0.153 2.696 0.007 0.784 0.790
## RAVEN3 0.354 0.135 2.623 0.009 0.675 0.684
## RAVEN4 0.464 0.171 2.719 0.007 0.883 0.895
## gZVT =~
## ZVT1 0.640 0.093 6.914 0.000 0.794 0.803
## ZVT2 0.640 0.092 6.942 0.000 0.795 0.806
## ZVT3 0.669 0.092 7.305 0.000 0.831 0.847
## ZVT4 0.665 0.092 7.198 0.000 0.825 0.835
## gPsy =~
## gRav 1.620 0.809 2.001 0.045 0.851 0.851
## gZVT 0.736 0.214 3.447 0.001 0.593 0.593
## gPia =~
## PIAGET1 0.689 0.116 5.938 0.000 0.689 0.700
## PIAGET2 0.491 0.118 4.143 0.000 0.491 0.510
## PIAGET3 0.467 0.116 4.044 0.000 0.467 0.500
## PIAGET4 0.599 0.104 5.764 0.000 0.599 0.682
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPsy ~~
## gPia 0.764 0.123 6.217 0.000 0.764 0.764
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .RAVEN1 0.532 0.097 5.497 0.000 0.532 0.549
## .RAVEN2 0.370 0.078 4.714 0.000 0.370 0.375
## .RAVEN3 0.519 0.095 5.447 0.000 0.519 0.533
## .RAVEN4 0.194 0.067 2.924 0.003 0.194 0.200
## .ZVT1 0.347 0.072 4.851 0.000 0.347 0.355
## .ZVT2 0.340 0.070 4.821 0.000 0.340 0.350
## .ZVT3 0.271 0.063 4.314 0.000 0.271 0.282
## .ZVT4 0.296 0.066 4.489 0.000 0.296 0.303
## .PIAGET1 0.494 0.117 4.220 0.000 0.494 0.510
## .PIAGET2 0.684 0.125 5.469 0.000 0.684 0.739
## .PIAGET3 0.657 0.119 5.509 0.000 0.657 0.750
## .PIAGET4 0.413 0.094 4.406 0.000 0.413 0.535
## .gRav 1.000 0.276 0.276
## .gZVT 1.000 0.649 0.649
## gPsy 1.000 1.000 1.000
## gPia 1.000 1.000 1.000semPaths(Shul.fit, "std", title = F, residuals = F, pastel = T, mar = c(2, 1, 3, 1), posCol = c("skyblue4"), layout = "circle", exoCov = T)
For Posterity: Lim (1988), Again
lowerLIM <-'
1
0.34 1
0.25 0.48 1
0.34 0.58 0.68 1
0.43 0.54 0.53 0.6 1
0.32 0.55 0.51 0.56 0.54 1
0.29 0.52 0.77 0.64 0.59 0.54 1
0.41 0.38 0.35 0.43 0.45 0.31 0.37 1
0.35 0.29 0.26 0.34 0.32 0.29 0.27 0.56 1
0.41 0.33 0.24 0.36 0.38 0.23 0.27 0.62 0.59 1
0.34 0.37 0.37 0.41 0.39 0.33 0.34 0.64 0.67 0.59 1
0.44 0.37 0.38 0.42 0.43 0.32 0.38 0.63 0.58 0.61 0.67 1
0.23 0.23 0.17 0.21 0.29 0.21 0.23 0.31 0.14 0.21 0.23 0.25 1
0.26 0.3 0.24 0.28 0.27 0.29 0.25 0.29 0.21 0.25 0.28 0.31 0.24 1
0.01 0.1 -0.01 0.04 0 0.1 0.02 -0.07 0 -0.01 0 -0.03 -0.09 0.04 1
0.29 0.29 0.27 0.27 0.35 0.27 0.28 0.27 0.18 0.21 0.27 0.27 0.24 0.29 0.01 1
0.35 0.36 0.28 0.37 0.36 0.3 0.32 0.4 0.27 0.39 0.34 0.34 0.28 0.31 -0.02 0.29 1
0.13 0.26 0.21 0.21 0.27 0.22 0.25 0.15 0.08 0.21 0.14 0.14 0.17 0.14 0.04 0.14 0.2 1
0.02 0.09 0.05 0.04 0.03 -0.01 0.03 0.07 -0.01 0.05 0.06 0.06 0.03 0.06 0.02 0 0.03 0.03 1
0.28 0.24 0.21 0.22 0.33 0.24 0.21 0.26 0.16 0.2 0.27 0.27 0.24 0.3 0.03 0.28 0.29 0.09 0.12 1
0.39 0.35 0.3 0.32 0.42 0.32 0.36 0.4 0.26 0.3 0.37 0.37 0.44 0.34 -0.01 0.32 0.41 0.2 0.05 0.33 1
0.36 0.38 0.26 0.3 0.39 0.33 0.31 0.3 0.24 0.27 0.29 0.29 0.28 0.3 -0.04 0.26 0.37 0.18 0.04 0.3 0.48 1
0.41 0.41 0.32 0.38 0.43 0.37 0.34 0.43 0.32 0.36 0.42 0.42 0.34 0.37 -0.05 0.31 0.46 0.24 0.03 0.28 0.53 0.45 1'
lowerLIMPSYC <- '
1
0.34 1
0.25 0.48 1
0.34 0.58 0.68 1
0.43 0.54 0.53 0.6 1
0.32 0.55 0.51 0.56 0.54 1
0.29 0.52 0.77 0.64 0.59 0.54 1
0.41 0.38 0.35 0.43 0.45 0.31 0.37 1
0.35 0.29 0.26 0.34 0.32 0.29 0.27 0.56 1
0.41 0.33 0.24 0.36 0.38 0.23 0.27 0.62 0.59 1
0.34 0.37 0.37 0.41 0.39 0.33 0.34 0.64 0.67 0.59 1
0.44 0.37 0.38 0.42 0.43 0.32 0.38 0.63 0.58 0.61 0.67 1'
lowerLIMPIA <- '
1
0.24 1
-0.09 0.04 1
0.24 0.29 0.01 1
