CFA Male v Female Latent Approach - Measurement Invariance
Load libraries
library(lavaan)## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.library(semTools) # For model comparison## ## ################################################################################# This is semTools 0.5-6## All users of R (or SEM) are invited to submit functions or ideas for functions.## ###############################################################################Building variance/covariance matrix for MALES
# We're not importing raw data. We're building a var/cov matrix
lowerM <- '
102.0100,
36.7781, 104.0400,
16.3423, 24.4999, 101.0025,
11.5271, 14.4228, 39.6885, 102.0100,
8.8597, 17.1666, 45.1044, 39.7657, 104.0400,
14.6167, 21.2196, 32.4218, 39.2824, 32.4957, 101.0025'
M.cov <- getCov(lowerM, names=c("Blocks", "Geo", "Info", "Arith", "Colors",
"SimDiff"))
M.cov## Blocks Geo Info Arith Colors SimDiff
## Blocks 102.0100 36.7781 16.3423 11.5271 8.8597 14.6167
## Geo 36.7781 104.0400 24.4999 14.4228 17.1666 21.2196
## Info 16.3423 24.4999 101.0025 39.6885 45.1044 32.4218
## Arith 11.5271 14.4228 39.6885 102.0100 39.7657 39.2824
## Colors 8.8597 17.1666 45.1044 39.7657 104.0400 32.4957
## SimDiff 14.6167 21.2196 32.4218 39.2824 32.4957 101.0025Getting means for male matrix
M.mean = matrix(c( 17.97, 16.14, 13.42, 16.75, 14.19, 17.49 ), nrow = 1,
ncol = 6, byrow = TRUE)
colnames(M.mean) = c("Blocks", "Geo", "Info", "Arith", "Colors", "SimDiff")
M.mean## Blocks Geo Info Arith Colors SimDiff
## [1,] 17.97 16.14 13.42 16.75 14.19 17.49Building variance/covariance matrix for FEMALES
lowerF <- '
98.0100,
42.1087, 104.0400,
22.2305, 23.5149, 99.6004,
13.6986, 12.0533, 23.9899, 102.0100,
15.7608, 17.3548, 32.9679, 32.1584, 99.0025,
14.5703, 24.1225, 38.4929, 37.7255, 27.3690, 103.0225'
F.cov <- getCov(lowerF, names=c("Blocks", "Geo", "Info", "Arith", "Colors",
"SimDiff"))
F.cov## Blocks Geo Info Arith Colors SimDiff
## Blocks 98.0100 42.1087 22.2305 13.6986 15.7608 14.5703
## Geo 42.1087 104.0400 23.5149 12.0533 17.3548 24.1225
## Info 22.2305 23.5149 99.6004 23.9899 32.9679 38.4929
## Arith 13.6986 12.0533 23.9899 102.0100 32.1584 37.7255
## Colors 15.7608 17.3548 32.9679 32.1584 99.0025 27.3690
## SimDiff 14.5703 24.1225 38.4929 37.7255 27.3690 103.0225Means for females matrix
F.mean = matrix(c( 16.79, 14.41, 16.42, 15.57, 15.91, 16.94 ), nrow = 1,
ncol = 6, byrow = TRUE)
colnames(F.mean) = c("Blocks", "Geo", "Info", "Arith", "Colors", "SimDiff")
F.mean## Blocks Geo Info Arith Colors SimDiff
## [1,] 16.79 14.41 16.42 15.57 15.91 16.94Configural Model (no ID Constraints)
#CFA function
model.lsyntax <- '
! regressions
NonV =~Blocks + Geo
V=~ Info + Arith + Colors + SimDiff
'
fit_configural<-cfa(model.lsyntax, sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=list(322, 262))
summary(fit_configural, fit.measures=T, standardized = T)## lavaan 0.6.15 ended normally after 192 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 20.773
## Degrees of freedom 16
## P-value (Chi-square) 0.187
## Test statistic for each group:
## Group 1 9.104
## Group 2 11.669
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.990
## Tucker-Lewis Index (TLI) 0.981
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12821.847
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25719.693
## Bayesian (BIC) 25885.750
## Sample-size adjusted Bayesian (SABIC) 25765.114
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.067
## P-value H_0: RMSEA <= 0.050 0.772
## P-value H_0: RMSEA >= 0.080 0.008
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.026
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks 1.000 4.928 0.489
## Geo 1.510 0.482 3.133 0.002 7.440 0.731
## V =~
## Info 1.000 6.588 0.657
## Arith 0.950 0.123 7.738 0.000 6.260 0.621
## Colors 0.968 0.125 7.767 0.000 6.374 0.626
## SimDiff 0.829 0.116 7.155 0.000 5.459 0.544
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 13.554 4.566 2.969 0.003 0.417 0.417
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 17.970 0.562 31.976 0.000 17.970 1.782