0.28 0.31 -0.02 0.29 1
0.17 0.14 0.04 0.14 0.2 1
0.03 0.06 0.02 0 0.03 0.03 1
0.24 0.3 0.03 0.28 0.29 0.09 0.12 1
0.44 0.34 -0.01 0.32 0.41 0.2 0.05 0.33 1
0.28 0.3 -0.04 0.26 0.37 0.18 0.04 0.3 0.48 1
0.34 0.37 -0.05 0.31 0.46 0.24 0.03 0.28 0.53 0.45 1'
nLIM <- 459
LIM.cor = getCov(lowerLIM, names = c("APM", "B1", "B2", "B3", "B4", "B5", "B6", "B7", "B8", "B9", "B10", "B11", "C1", "C2", "C3", "C4", "C5", "C6", "C7", "C8", "T1", "T2", "T3"))
LIMPSYC.cor = getCov(lowerLIMPSYC, names = c("APM", "B1", "B2", "B3", "B4", "B5", "B6", "B7", "B8", "B9", "B10", "B11"))
LIMPIA.cor = getCov(lowerLIMPIA, names = c("C1", "C2", "C3", "C4", "C5", "C6", "C7", "C8", "T1", "T2", "T3"))fa.parallel(LIM.cor, n.obs = nLIM)
## Parallel analysis suggests that the number of factors = 3 and the number of components = 3fa.parallel(LIMPSYC.cor, n.obs = nLIM)
## Parallel analysis suggests that the number of factors = 2 and the number of components = 2fa.parallel(LIMPIA.cor, n.obs = nLIM)
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1FATOT1 <- fa(LIM.cor, n.obs = nLIM, nfactors = 1)
FATOT2 <- fa(LIM.cor, n.obs = nLIM, nfactors = 2)
FATOT3 <- fa(LIM.cor, n.obs = nLIM, nfactors = 3)
FAPSYC1 <- fa(LIMPSYC.cor, n.obs = nLIM, nfactors = 1)
FAPSYC2 <- fa(LIMPSYC.cor, n.obs = nLIM, nfactors = 2)
FAPIA <- fa(LIMPIA.cor, n.obs = nLIM, nfactors = 1)
print(FATOT1$loadings)##
## Loadings:
## MR1
## APM 0.568
## B1 0.658
## B2 0.624
## B3 0.699
## B4 0.723
## B5 0.611
## B6 0.659
## B7 0.698
## B8 0.564
## B9 0.612
## B10 0.678
## B11 0.692
## C1 0.411
## C2 0.462
## C3
## C4 0.448
## C5 0.567
## C6 0.305
## C7
## C8 0.418
## T1 0.608
## T2 0.535
## T3 0.646
##
## MR1
## SS loadings 7.333
## Proportion Var 0.319print(FATOT2$loadings)##
## Loadings:
## MR1 MR2
## APM 0.224 0.418
## B1 0.656
## B2 0.789
## B3 0.737
## B4 0.672 0.141
## B5 0.709
## B6 0.838
## B7 0.751
## B8 0.749
## B9 0.795
## B10 0.781
## B11 0.749
## C1 0.226 0.236
## C2 0.273 0.246
## C3
## C4 0.321 0.181
## C5 0.296 0.342
## C6 0.309
## C7
## C8 0.246 0.223
## T1 0.351 0.331
## T2 0.358 0.241
## T3 0.341 0.386
##
## MR1 MR2
## SS loadings 4.172 3.791
## Proportion Var 0.181 0.165
## Cumulative Var 0.181 0.346print(FATOT3$loadings)##
## Loadings:
## MR1 MR2 MR3
## APM 0.249 0.382
## B1 0.536 0.222
## B2 0.877 -0.102
## B3 0.766 0.110
## B4 0.531 0.271
## B5 0.614 0.161
## B6 0.855
## B7 0.686 0.139
## B8 0.841 -0.127
## B9 0.769
## B10 0.795
## B11 0.730
## C1 0.541
## C2 0.443
## C3 0.113
## C4 0.122 0.398
## C5 0.126 0.488
## C6 0.199 0.208
## C7
## C8 0.462
## T1 0.735
## T2 0.606
## T3 0.115 0.615
##
## MR1 MR2 MR3
## SS loadings 3.127 3.054 2.783
## Proportion Var 0.136 0.133 0.121
## Cumulative Var 0.136 0.269 0.390print(FAPSYC1$loadings)##
## Loadings:
## MR1
## APM 0.526
## B1 0.649
## B2 0.667
## B3 0.742
## B4 0.715
## B5 0.613
## B6 0.687
## B7 0.707
## B8 0.614
## B9 0.629
## B10 0.703
## B11 0.717
##
## MR1
## SS loadings 5.334
## Proportion Var 0.444print(FAPSYC2$loadings)##
## Loadings:
## MR1 MR2
## APM 0.199 0.395
## B1 0.624 0.109
## B2 0.839
## B3 0.773
## B4 0.647 0.160
## B5 0.687
## B6 0.868
## B7 0.740
## B8 0.789
## B9 0.811
## B10 0.797
## B11 0.760
##
## MR1 MR2
## SS loadings 3.395 3.249
## Proportion Var 0.283 0.271
## Cumulative Var 0.283 0.554print(FAPIA$loadings)##
## Loadings:
## MR1
## C1 0.507
## C2 0.516
## C3
## C4 0.471
## C5 0.602
## C6 0.296
## C7
## C8 0.475
## T1 0.731
## T2 0.614
## T3 0.709
##
## MR1
## SS loadings 2.840
## Proportion Var 0.258EFATOGL88 <- c(.568, .658, .624, .699, .723, .611, .659, .698, .564, .612, .678, .692, .411, .462, .448, .567, .305, .418, .608, .535, .646)
EFATOGL88Psy <- c(.568, .658, .624, .699, .723, .611, .659, .698, .564, .612, .678, .692); EFATOGL88Pia <- c(.411, .462, .448, .567, .305, .418, .608, .535, .646)