## .Geo 16.140 0.568 28.439 0.000 16.140 1.585
## .Info 13.420 0.559 23.999 0.000 13.420 1.337
## .Arith 16.750 0.562 29.806 0.000 16.750 1.661
## .Colors 14.190 0.568 25.003 0.000 14.190 1.393
## .SimDiff 17.490 0.559 31.277 0.000 17.490 1.743
## NonV 0.000 0.000 0.000
## V 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 77.406 9.746 7.942 0.000 77.406 0.761
## .Geo 48.368 17.736 2.727 0.006 48.368 0.466
## .Info 57.288 6.537 8.764 0.000 57.288 0.569
## .Arith 62.502 6.617 9.446 0.000 62.502 0.615
## .Colors 63.083 6.743 9.355 0.000 63.083 0.608
## .SimDiff 70.887 6.723 10.544 0.000 70.887 0.704
## NonV 24.287 9.208 2.638 0.008 1.000 1.000
## V 43.401 8.058 5.386 0.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks 1.000 5.928 0.600
## Geo 1.194 0.313 3.818 0.000 7.076 0.695
## V =~
## Info 1.000 5.892 0.592
## Arith 0.883 0.159 5.566 0.000 5.205 0.516
## Colors 0.879 0.157 5.599 0.000 5.180 0.522
## SimDiff 1.074 0.178 6.039 0.000 6.328 0.625
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 17.156 4.878 3.517 0.000 0.491 0.491
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 16.790 0.610 27.504 0.000 16.790 1.699
## .Geo 14.410 0.629 22.911 0.000 14.410 1.415
## .Info 16.420 0.615 26.682 0.000 16.420 1.648
## .Arith 15.570 0.623 25.000 0.000 15.570 1.545
## .Colors 15.910 0.614 25.932 0.000 15.910 1.602
## .SimDiff 16.940 0.626 27.066 0.000 16.940 1.672
## NonV 0.000 0.000 0.000
## V 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 62.489 10.493 5.955 0.000 62.489 0.640
## .Geo 53.578 13.595 3.941 0.000 53.578 0.517
## .Info 64.500 7.719 8.356 0.000 64.500 0.650
## .Arith 74.532 7.941 9.385 0.000 74.532 0.733
## .Colors 71.788 7.699 9.324 0.000 71.788 0.728
## .SimDiff 62.588 8.046 7.779 0.000 62.588 0.610
## NonV 35.147 11.102 3.166 0.002 1.000 1.000
## V 34.721 8.439 4.114 0.000 1.000 1.000Weak FI Model (no ID constraints; but look at group.equal function)
model.lsyntax <- '
! regressions
NonV =~Blocks + Geo
V=~ Info + Arith + Colors + SimDiff
'
fit_weak<-cfa(model.lsyntax, sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=list(322, 262),
group.equal=c("loadings"))
summary(fit_weak, fit.measures=T, standardized = T)## lavaan 0.6.15 ended normally after 165 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
## Number of equality constraints 4
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 24.202
## Degrees of freedom 20
## P-value (Chi-square) 0.234
## Test statistic for each group:
## Group 1 10.420
## Group 2 13.782
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.991
## Tucker-Lewis Index (TLI) 0.987
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12823.561
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25715.123
## Bayesian (BIC) 25863.699
## Sample-size adjusted Bayesian (SABIC) 25755.762
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.027
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.060
## P-value H_0: RMSEA <= 0.050 0.858
## P-value H_0: RMSEA >= 0.080 0.002
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.031
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks 1.000 5.323 0.526
## Geo (.p2.) 1.304 0.261 4.995 0.000 6.939 0.683
## V =~
## Info 1.000 6.498 0.649
## Arith (.p4.) 0.934 0.099 9.481 0.000 6.072 0.607
## Colors (.p5.) 0.946 0.099 9.532 0.000 6.146 0.608
## SimDiff (.p6.) 0.922 0.098 9.394 0.000 5.993 0.586
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 15.003 3.910 3.837 0.000 0.434 0.434
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 17.970 0.564 31.861 0.000 17.970 1.776
## .Geo 16.140 0.566 28.514 0.000 16.140 1.589
## .Info 13.420 0.558 24.046 0.000 13.420 1.340
## .Arith 16.750 0.557 30.058 0.000 16.750 1.675
## .Colors 14.190 0.564 25.179 0.000 14.190 1.403
## .SimDiff 17.490 0.570 30.695 0.000 17.490 1.711
## NonV 0.000 0.000 0.000
## V 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 74.095 8.594 8.622 0.000 74.095 0.723
## .Geo 55.026 11.558 4.761 0.000 55.026 0.533
## .Info 58.069 6.278 9.250 0.000 58.069 0.579
## .Arith 63.126 6.350 9.941 0.000 63.126 0.631
## .Colors 64.497 6.488 9.940 0.000 64.497 0.631
## .SimDiff 68.631 6.695 10.251 0.000 68.631 0.656
## NonV 28.334 7.566 3.745 0.000 1.000 1.000
## V 42.227 6.962 6.066 0.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks 1.000 5.654 0.575
## Geo (.p2.) 1.304 0.261 4.995 0.000 7.370 0.722
## V =~
## Info 1.000 5.944 0.595
## Arith (.p4.) 0.934 0.099 9.481 0.000 5.554 0.544
## Colors (.p5.) 0.946 0.099 9.532 0.000 5.621 0.561
## SimDiff (.p6.) 0.922 0.098 9.394 0.000 5.481 0.554
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 16.252 4.216 3.855 0.000 0.484 0.484