EFASEPL88 <- c(.526, .649, .667, .742, .715, .613, .687, .707, .614, .629, .703, .717, .507, .516, .471, .602, .296, .475, .731, .614, .709)
EFASEPL88Psy <- c(.526, .649, .667, .742, .715, .613, .687, .707, .614, .629, .703, .717); EFASEPL88Pia <- c(.507, .516, .471, .602, .296, .475, .731, .614, .709)
cor(EFATOGL88, EFASEPL88, method = "pearson"); cor(EFATOGL88, EFASEPL88, method = "spearman"); CONGO(EFATOGL88, EFASEPL88)## [1] 0.9424816## [1] 0.8749594## [1] 0.998043cor(EFATOGL88Psy, EFASEPL88Psy, method = "pearson"); cor(EFATOGL88Psy, EFASEPL88Psy, method = "spearman"); CONGO(EFATOGL88Psy, EFASEPL88Psy)## [1] 0.9017536## [1] 0.9370629## [1] 0.9992802cor(EFATOGL88Pia, EFASEPL88Pia, method = "pearson"); cor(EFATOGL88Pia, EFASEPL88Pia, method = "spearman"); CONGO(EFATOGL88Pia, EFASEPL88Pia)## [1] 0.9693414## [1] 0.9## [1] 0.9983633LIMTOG.model <- '
F1 =~ APM + B7 + B8 + B9 + B10 + B11
F2 =~ B1 + B2 + B3 + B4 + B5 + B6
F3 =~ C1 + C5 + C6 + T1 + T2 + T3
F4 =~ C2 + C4 + C8
g =~ F1 + F2 + F3 + F4'
LIMCGF.model <- '
F1 =~ APM + B7 + B8 + B9 + B10 + B11
F2 =~ B1 + B2 + B3 + B4 + B5 + B6
F3 =~ C1 + C5 + C6 + T1 + T2 + T3
F4 =~ C2 + C4 + C8'
LIMBF.model <- '
F1 =~ APM + B7 + B8 + B9 + B10 + B11
F2 =~ B1 + B2 + B3 + B4 + B5 + B6
F3 =~ C1 + C5 + C6 + T1 + T2 + T3
F4 =~ C2 + C4 + C8
g =~ APM + B7 + B8 + B9 + B10 + B11 + B1 + B2 + B3 + B4 + B5 + B6 + C1 + C5 + C6 + T1 + T2 + T3 + C2 + C4 + C8'
LIMTOG.fit <- cfa(LIMTOG.model, sample.cov = LIM.cor, sample.nobs = nLIM, std.lv = T)
LIMCGF.fit <- cfa(LIMCGF.model, sample.cov = LIM.cor, sample.nobs = nLIM, std.lv = T)
LIMBF.fit <- cfa(LIMBF.model, sample.cov = LIM.cor, sample.nobs = nLIM, std.lv = T, orthogonal = T)
round(cbind("HOF" = fitMeasures(LIMTOG.fit, FITM),
"CGF" = fitMeasures(LIMCGF.fit, FITM),
"BF" = fitMeasures(LIMBF.fit, FITM)), 3)## HOF CGF BF
## chisq 412.428 405.420 236.523
## df 185.000 183.000 168.000
## npar 46.000 48.000 63.000
## cfi 0.945 0.947 0.984
## rmsea 0.052 0.051 0.030
## rmsea.ci.lower 0.045 0.045 0.020
## rmsea.ci.upper 0.058 0.058 0.038
## aic 23460.726 23457.717 23318.821
## bic 23650.662 23655.912 23578.951
## srmr 0.053 0.052 0.0311 - pchisq(c((412.428-405.420), (412.428-236.523), (405.420-236.523)), c(2, 17, 15), lower.tail = T)## [1] 0.03007684 0.00000000 0.00000000Not significant with scaling, but p just below 0.05 without it. BIC is better with the HOF and AIC is slightly worse. Other fit indices are indeterminate. The evidence is more strongly in favor of the higher-order model. Considering the bifactor model, it fits staggeringly better than both, but it is theoretically inadmissible for a number of reasons, ranging from how invariance is tested to the fact that it seems to model away local independence violations that may, better, be interpreted as part of the specificities, rather than group factors, alongside modeling out misfit (i.e., overfitting).