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 16.790 0.608 27.616 0.000 16.790 1.706
## .Geo 14.410 0.631 22.844 0.000 14.410 1.411
## .Info 16.420 0.617 26.611 0.000 16.420 1.644
## .Arith 15.570 0.630 24.708 0.000 15.570 1.526
## .Colors 15.910 0.619 25.685 0.000 15.910 1.587
## .SimDiff 16.940 0.611 27.706 0.000 16.940 1.712
## NonV 0.000 0.000 0.000
## V 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 64.880 8.865 7.319 0.000 64.880 0.670
## .Geo 49.940 12.375 4.035 0.000 49.940 0.479
## .Info 64.429 7.270 8.863 0.000 64.429 0.646
## .Arith 73.197 7.713 9.490 0.000 73.197 0.704
## .Colors 68.931 7.410 9.302 0.000 68.931 0.686
## .SimDiff 67.897 7.244 9.372 0.000 67.897 0.693
## NonV 31.964 8.492 3.764 0.000 1.000 1.000
## V 35.328 6.457 5.471 0.000 1.000 1.000Strong FI Model (no ID constraints, but equate loadings & intercepts)
model.lsyntax <- '
! regressions
NonV =~Blocks + Geo
V=~ Info + Arith + Colors + SimDiff
'
fit_strong<-cfa(model.lsyntax, sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=list(322, 262),
group.equal=c("loadings", "intercepts"))
summary(fit_strong, fit.measures=T, standardized = T)## lavaan 0.6.15 ended normally after 204 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 40
## Number of equality constraints 10
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 48.321
## Degrees of freedom 24
## P-value (Chi-square) 0.002
## Test statistic for each group:
## Group 1 20.327
## Group 2 27.995
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.949
## Tucker-Lewis Index (TLI) 0.936
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12835.621
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25731.242
## Bayesian (BIC) 25862.339
## Sample-size adjusted Bayesian (SABIC) 25767.100
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.059
## 90 Percent confidence interval - lower 0.034
## 90 Percent confidence interval - upper 0.083
## P-value H_0: RMSEA <= 0.050 0.250
## P-value H_0: RMSEA >= 0.080 0.076
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.044
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks 1.000 5.294 0.523
## Geo (.p2.) 1.317 0.253 5.217 0.000 6.975 0.687
## V =~
## Info 1.000 6.627 0.656
## Arith (.p4.) 0.889 0.095 9.324 0.000 5.891 0.590
## Colors (.p5.) 0.941 0.098 9.580 0.000 6.237 0.615
## SimDiff (.p6.) 0.885 0.095 9.286 0.000 5.866 0.575
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 15.250 3.928 3.883 0.000 0.435 0.435
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (.16.) 18.015 0.497 36.247 0.000 18.015 1.780
## .Geo (.17.) 16.115 0.546 29.496 0.000 16.115 1.586
## .Info (.18.) 14.266 0.515 27.696 0.000 14.266 1.412
## .Arith (.19.) 15.906 0.495 32.112 0.000 15.906 1.592
## .Colors (.20.) 14.533 0.506 28.696 0.000 14.533 1.433
## .SimDiff (.21.) 16.852 0.498 33.834 0.000 16.852 1.651
## NonV 0.000 0.000 0.000
## V 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 74.365 8.443 8.808 0.000 74.365 0.726
## .Geo 54.551 11.391 4.789 0.000 54.551 0.529
## .Info 58.123 6.409 9.070 0.000 58.123 0.570
## .Arith 65.103 6.408 10.160 0.000 65.103 0.652
## .Colors 63.957 6.530 9.795 0.000 63.957 0.622
## .SimDiff 69.779 6.729 10.371 0.000 69.779 0.670
## NonV 28.031 7.295 3.842 0.000 1.000 1.000
## V 43.918 7.197 6.102 0.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks 1.000 5.621 0.571
## Geo (.p2.) 1.317 0.253 5.217 0.000 7.405 0.725
## V =~
## Info 1.000 6.038 0.598
## Arith (.p4.) 0.889 0.095 9.324 0.000 5.367 0.525
## Colors (.p5.) 0.941 0.098 9.580 0.000 5.682 0.566
## SimDiff (.p6.) 0.885 0.095 9.286 0.000 5.344 0.540
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 16.511 4.234 3.899 0.000 0.487 0.487
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (.16.) 18.015 0.497 36.247 0.000 18.015 1.831
## .Geo (.17.) 16.115 0.546 29.496 0.000 16.115 1.578
## .Info (.18.) 14.266 0.515 27.696 0.000 14.266 1.412
## .Arith (.19.) 15.906 0.495 32.112 0.000 15.906 1.555
## .Colors (.20.) 14.533 0.506 28.696 0.000 14.533 1.446
## .SimDiff (.21.) 16.852 0.498 33.834 0.000 16.852 1.701
## NonV -1.273 0.617 -2.062 0.039 -0.226 -0.226
## V 0.981 0.642 1.528 0.127 0.163 0.163
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 65.168 8.684 7.504 0.000 65.168 0.674