LIMTOIINo.model <- '
F1 =~ APM + B7 + B8 + B9 + B10 + B11
F2 =~ B1 + B2 + B3 + B4 + B5 + B6
gPSY =~ F1 + F2
F3 =~ C1 + C5 + C6 + T1 + T2 + T3
F4 =~ C2 + C4 + C8
gPIA =~ F3 + F4
gPSY ~~ 0*gPIA'
LIMTOII.model <- '
F1 =~ APM + B7 + B8 + B9 + B10 + B11
F2 =~ B1 + B2 + B3 + B4 + B5 + B6
gPSY =~ F1 + F2
F3 =~ C1 + C5 + C6 + T1 + T2 + T3
F4 =~ C2 + C4 + C8
gPIA =~ F3 + F4
gPSY ~~ gPIA'
LIMTOIIID.model <- '
F1 =~ APM + B7 + B8 + B9 + B10 + B11
F2 =~ B1 + B2 + B3 + B4 + B5 + B6
gPSY =~ F1 + F2
F3 =~ C1 + C5 + C6 + T1 + T2 + T3
F4 =~ C2 + C4 + C8
gPIA =~ F3 + F4
gPSY ~~ 1*gPIA'
LIMPTOIINo.fit <- cfa(LIMTOIINo.model, sample.cov = LIM.cor, sample.nobs = nLIM, std.lv = T); "\n"## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## [1] "\n"LIMPTOII.fit <- cfa(LIMTOII.model, sample.cov = LIM.cor, sample.nobs = nLIM, std.lv = T)
LIMPTOIIID.fit <- cfa(LIMTOIIID.model, sample.cov = LIM.cor, sample.nobs = nLIM, std.lv = T)
round(cbind("Lim No" = fitMeasures(LIMPTOIINo.fit, FITM),
"Lim" = fitMeasures(LIMPTOII.fit, FITM),
"Lim ID" = fitMeasures(LIMPTOIIID.fit, FITM)), 3)## Lim No Lim Lim ID
## chisq 663.253 405.657 412.428
## df 185.000 184.000 185.000
## npar 46.000 47.000 46.000
## cfi 0.885 0.947 0.945
## rmsea 0.075 0.051 0.052
## rmsea.ci.lower 0.069 0.044 0.045
## rmsea.ci.upper 0.081 0.058 0.058
## aic 23711.551 23455.954 23460.726
## bic 23901.487 23650.020 23650.662
## srmr 0.205 0.052 0.0531 - pchisq(412.428 - 405.657, 1, lower.tail = T)## [1] 0.009265091Not significant with scaling.
resid(LIMPTOII.fit, "cor"); sum(abs(resid(LIMPTOII.fit, "cor")$cov > CRITR(459))); sum(abs(resid(LIMPTOII.fit, "cor")$cov > CRITR(459, NP(459))))## $type
## [1] "cor.bollen"
##
## $cov
## APM B7 B8 B9 B10 B11 B1 B2 B3 B4
## APM 0.000
## B7 -0.003 0.000
## B8 -0.035 -0.025 0.000
## B9 0.017 0.022 0.033 0.000
## B10 -0.086 -0.007 0.067 -0.026 0.000
## B11 0.019 -0.010 -0.017 0.000 0.010 0.000
## B1 0.128 0.058 -0.011 0.023 0.038 0.041 0.000
## B2 0.004 -0.025 -0.089 -0.117 -0.016 -0.002 -0.073 0.000
## B3 0.090 0.050 -0.015 -0.002 0.018 0.032 0.018 0.027 0.000
## B4 0.202 0.104 -0.003 0.050 0.033 0.076 0.028 -0.064 -0.004 0.000
## B5 0.108 -0.012 -0.011 -0.077 -0.002 -0.009 0.074 -0.043 -0.002 0.028
## B6 0.038 -0.013 -0.087 -0.095 -0.055 -0.011 -0.046 0.112 -0.028 -0.018
## C1 0.059 0.051 -0.102 -0.037 -0.037 -0.015 0.005 -0.091 -0.055 0.048
## C5 0.139 0.079 -0.030 0.084 0.009 0.012 0.081 -0.044 0.041 0.060
## C6 0.022 -0.014 -0.073 0.054 -0.029 -0.028 0.118 0.044 0.042 0.117
## T1 0.142 0.023 -0.091 -0.059 -0.018 -0.015 0.023 -0.080 -0.066 0.069
## T2 0.149 -0.021 -0.060 -0.036 -0.041 -0.038 0.101 -0.064 -0.029 0.090
## T3 0.159 0.049 -0.036 -0.003 0.027 0.031 0.079 -0.064 -0.010 0.075
## C2 0.075 0.009 -0.052 -0.018 -0.010 0.023 0.056 -0.043 -0.008 0.008
## C4 0.118 0.008 -0.064 -0.039 0.000 0.003 0.063 0.006 0.002 0.106
## C8 0.112 0.005 -0.078 -0.043 0.007 0.010 0.019 -0.047 -0.041 0.092
## B5 B6 C1 C5 C6 T1 T2 T3 C2 C4
## APM
## B7
## B8
## B9
## B10
## B11
## B1
## B2
## B3
## B4
## B5 0.000
## B6 -0.026 0.000
## C1 -0.015 -0.037 0.000
## C5 0.021 -0.012 -0.027 0.000
## C6 0.078 0.081 0.013 0.005 0.000
## T1 -0.007 -0.029 0.080 -0.037 -0.028 0.000
## T2 0.051 -0.022 -0.027 -0.011 -0.015 0.033 0.000
## T3 0.039 -0.053 -0.025 0.008 0.009 0.000 -0.002 0.000
## C2 0.046 -0.040 0.000 0.012 -0.012 -0.009 0.002 0.017 0.000
## C4 0.043 0.010 0.016 0.013 -0.002 -0.005 -0.017 -0.019 -0.011 0.000
## C8 0.019 -0.053 0.022 0.020 -0.048 0.013 0.030 -0.040 0.006 0.006
## C8
## APM
## B7
## B8
## B9
## B10
## B11
## B1
## B2
## B3
## B4
## B5
## B6
## C1
## C5
## C6
## T1
## T2
## T3
## C2
## C4
## C8 0.000## [1] 32## [1] 2There were 32 violations of local independence but this reduced to two with scaling. This could be reduced further with a handful of residual covariances, but that does not affect the result and does not matter, since they could be entirely attributed to intra-psychometric residual covariances.