## .Geo 49.476 12.174 4.064 0.000 49.476 0.474
## .Info 65.562 7.475 8.771 0.000 65.562 0.643
## .Arith 75.894 7.858 9.658 0.000 75.894 0.725
## .Colors 68.668 7.465 9.199 0.000 68.668 0.680
## .SimDiff 69.543 7.328 9.489 0.000 69.543 0.709
## NonV 31.592 8.181 3.862 0.000 1.000 1.000
## V 36.453 6.671 5.464 0.000 1.000 1.000Strict FI Model (no ID constraints, but equate loadings, intercepts, & ?)
#model.lsyntax <- Compare Fit of models with no ID constraints
#Fit<-compareFit(fit_configural, fit_weak, fit_strong, fit_strict)
#summary(Fit)Configural Model (equate one set of lambdas per latent variable and one set of intercepts per latent)
# Note: Identifying constraints on b1 and b3, nu1 and nu3
# Latent variables: NonV = Non Verbal; V = Verbal
Conf.Model <- '
! regressions
NonV =~NA*Blocks + c(b1,b1)*Blocks + c(b21,b22)*Geo
V=~NA*Info + c(b3,b3)*Info + c(b41,b42)*Arith + c(b51,b52)*Colors +
c(b61,b62)*SimDiff
! residuals, variances and covariances
Blocks~~Blocks;
Geo~~Geo;
Info~~Info;
Arith~~Arith;
Colors~~Colors;
SimDiff~~SimDiff;
NonV~~V
V ~~ c(1,NA)*V
NonV ~~ c(1,NA)*NonV
! intercepts (nu) & means (alphas)
Blocks~c(n1,n1)*1;
Geo~c(n21,n22)*1;
Info~c(n3,n3)*1;
Arith~c(n41,n42)*1;
Colors~c(n51,n52)*1;
SimDiff~c(n61,n62)*1;
! Constrain Males to factor mean of 0, females are relative to males
NonV~c(a11,a12)*1;
V~c(a21,a22)*1;
a11==0
a21==0
'
Model1 <- cfa(model=Conf.Model,fixed.x=FALSE,std.lv = F,
sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=c(322, 262),
meanstructure = TRUE)
summary(Model1, standardized = TRUE, fit.measures=TRUE)## lavaan 0.6.15 ended normally after 146 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 44
## Number of equality constraints 6
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 20.773
## Degrees of freedom 16
## P-value (Chi-square) 0.187
## Test statistic for each group:
## Group 1 9.104
## Group 2 11.669
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.990
## Tucker-Lewis Index (TLI) 0.981
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12821.847
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25719.693
## Bayesian (BIC) 25885.750
## Sample-size adjusted Bayesian (SABIC) 25765.114
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.067
## P-value H_0: RMSEA <= 0.050 0.772
## P-value H_0: RMSEA >= 0.080 0.008
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.026
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 4.928 0.934 5.275 0.000 4.928 0.489
## Geo (b21) 7.440 1.261 5.897 0.000 7.440 0.731
## V =~
## Info (b3) 6.588 0.612 10.772 0.000 6.588 0.657
## Arith (b41) 6.260 0.616 10.163 0.000 6.260 0.621
## Colors (b51) 6.374 0.622 10.251 0.000 6.374 0.626
## SimDiff (b61) 5.459 0.619 8.812 0.000 5.459 0.544
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.417 0.087 4.823 0.000 0.417 0.417
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 17.970 0.562 31.976 0.000 17.970 1.782
## .Geo (n21) 16.140 0.568 28.439 0.000 16.140 1.585
## .Info (n3) 13.420 0.559 23.999 0.000 13.420 1.337
## .Arith (n41) 16.750 0.562 29.806 0.000 16.750 1.661
## .Colors (n51) 14.190 0.568 25.003 0.000 14.190 1.393
## .SimDiff (n61) 17.490 0.559 31.277 0.000 17.490 1.743
## NonV (a11) 0.000 0.000 0.000
## V (a21) 0.000 NA 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 77.406 9.746 7.942 0.000 77.406 0.761
## .Geo 48.368 17.736 2.727 0.006 48.368 0.466
## .Info 57.288 6.537 8.764 0.000 57.288 0.569
## .Arith 62.502 6.617 9.446 0.000 62.502 0.615
## .Colors 63.083 6.743 9.355 0.000 63.083 0.608
## .SimDiff 70.887 6.723 10.544 0.000 70.887 0.704
## V 1.000 1.000 1.000
## NonV 1.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 4.928 0.934 5.275 0.000 5.928 0.600
## Geo (b22) 5.882 1.902 3.093 0.002 7.076 0.695
## V =~
## Info (b3) 6.588 0.612 10.772 0.000 5.892 0.592
## Arith (b42) 5.819 1.177 4.945 0.000 5.205 0.516
## Colors (b52) 5.792 1.166 4.968 0.000 5.180 0.522
## SimDiff (b62) 7.075 1.343 5.267 0.000 6.328 0.625
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.528 0.188 2.818 0.005 0.491 0.491
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 17.970 0.562 31.976 0.000 17.970 1.819
## .Geo (n22) 15.818 1.063 14.879 0.000 15.818 1.554
## .Info (n3) 13.420 0.559 23.999 0.000 13.420 1.347
## .Arith (n42) 12.920 0.973 13.276 0.000 12.920 1.282
## .Colors (n52) 13.272 0.963 13.779 0.000 13.272 1.336
## .SimDiff (n62) 13.718 1.081 12.693 0.000 13.718 1.354
## NonV (a12) -0.239 0.174 -1.373 0.170 -0.199 -0.199
## V (a22) 0.455 0.133 3.421 0.001 0.509 0.509
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 62.489 10.493 5.955 0.000 62.489 0.640
## .Geo 53.578 13.595 3.941 0.000 53.578 0.517
## .Info 64.500 7.719 8.356 0.000 64.500 0.650
## .Arith 74.532 7.941 9.385 0.000 74.532 0.733
## .Colors 71.788 7.699 9.324 0.000 71.788 0.728
## .SimDiff 62.588 8.046 7.779 0.000 62.588 0.610
## V 0.800 0.245 3.269 0.001 1.000 1.000
## NonV 1.447 0.714 2.026 0.043 1.000 1.000
##
## Constraints:
## |Slack|
## a11 - 0 0.000
## a21 - 0 0.000Weak (Configural + equate all loadings)
Weak.Model <- '
! regressions
NonV =~NA*Blocks + c(b1,b1)*Blocks + c(b2,b2)*Geo
V=~NA*Info + c(b3,b3)*Info + c(b4,b4)*Arith + c(b5,b5)*Colors +
c(b6,b6)*SimDiff
! residuals, variances and covariances
Blocks~~Blocks;
Geo~~Geo;
Info~~Info;
Arith~~Arith;
Colors~~Colors;
SimDiff~~SimDiff;
NonV~~V
V ~~ c(1,NA)*V
NonV ~~ c(1,NA)*NonV
! intercepts (nu) & means (alphas)
Blocks~c(n1,n1)*1;
Geo~c(n21,n22)*1;
Info~c(n3,n3)*1;
Arith~c(n41,n42)*1;
Colors~c(n51,n52)*1;
SimDiff~c(n61,n62)*1;
! Constrain Males to factor mean of 0, females are relative to males
NonV~c(a11,a12)*1;
V~c(a21,a22)*1;
a11==0
a21==0
'
Model2 <- cfa(model=Weak.Model,fixed.x=FALSE,std.lv = F,
sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=c(322, 262),
meanstructure = TRUE)
summary(Model2, standardized = TRUE, fit.measures=TRUE)## lavaan 0.6.15 ended normally after 76 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 44
## Number of equality constraints 10
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 24.202
## Degrees of freedom 20
## P-value (Chi-square) 0.234
## Test statistic for each group:
## Group 1 10.420
## Group 2 13.782
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.991
## Tucker-Lewis Index (TLI) 0.987
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12823.561
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25715.123
## Bayesian (BIC) 25863.699
## Sample-size adjusted Bayesian (SABIC) 25755.762
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.027
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.060
## P-value H_0: RMSEA <= 0.050 0.858
## P-value H_0: RMSEA >= 0.080 0.002
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.031
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 5.323 0.711 7.490 0.000 5.323 0.526
## Geo (b2) 6.939 0.870 7.972 0.000 6.939 0.683
## V =~
## Info (b3) 6.498 0.536 12.131 0.000 6.498 0.649
## Arith (b4) 6.072 0.532 11.416 0.000 6.072 0.607
## Colors (b5) 6.146 0.536 11.468 0.000 6.146 0.608
## SimDiff (b6) 5.993 0.538 11.142 0.000 5.993 0.586
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.434 0.083 5.218 0.000 0.434 0.434
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 17.970 0.564 31.861 0.000 17.970 1.776
## .Geo (n21) 16.140 0.566 28.514 0.000 16.140 1.589
## .Info (n3) 13.420 0.558 24.046 0.000 13.420 1.340
## .Arith (n41) 16.750 0.557 30.058 0.000 16.750 1.675
## .Colors (n51) 14.190 0.564 25.179 0.000 14.190 1.403
## .SimDiff (n61) 17.490 0.570 30.695 0.000 17.490 1.711
## NonV (a11) 0.000 0.000 0.000
## V (a21) 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 74.095 8.594 8.622 0.000 74.095 0.723
## .Geo 55.026 11.558 4.761 0.000 55.026 0.533
## .Info 58.069 6.278 9.250 0.000 58.069 0.579
## .Arith 63.126 6.350 9.941 0.000 63.126 0.631
## .Colors 64.497 6.488 9.940 0.000 64.497 0.631
## .SimDiff 68.631 6.695 10.251 0.000 68.631 0.656
## V 1.000 1.000 1.000
## NonV 1.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 5.323 0.711 7.490 0.000 5.654 0.575
## Geo (b2) 6.939 0.870 7.972 0.000 7.370 0.722
## V =~
## Info (b3) 6.498 0.536 12.131 0.000 5.944 0.595
## Arith (b4) 6.072 0.532 11.416 0.000 5.554 0.544
## Colors (b5) 6.146 0.536 11.468 0.000 5.621 0.561
## SimDiff (b6) 5.993 0.538 11.142 0.000 5.481 0.554
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.470 0.111 4.216 0.000 0.484 0.484