summary(LIMPTOII.fit, stand = T, fit = T)## lavaan 0.6-12 ended normally after 63 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 47
##
## Number of observations 459
##
## Model Test User Model:
##
## Test statistic 405.657
## Degrees of freedom 184
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4376.977
## Degrees of freedom 210
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.947
## Tucker-Lewis Index (TLI) 0.939
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11680.977
## Loglikelihood unrestricted model (H1) -11478.149
##
## Akaike (AIC) 23455.954
## Bayesian (BIC) 23650.020
## Sample-size adjusted Bayesian (BIC) 23500.855
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.051
## 90 Percent confidence interval - lower 0.044
## 90 Percent confidence interval - upper 0.058
## P-value RMSEA <= 0.05 0.372
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.052
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## APM 0.332 0.034 9.903 0.000 0.520 0.521
## B7 0.505 0.036 13.893 0.000 0.791 0.792
## B8 0.471 0.036 13.195 0.000 0.738 0.739
## B9 0.482 0.036 13.408 0.000 0.754 0.755
## B10 0.521 0.037 14.195 0.000 0.816 0.817
## B11 0.516 0.037 14.098 0.000 0.808 0.809
## F2 =~
## B1 0.443 0.035 12.640 0.000 0.689 0.690
## B2 0.514 0.036 14.184 0.000 0.801 0.802
## B3 0.522 0.036 14.343 0.000 0.813 0.814
## B4 0.476 0.036 13.374 0.000 0.741 0.741
## B5 0.443 0.035 12.638 0.000 0.689 0.690
## B6 0.526 0.036 14.418 0.000 0.819 0.820
## gPSY =~
## F1 1.204 0.126 9.557 0.000 0.769 0.769
## F2 1.194 0.124 9.629 0.000 0.767 0.767
## F3 =~
## C1 0.163 0.049 3.345 0.001 0.497 0.498
## C5 0.201 0.059 3.412 0.001 0.617 0.617
## C6 0.103 0.033 3.089 0.002 0.315 0.315
## T1 0.236 0.069 3.441 0.001 0.723 0.724
## T2 0.202 0.059 3.412 0.001 0.617 0.617
## T3 0.239 0.069 3.442 0.001 0.731 0.732
## F4 =~
## C2 0.252 0.061 4.102 0.000 0.568 0.569
## C4 0.234 0.057 4.085 0.000 0.529 0.530
## C8 0.228 0.056 4.074 0.000 0.516 0.516
## gPIA =~
## F3 2.893 0.922 3.137 0.002 0.945 0.945
## F4 2.024 0.525 3.852 0.000 0.897 0.897
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## gPSY ~~
## gPIA 0.904 0.037 24.169 0.000 0.904 0.904
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .APM 0.727 0.050 14.536 0.000 0.727 0.728
## .B7 0.372 0.030 12.336 0.000 0.372 0.373
## .B8 0.453 0.034 13.151 0.000 0.453 0.454
## .B9 0.430 0.033 12.947 0.000 0.430 0.431
## .B10 0.332 0.028 11.798 0.000 0.332 0.333
## .B11 0.345 0.029 11.987 0.000 0.345 0.346
## .B1 0.523 0.038 13.703 0.000 0.523 0.524
## .B2 0.356 0.029 12.262 0.000 0.356 0.357
## .B3 0.336 0.028 11.991 0.000 0.336 0.337
## .B4 0.449 0.034 13.202 0.000 0.449 0.450
## .B5 0.523 0.038 13.704 0.000 0.523 0.524
## .B6 0.326 0.028 11.845 0.000 0.326 0.327
## .C1 0.750 0.053 14.227 0.000 0.750 0.752
## .C5 0.618 0.046 13.412 0.000 0.618 0.619
## .C6 0.899 0.061 14.842 0.000 0.899 0.901
## .T1 0.475 0.040 12.007 0.000 0.475 0.476
## .T2 0.617 0.046 13.412 0.000 0.617 0.619
## .T3 0.463 0.039 11.845 0.000 0.463 0.464
## .C2 0.675 0.055 12.227 0.000 0.675 0.676
## .C4 0.718 0.056 12.848 0.000 0.718 0.719
## .C8 0.732 0.056 13.029 0.000 0.732 0.733
## .F1 1.000 0.408 0.408
## .F2 1.000 0.412 0.412
## gPSY 1.000 1.000 1.000
## .F3 1.000 0.107 0.107
## .F4 1.000 0.196 0.196
## gPIA 1.000 1.000 1.000LIMLAT <- list(
F1 = c("APM", "B7", "B8", "B9", "B10", "B11"),
F2 = c("B1", "B2", "B3", "B4", "B5", "B6"),
F3 = c("C1", "C5", "C6", "T1", "T2", "T3"),
F4 = c("C2", "C4", "C8"))
semPaths(LIMPTOII.fit, "model", "std", title = F, residuals = F, groups = "LIMLAT", pastel = T, mar = c(2, 1, 3, 1), bifactor = c("gPSY", "gPIA"), layout = "tree2", exoCov = T)
Overview
| Dataset | Sample Size | Good Fit? | Consistent Loadings? | Base relationship | Standard Error | Identity? | Dimensionality? | |
|---|---|---|---|---|---|---|---|---|
| DeVries & Kohlberg (1977) | 47 | Yes | Yes | 0.876 | 0.096 | Yes | Yes | |
| DeVries (1974) - A | 50 | No | Yes | 0.812 | 0.109 | Yes | Yes | |
| DeVries (1974) - B | 79 | No | Yes | 0.788 | 0.096 | Yes | Yes | |
| DeVries (1974) - C | 126 | NA | Yes | NA | NA | NA | NA | |
| Hathaway (1972) - K | 56 | No | Yes | 0.892 | 0.109 | Yes | Yes | |
| Hathaway (1972) - I | 56 | NA | Yes | NA | NA | NA | NA | |
| Hathaway (1972) - II | 56 | No | Yes | 0.924 | 0.073 | Yes | Yes | |
| Kiga | 39 | Yes | Yes | 0.575 | 0.189 | No* | Yes | |
| Shul (6-8) | 35 | Yes | Yes | 0.628 | 0.153 | No* | Yes | |
| Shul (9-10) | 41 | Yes | Yes | 0.964 | 0.239 | Yes | Yes | |
| Shul (Combined) | 76 | Yes | Yes | 0.764 | 0.123 | Yes | Yes | |