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 17.970 0.564 31.861 0.000 17.970 1.826
## .Geo (n22) 15.948 1.117 14.283 0.000 15.948 1.562
## .Info (n3) 13.420 0.558 24.046 0.000 13.420 1.344
## .Arith (n42) 12.767 0.924 13.819 0.000 12.767 1.252
## .Colors (n52) 13.073 0.922 14.177 0.000 13.073 1.304
## .SimDiff (n62) 14.173 0.905 15.653 0.000 14.173 1.432
## NonV (a12) -0.222 0.159 -1.398 0.162 -0.209 -0.209
## V (a22) 0.462 0.134 3.456 0.001 0.505 0.505
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 64.880 8.865 7.319 0.000 64.880 0.670
## .Geo 49.940 12.375 4.035 0.000 49.940 0.479
## .Info 64.429 7.270 8.863 0.000 64.429 0.646
## .Arith 73.197 7.713 9.490 0.000 73.197 0.704
## .Colors 68.931 7.410 9.302 0.000 68.931 0.686
## .SimDiff 67.897 7.244 9.372 0.000 67.897 0.693
## V 0.837 0.148 5.634 0.000 1.000 1.000
## NonV 1.128 0.259 4.356 0.000 1.000 1.000
##
## Constraints:
## |Slack|
## a11 - 0 0.000
## a21 - 0 0.000Strong (Weak + equate all sets of intercepts)
Strong.Model <- '
! regressions
NonV =~NA*Blocks + c(b1,b1)*Blocks + c(b2,b2)*Geo
V=~NA*Info + c(b3,b3)*Info + c(b4,b4)*Arith + c(b5,b5)*Colors +
c(b6,b6)*SimDiff
! residuals, variances and covariances
Blocks~~Blocks;
Geo~~Geo;
Info~~Info;
Arith~~Arith;
Colors~~Colors;
SimDiff~~SimDiff;
NonV~~V
V ~~ c(1,NA)*V
NonV ~~ c(1,NA)*NonV
! intercepts (nu) & means (alphas)
Blocks~c(n1,n1)*1;
Geo~c(n2,n2)*1;
Info~c(n3,n3)*1;
Arith~c(n4,n4)*1;
Colors~c(n5,n5)*1;
SimDiff~c(n6,n6)*1;
! Constrain Males to factor mean of 0, females are relative to males
NonV~c(a11,a12)*1;
V~c(a21,a22)*1;
a11==0
a21==0
'
Model3 <- cfa(model=Strong.Model,fixed.x=FALSE,std.lv = F,
sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=c(322, 262),
meanstructure = TRUE)
summary(Model3, standardized = TRUE, fit.measures=TRUE)## lavaan 0.6.15 ended normally after 86 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 44
## Number of equality constraints 14
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 48.321
## Degrees of freedom 24
## P-value (Chi-square) 0.002
## Test statistic for each group:
## Group 1 20.327
## Group 2 27.995
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.949
## Tucker-Lewis Index (TLI) 0.936
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12835.621
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25731.242
## Bayesian (BIC) 25862.339
## Sample-size adjusted Bayesian (SABIC) 25767.100
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.059
## 90 Percent confidence interval - lower 0.034
## 90 Percent confidence interval - upper 0.083
## P-value H_0: RMSEA <= 0.050 0.250
## P-value H_0: RMSEA >= 0.080 0.076
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.044
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 5.294 0.689 7.684 0.000 5.294 0.523
## Geo (b2) 6.975 0.853 8.179 0.000 6.975 0.687
## V =~
## Info (b3) 6.627 0.543 12.204 0.000 6.627 0.656
## Arith (b4) 5.891 0.532 11.083 0.000 5.891 0.590
## Colors (b5) 6.237 0.540 11.558 0.000 6.237 0.615
## SimDiff (b6) 5.866 0.537 10.916 0.000 5.866 0.575
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.435 0.083 5.230 0.000 0.435 0.435
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 18.015 0.497 36.247 0.000 18.015 1.780