| Lim (1988) | 459 | Yes | Yes | 0.904 | 0.037 | Yes | Yes |
Sample sizes were all on the small side, CFA/JCFA fits were mostly poor, as is the case with most summary-derived data from small samples, and some datasets did not allow fit to be tested because they lacked the number of indicators (DeVries (1974) - C) or they suffered from NPD (Hathaway (1972) - I). Despite this, all datasets showed exceptional stability in factor loadings, when possible, good-to-excellent construct identity despite substantial psychometric sampling error, and good unidimensionality as indicated by the distributions of eigenvalues and the evaluation of local independence. Identity was based on identity with scaled p-values. The consistency of loadings for DeVries - C was based on comparison with the other batteries from those studies.
* There was low power to discriminate between all models, but in this case, that issue was somewhat more egregious than the rest. In it, it appeared the information-theoretic fit criteria were acceptably worse and the \(\chi^2\) fit decrement was likewise acceptable, but because of low power, this ought to be considered tentative at best. Combining both Shul studies’ data - which is viable because invariance held - there was stronger evidence for identity between the two constructs, but power was clearly still low.
Meta-Analysis
The Shul Combined datapoint is not admissible when included along the two it is composed of. However, if the two others are removed and it is used instead, it is more accurately estimated than either and we know the scores can be compared between the two samples, so it absolutely should be worth it. I checked both possibilities - Shul (6-8)/Shul (9-10) separate and Shul (Combined) used - and using the combined sample produced tighter, but slightly lower, estimates. It would be improper to do the same with the Hathaway sample because of the fact that it is not separate, but is, instead, just the same sample, aged. Importantly, because of the developmental predictions of Piagetian theory, the Hathaway samples are doubly valid for separate inclusion, since they should be unconfounded due to the discrete nature of stages. One could argue that the Shul samples need included separately because measurement invariance may have actually failed and we could not detect it due to the small sample size, but that is (1) immaterial because the results are virtually identical and (2) impossible to show.
MetaData <- data.frame("Dataset" = c("DeVries & Kohlberg", "DeVries A", "DeVries B", "Hathaway K", "Hathaway II", "Kiga", "Shul Combined", "Lim"), "R" = c(0.876, 0.812, 0.788, 0.892, 0.924, 0.575, 0.764, 0.904), "SE" = c(0.096, 0.109, 0.096, 0.109, 0.073, 0.189, 0.123, 0.037))
MetaData$ZR <- atanh(MetaData$R); MetaData$ZSE <- atanh(MetaData$SE)
p_load(meta, metafor, dmetar, metasens)
PiaMeta <- metagen(TE = ZR,
seTE = ZSE,
MetaData,
studlab = Dataset,
sm = "ZCOR",
method.tau = "SJ",
hakn = T,
backtrans = T,
title = "Piagetian g Correlations with Psychometric g"); summary(PiaMeta)## Review: Piagetian g Correlations with Psychometric g
##
## COR 95%-CI %W(common) %W(random)
## DeVries & Kohlberg 0.8760 [0.8241; 0.9133] 7.7 12.8
## DeVries A 0.8120 [0.7251; 0.8734] 6.0 12.5
## DeVries B 0.7880 [0.7051; 0.8496] 7.7 12.8
## Hathaway K 0.8920 [0.8388; 0.9283] 6.0 12.5
## Hathaway II 0.9240 [0.9000; 0.9424] 13.4 13.4
## Kiga 0.5750 [0.2729; 0.7739] 2.0 9.9
## Shul Combined 0.7640 [0.6431; 0.8477] 4.7 12.0
## Lim 0.9040 [0.8898; 0.9164] 52.4 14.1
##
## Number of studies combined: k = 8
##
## COR 95%-CI z|t p-value
## Common effect model 0.8857 [0.8739; 0.8965] 52.30 0
## Random effects model 0.8465 [0.7578; 0.9045] 11.63 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 0.0808 [0.0259; 0.3890]; tau = 0.2843 [0.1608; 0.6237]
## I^2 = 88.1% [78.8%; 93.3%]; H = 2.90 [2.17; 3.86]
##
## Test of heterogeneity:
## Q d.f. p-value
## 58.69 7 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Fisher's z transformation of correlationsforest.meta(PiaMeta, layout = "JAMA",
col.diamond = "gold",
sortvar = TE,
predict = T,
print.tau2 = T,
leftlabs = c("Author", "Correlation", "95% CI"),
xlim = c(-0.15, 1.05),
digits = 3)
metabias(PiaMeta, method.bias = "linreg"); pcurve(PiaMeta); TF = trimfill(PiaMeta, side = "left"); summary(TF); funnel(TF, legend = T); limit <- limitmeta(PiaMeta); summary(limit); funnel.limitmeta(limit, xlim = c(0.3, 2.0), shrunken = T)## Warning: Number of studies (k=8) too small to test for small study effects