## .Geo (n2) 16.115 0.546 29.496 0.000 16.115 1.586
## .Info (n3) 14.266 0.515 27.695 0.000 14.266 1.412
## .Arith (n4) 15.906 0.495 32.112 0.000 15.906 1.592
## .Colors (n5) 14.533 0.506 28.696 0.000 14.533 1.433
## .SimDiff (n6) 16.852 0.498 33.834 0.000 16.852 1.651
## NonV (a11) 0.000 NA 0.000 0.000
## V (a21) 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 74.365 8.443 8.808 0.000 74.365 0.726
## .Geo 54.551 11.391 4.789 0.000 54.551 0.529
## .Info 58.123 6.409 9.069 0.000 58.123 0.570
## .Arith 65.103 6.408 10.160 0.000 65.103 0.652
## .Colors 63.957 6.530 9.795 0.000 63.957 0.622
## .SimDiff 69.779 6.729 10.371 0.000 69.779 0.670
## V 1.000 1.000 1.000
## NonV 1.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 5.294 0.689 7.684 0.000 5.621 0.571
## Geo (b2) 6.975 0.853 8.179 0.000 7.405 0.725
## V =~
## Info (b3) 6.627 0.543 12.204 0.000 6.038 0.598
## Arith (b4) 5.891 0.532 11.083 0.000 5.367 0.525
## Colors (b5) 6.237 0.540 11.558 0.000 5.682 0.566
## SimDiff (b6) 5.866 0.537 10.916 0.000 5.344 0.540
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.471 0.111 4.222 0.000 0.487 0.487
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 18.015 0.497 36.247 0.000 18.015 1.831
## .Geo (n2) 16.115 0.546 29.496 0.000 16.115 1.578
## .Info (n3) 14.266 0.515 27.695 0.000 14.266 1.412
## .Arith (n4) 15.906 0.495 32.112 0.000 15.906 1.555
## .Colors (n5) 14.533 0.506 28.696 0.000 14.533 1.446
## .SimDiff (n6) 16.852 0.498 33.834 0.000 16.852 1.701
## NonV (a12) -0.240 0.114 -2.108 0.035 -0.226 -0.226
## V (a22) 0.148 0.097 1.528 0.126 0.163 0.163
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks 65.168 8.684 7.504 0.000 65.168 0.673
## .Geo 49.475 12.174 4.064 0.000 49.475 0.474
## .Info 65.562 7.475 8.771 0.000 65.562 0.643
## .Arith 75.895 7.858 9.658 0.000 75.895 0.725
## .Colors 68.669 7.465 9.199 0.000 68.669 0.680
## .SimDiff 69.543 7.328 9.489 0.000 69.543 0.709
## V 0.830 0.149 5.586 0.000 1.000 1.000
## NonV 1.127 0.259 4.356 0.000 1.000 1.000
##
## Constraints:
## |Slack|
## a11 - 0 0.000
## a21 - 0 0.000Strict (Strong + equate all sets of residuals)
Strict.Model<- '
! regressions
NonV =~NA*Blocks + c(b1,b1)*Blocks + c(b2,b2)*Geo
V=~NA*Info + c(b3,b3)*Info + c(b4,b4)*Arith + c(b5,b5)*Colors +
c(b6,b6)*SimDiff
! residuals, variances and covariances
Blocks~~e1*Blocks;
Geo~~e2*Geo;
Info~~e3*Info;
Arith~~e4*Arith;
Colors~~e5*Colors;
SimDiff~~e6*SimDiff;
NonV~~V
V ~~ c(1,NA)*V
NonV ~~ c(1,NA)*NonV
! intercepts (nu) & means (alphas)
Blocks~c(n1,n1)*1;
Geo~c(n21,n22)*1;
Info~c(n3,n3)*1;
Arith~c(n4,n4)*1;
Colors~c(n5,n5)*1;
SimDiff~c(n6,n6)*1;
! Constrain Males to factor mean of 0, females are relative to males
NonV~c(a11,a12)*1;
V~c(a21,a22)*1;
a11==0
a21==0
'
Model4 <- cfa(model=Strict.Model,fixed.x=FALSE,std.lv = F,
sample.cov=list(M.cov,F.cov),
sample.mean = list(M.mean, F.mean),
sample.nobs=c(322, 262),
meanstructure = TRUE)## Warning in lavaanify(model = FLAT, constraints = constraints, varTable = DataOV, : lavaan WARNING: using a single label per parameter in a multiple group
## setting implies imposing equality constraints across all the groups;
## If this is not intended, either remove the label(s), or use a vector
## of labels (one for each group);
## See the Multiple groups section in the man page of model.syntax.summary(Model4, standardized = TRUE, fit.measures=TRUE)## lavaan 0.6.15 ended normally after 63 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 44
## Number of equality constraints 19
##
## Number of observations per group:
## Group 1 322
## Group 2 262
##
## Model Test User Model:
##
## Test statistic 51.578
## Degrees of freedom 29
## P-value (Chi-square) 0.006
## Test statistic for each group:
## Group 1 23.288
## Group 2 28.291
##
## Model Test Baseline Model:
##
## Test statistic 504.692
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.952
## Tucker-Lewis Index (TLI) 0.951
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12837.249
## Loglikelihood unrestricted model (H1) -12811.460
##
## Akaike (AIC) 25724.499
## Bayesian (BIC) 25833.746
## Sample-size adjusted Bayesian (SABIC) 25754.380
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.052
## 90 Percent confidence interval - lower 0.027
## 90 Percent confidence interval - upper 0.074
## P-value H_0: RMSEA <= 0.050 0.425
## P-value H_0: RMSEA >= 0.080 0.018
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.045