## (k.min=10). Change argument 'k.min' if appropriate.
## P-curve analysis
## -----------------------
## - Total number of provided studies: k = 8
## - Total number of p<0.05 studies included into the analysis: k = 8 (100%)
## - Total number of studies with p<0.025: k = 8 (100%)
##
## Results
## -----------------------
## pBinomial zFull pFull zHalf pHalf
## Right-skewness test 0.004 -19.956 0 -19.638 0
## Flatness test 1.000 19.996 1 20.172 1
## Note: p-values of 0 or 1 correspond to p<0.001 and p>0.999, respectively.
## Power Estimate: 99% (99%-99%)
##
## Evidential value
## -----------------------
## - Evidential value present: yes
## - Evidential value absent/inadequate: no## Review: Piagetian g Correlations with Psychometric g
##
## COR 95%-CI %W(random)
## DeVries & Kohlberg 0.8760 [0.8241; 0.9133] 9.3
## DeVries A 0.8120 [0.7251; 0.8734] 9.2
## DeVries B 0.7880 [0.7051; 0.8496] 9.3
## Hathaway K 0.8920 [0.8388; 0.9283] 9.2
## Hathaway II 0.9240 [0.9000; 0.9424] 9.5
## Kiga 0.5750 [0.2729; 0.7739] 8.2
## Shul Combined 0.7640 [0.6431; 0.8477] 9.0
## Lim 0.9040 [0.8898; 0.9164] 9.7
## Filled: DeVries B 0.9541 [0.9338; 0.9683] 9.3
## Filled: Shul Combined 0.9592 [0.9346; 0.9747] 9.0
## Filled: Kiga 0.9796 [0.9573; 0.9903] 8.2
##
## Number of studies combined: k = 11 (with 3 added studies)
##
## COR 95%-CI t p-value
## Random effects model 0.8940 [0.8120; 0.9414] 10.40 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 0.1978 [0.0836; 0.6611]; tau = 0.4447 [0.2891; 0.8131]
## I^2 = 91.3% [86.5%; 94.4%]; H = 3.40 [2.72; 4.24]
##
## Test of heterogeneity:
## Q d.f. p-value
## 115.39 10 < 0.0001
##
## Details on meta-analytical method:
## - Inverse variance method
## - Sidik-Jonkman estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Trim-and-fill method to adjust for funnel plot asymmetry
## - Fisher's z transformation of correlations
## Results for individual studies
## (left: original data; right: shrunken estimates)
##
## COR 95%-CI COR 95%-CI
## DeVries & Kohlberg 0.8760 [0.8241; 0.9133] 0.9243 [0.8915; 0.9475]
## DeVries A 0.8120 [0.7251; 0.8734] 0.9006 [0.8513; 0.9341]
## DeVries B 0.7880 [0.7051; 0.8496] 0.8719 [0.8185; 0.9104]
## Hathaway K 0.8920 [0.8388; 0.9283] 0.9419 [0.9121; 0.9618]
## Hathaway II 0.9240 [0.9000; 0.9424] 0.9428 [0.9245; 0.9567]
## Kiga 0.5750 [0.2729; 0.7739] 0.9233 [0.8442; 0.9630]
## Shul Combined 0.7640 [0.6431; 0.8477] 0.8941 [0.8336; 0.9334]
## Lim 0.9040 [0.8898; 0.9164] 0.9110 [0.8979; 0.9226]
##
## Result of limit meta-analysis:
##
## Random effects model COR 95%-CI z pval
## Adjusted estimate 0.9166 [0.8379; 0.9579] 8.70 < 0.0001
## Unadjusted estimate 0.8465 [0.7578; 0.9045] 11.63 < 0.0001
##
## Quantifying heterogeneity:
## tau^2 = 0.0808; I^2 = 88.1% [78.8%; 93.3%]; G^2 = 2.4%
##
## Test of heterogeneity:
## Q d.f. p-value
## 58.69 7 < 0.0001
##
## Test of small-study effects:
## Q-Q' d.f. p-value
## 34.29 1 < 0.0001
##
## Test of residual heterogeneity beyond small-study effects:
## Q' d.f. p-value
## 24.40 6 0.0004
##
## Details on adjustment method:
## - expectation (beta0)
Discussion
It should be noted that many of the members of these samples were bright, provoking concern about range restriction.
Humphreys & Parson’s (1979) conclusion that the scale scores from different tests seem to be as correlated with one another as they are with the ones from conceptually unrelated tests like Piaget’s seems to be confirmed. For example, in the Hathaway Kindergarten data, the WISC PIQ and VIQ scales correlate at r = 0.51 and they each correlate with the total Piagetian score at r’s of 0.46 and 0.51, respectively. The Piaget total score correlated with the Lorge-Thorndike total at 0.41, while the WISC PIQ and VIQ correlated with it at 0.65 and 0.34. In the later age group - second grade -, these correlations become 0.54, 0.54, 0.55, 0.49, 0.45, and 0.61. In this older year, the PIQ, VIQ, Lorge-Thorndike total and Piaget total correlated with the CAT reading, arithmetic and language totals and the aggregate CAT total at 0.54/0.61/0.46/0.62 (PIQ), 0.41/0.48/0.37/0.50 (VIQ), 0.57/0.47/0.49/0.56 (LT), 0.57/0.66/0.48/0.65 (Piaget). All of this occurs despite a lack of content overlap.