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [Group 1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 5.398 0.696 7.752 0.000 5.398 0.542
## Geo (b2) 7.089 0.857 8.269 0.000 7.089 0.700
## V =~
## Info (b3) 6.546 0.545 12.021 0.000 6.546 0.640
## Arith (b4) 5.807 0.534 10.875 0.000 5.807 0.570
## Colors (b5) 6.168 0.539 11.450 0.000 6.168 0.604
## SimDiff (b6) 5.853 0.534 10.969 0.000 5.853 0.575
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.432 0.081 5.309 0.000 0.432 0.432
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 17.970 0.555 32.362 0.000 17.970 1.803
## .Geo (n21) 16.140 0.565 28.583 0.000 16.140 1.593
## .Info (n3) 14.329 0.516 27.778 0.000 14.329 1.401
## .Arith (n4) 15.833 0.496 31.889 0.000 15.833 1.554
## .Colors (n5) 14.550 0.506 28.764 0.000 14.550 1.425
## .SimDiff (n6) 16.852 0.497 33.908 0.000 16.852 1.656
## NonV (a11) 0.000 NA 0.000 0.000
## V (a21) 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (e1) 70.154 7.158 9.800 0.000 70.154 0.707
## .Geo (e2) 52.413 10.571 4.958 0.000 52.413 0.510
## .Info (e3) 61.741 5.166 11.952 0.000 61.741 0.590
## .Arith (e4) 70.126 5.174 13.553 0.000 70.126 0.675
## .Colors (e5) 66.191 5.155 12.839 0.000 66.191 0.635
## .SimDiff (e6) 69.244 5.149 13.447 0.000 69.244 0.669
## V 1.000 1.000 1.000
## NonV 1.000 1.000 1.000
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV =~
## Blocks (b1) 5.398 0.696 7.752 0.000 5.517 0.550
## Geo (b2) 7.089 0.857 8.269 0.000 7.247 0.707
## V =~
## Info (b3) 6.546 0.545 12.021 0.000 6.092 0.613
## Arith (b4) 5.807 0.534 10.875 0.000 5.404 0.542
## Colors (b5) 6.168 0.539 11.450 0.000 5.741 0.577
## SimDiff (b6) 5.853 0.534 10.969 0.000 5.447 0.548
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## NonV ~~
## V 0.466 0.110 4.256 0.000 0.490 0.490
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (n1) 17.970 0.555 32.362 0.000 17.970 1.792
## .Geo (n22) 15.960 1.136 14.044 0.000 15.960 1.558
## .Info (n3) 14.329 0.516 27.778 0.000 14.329 1.441
## .Arith (n4) 15.833 0.496 31.889 0.000 15.833 1.589
## .Colors (n5) 14.550 0.506 28.764 0.000 14.550 1.461
## .SimDiff (n6) 16.852 0.497 33.908 0.000 16.852 1.694
## NonV (a12) -0.219 0.157 -1.395 0.163 -0.214 -0.214
## V (a22) 0.149 0.098 1.522 0.128 0.160 0.160
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Blocks (e1) 70.154 7.158 9.800 0.000 70.154 0.697
## .Geo (e2) 52.413 10.571 4.958 0.000 52.413 0.500
## .Info (e3) 61.741 5.166 11.952 0.000 61.741 0.625
## .Arith (e4) 70.126 5.174 13.553 0.000 70.126 0.706
## .Colors (e5) 66.191 5.155 12.839 0.000 66.191 0.668
## .SimDiff (e6) 69.244 5.149 13.447 0.000 69.244 0.700
## V 0.866 0.151 5.727 0.000 1.000 1.000
## NonV 1.045 0.210 4.967 0.000 1.000 1.000
##
## Constraints:
## |Slack|
## a11 - 0 0.000
## a21 - 0 0.000Fit Comparisons Across Models
Mod.Fit.Comp <- compareFit(Model1, Model2, Model3, Model4)
summary(Mod.Fit.Comp)## ################### Nested Model Comparison #########################
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## Model1 16 25720 25886 20.773
## Model2 20 25715 25864 24.202 3.4292 0.00000 4 0.4887
## Model3 24 25731 25862 48.321 24.1191 0.13125 4 7.56e-05 ***
## Model4 29 25724 25834 51.578 3.2568 0.00000 5 0.6605
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ####################### Model Fit Indices ###########################
## chisq df pvalue rmsea cfi tli srmr aic bic
## Model1 20.773† 16 .187 .032 .990 .981 .026† 25719.693 25885.750
## Model2 24.202 20 .234 .027† .991† .987† .031 25715.123† 25863.699
## Model3 48.321 24 .002 .059 .949 .936 .044 25731.242 25862.339
## Model4 51.578 29 .006 .052 .952 .951 .045 25724.499 25833.746†
##
## ################## Differences in Fit Indices #######################
## df rmsea cfi tli srmr aic bic
## Model2 - Model1 4 -0.005 0.001 0.006 0.005 -4.571 -22.050
## Model3 - Model2 4 0.032 -0.042 -0.051 0.013 16.119 -1.360
## Model4 - Model3 5 -0.007 0.004 0.015 0.000 -6.743 -28.593