Loadings estimated in batteries with Piagetian or psychometric tests only do not produce meaningfully different g loadings, indicating that, as Jensen was wont to exclaim (2001; see also Thorndike, 1987; Vernon, 1989), the g loadings of measures are more a product of the measure than of the battery of tests they are found among. It is undoubtedly true that, despite a lack of shared content, these diverse tests are strongly related and they share perplexingly much in common if one subscribes to the idea that there is no psychometric g. It is always interesting to see just how robust the indifference of the indicator is.
In those batteries in which it could be tested, it appeared that a model with an identical g between the measures was better, and especially so when psychometric sampling error was to some degree reduced. The inability to fully handle that issue surely drives down g factor correlations, but in all batteries in which testing was possible, it is clearly the case that the constructs share too much to interpret independently; despite no shared content in many cases, the measures lack discriminant validity. Sampling error of the regular sort could explain much of the rest of this. The local independence observed reinforces this point. There was low power for reasonably definitive tests and, again, because the data were summary statistics, it’s hard to conclude much from these, but the result does seem to generalize, as in Lim’s (1988) data, which is much higher quality and yields basically the same conclusion.
Unfortunately, invariance between grades could not be tested in Hathaway’s data due to NPD issues and poor overall fits.
An interesting thing to note based on the Hathaway data is that the Piagetian total was always more related to the cognitive tests than it was to chronological age, but, it is worth noting that age was range restricted and there was a discrepancy in Hathaway’s summary statistics, where the standard deviation for age somehow increased in the last grade when that would only be possible if, say, testing were lagged for some members of the sample or unmentioned attrition took place. Despite these issues, this finding is similar to Carpenter’s (1955), that mental age (IQ) is more closely related to Piagetian concept formation development than is chronological age (see also Russell, 1942; Elkind, 1961; Freyberg, 1966).
I am grateful that Laura Ackermann provided me with the data from her analysis (Rindermann & Ackermann, 2020). My reanalysis reached much the same conclusion as the other studies analyzed here, but with raw data. These datasets were small, had minimal missingness, and suffered considerably from psychometric sampling error, but they nonetheless confirmed that psychometric general intelligence is at least strongly related to Piagetian intelligence and their data is by no means inconsistent with these constructs being identical. Interestingly, invariance was achievably in Shul’s different-aged samples.
From these samples, it appears that Piagetian “intelligence” is comparable to more typically-defined psychometric or achievement-based measurement/representation of intelligence. At the least, it is too similar to be reliably distinguished from it, despite sharing, in many cases, no content between their testing instruments.
References
Carroll, J. B., Kohlberg, L., & DeVries, R. (1984). Psychometric and Piagetian intelligences: Toward resolution of controversy. Intelligence, 8(1), 67–91. https://doi.org/10.1016/0160-2896(84)90007-2
DeVries, R., & Kohlberg, L. (1977). Relations between Piagetian and psychometric assessments of intelligence. In L. Katz (Ed.), Current topics in early childhood education (Vol. 1). Ablex Publishing.
DeVries, R. (1974). Relationships among Piagetian, IQ, and Achievement Assessments. Child Development, 45(3), 746–756. https://doi.org/10.2307/1127841
Hathaway, Walter Ennis. The Degree and Nature of the Relations Between Traditional Psychometric and Piagetian Developmental Measures of Mental Development, 1972. https://eric.ed.gov/?id=ED075485.
Humphreys, L. G., & Parsons, C. K. (1979). Piagetian tasks measure intelligence and intelligence tests assess cognitive development: A reanalysis. Intelligence, 3(4), 369–381. https://doi.org/10.1016/0160-2896(79)90005-9
Jensen, A. R. (2001). Vocabulary and general intelligence. Behavioral and Brain Sciences, 24(6), 1109–1110. https://doi.org/10.1017/S0140525X01280133
Thorndike, R. L. (1987). Stability of factor loadings. Personality and Individual Differences, 8(4), 585–586. https://doi.org/10.1016/0191-8869(87)90224-8
Vernon, P. A. (1989). The generality of g. Personality and Individual Differences, 10(7), 803–804. https://doi.org/10.1016/0191-8869(89)90129-3
Lim, T. K. (1988). Relationships between standardized psychometric and Piagetian measures of intelligence at the formal operations level. Intelligence, 12(2), 167–182. https://doi.org/10.1016/0160-2896(88)90014-1
Carpenter, T. E. (1955). A Pilot Study for a Quantitative Investigation of Jean Piaget’s Original Work on Concept Formation. Educational Review, 7(2), 142–149. https://doi.org/10.1080/0013191550070207
Russell, R. W. (1942). Studies in animism: V. Animism in older children. The Pedagogical Seminary and Journal of Genetic Psychology, 60, 329–335. https://doi.org/10.1080/08856559.1942.10534642
Elkind, D. (1961). The development of quantitative thinking: A systematic replication of Piaget’s studies. The Journal of Genetic Psychology: Research and Theory on Human Development, 98, 37–46. https://doi.org/10.1080/00221325.1961.10534349
Freyberg, P. S. (1966). Concept development in Piagetian terms in relation to school attainment. Journal of Educational Psychology, 57(3), 164–168. https://doi.org/10.1037/h0023411
Rindermann, H., & Ackermann, A.L., (2020). Piagetian Tasks and Psychometric Intelligence: Different or Similar Constructs? Psychological Reports. https://doi.org/10.1177/0033294120965876
Post-Script: Laura Ackermann’s Data
#Provided with permission from Dr. Ackermann.
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