Chapter 7 Models with Mean Structures
library(lavaan); library(semPlot)7.1 Syntax - R - MIMIC model
MATHSINGLEGROUP.cor <- '
1.000
0.747 1.000
0.736 0.666 1.000
0.092 0.080 0.079 1.000'
MATHSINGLEGROUP.SDs <- c(37.24, 36.97, 46.03, 0.50)
MATHSINGLEGROUP.cov <- getCov(MATHSINGLEGROUP.cor, sds = MATHSINGLEGROUP.SDs, names = c("math", "prob", "proc", "dummy"))
MIMIC.model <- '
f =~ math + prob + proc
f ~ dummy
dummy ~~ dummy'
MIMIC.fit <- sem(MIMIC.model, sample.cov = MATHSINGLEGROUP.cov, sample.nobs = 2000)
summary(MIMIC.fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)## lavaan 0.6-8 ended normally after 144 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 8
##
## Number of observations 2000
##
## Model Test User Model:
##
## Test statistic 0.064
## Degrees of freedom 2
## P-value (Chi-square) 0.968
##
## Model Test Baseline Model:
##
## Test statistic 3349.268
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -30402.179
## Loglikelihood unrestricted model (H1) -30402.146
##
## Akaike (AIC) 60820.357
## Bayesian (BIC) 60865.164
## Sample-size adjusted Bayesian (BIC) 60839.748
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.001
##
## 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
## f =~
## math 1.000 33.832 0.909
## prob 0.898 0.021 43.630 0.000 30.384 0.822
## proc 1.102 0.026 42.916 0.000 37.274 0.810
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f ~
## dummy 6.734 1.592 4.231 0.000 0.199 0.099
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dummy 0.250 0.008 31.623 0.000 0.250 1.000
## .math 241.519 18.975 12.729 0.000 241.519 0.174
## .prob 442.883 19.819 22.347 0.000 442.883 0.324
## .proc 728.355 31.242 23.314 0.000 728.355 0.344
## .f 1133.275 46.117 24.574 0.000 0.990 0.990
##
## R-Square:
## Estimate
## math 0.826
## prob 0.676
## proc 0.656
## f 0.0107.2 Syntax - R - Structured Means Modeling
SMM.G1.cor <- '
1.000
0.738 1.000
0.714 0.645 1.000'
SMM.G1.SDs <- c(37.09, 37.33, 45.10)
SMM.G1.means <- c(685.34, 679.10, 694.60)
SMM.G2.cor <- '
1.000
0.752 1.000
0.754 0.684 1.000'
SMM.G2.SDs <- c(37.07, 36.36, 46.67)
SMM.G2.means <- c(692.18, 685.03, 701.84)
SMM.G1.cov <- getCov(SMM.G1.cor, sds = SMM.G1.SDs, names = c("math", "prob", "proc"))
SMM.G2.cov <- getCov(SMM.G2.cor, sds = SMM.G2.SDs, names = c("math", "prob", "proc"))
SMM.model <- 'f =~ math + prob + proc'
SMM.fit <- cfa(SMM.model, sample.cov = list(SMM.G1.cov, SMM.G2.cov), sample.mean = list(SMM.G1.means, SMM.G2.means), sample.nobs = c(1000, 1000), group.equal = c("loadings", "intercepts"))
summary(SMM.fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)## lavaan 0.6-8 ended normally after 393 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
## Number of equality constraints 5
##
## Number of observations per group:
## Group 1 1000
## Group 2 1000
##
## Model Test User Model:
##
## Test statistic 4.246
## Degrees of freedom 4
## P-value (Chi-square) 0.374
## Test statistic for each group:
## Group 1 2.231
## Group 2 2.015
##
## Model Test Baseline Model:
##
## Test statistic 3313.997
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -28947.160
## Loglikelihood unrestricted model (H1) -28945.037
##
## Akaike (AIC) 57922.320
## Bayesian (BIC) 58000.732
## Sample-size adjusted Bayesian (BIC) 57956.254
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.008
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.049
## P-value RMSEA <= 0.05 0.956
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.016
##
## 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
## f =~
## math 1.000 33.292 0.901
## prob (.p2.) 0.898 0.021 43.710 0.000 29.896 0.810
## proc (.p3.) 1.105 0.026 43.059 0.000 36.800 0.803
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .math (.p8.) 685.404 1.142 600.137 0.000 685.404 18.543
## .prob (.p9.) 679.045 1.085 626.045 0.000 679.045 18.393
## .proc (.10.) 694.503 1.344 516.872 0.000 694.503 15.149
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .math 257.931 25.677 10.045 0.000 257.931 0.189
## .prob 469.226 28.390 16.528 0.000 469.226 0.344
## .proc 747.461 44.332 16.860 0.000 747.461 0.356
## f 1108.340 60.376 18.357 0.000 1.000 1.000
##
## R-Square:
## Estimate
## math 0.811
## prob 0.656
## proc 0.644
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f =~
## math 1.000 33.943 0.913
## prob (.p2.) 0.898 0.021 43.710 0.000 30.480 0.831
## proc (.p3.) 1.105 0.026 43.059 0.000 37.519 0.817
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .math (.p8.) 685.404 1.142 600.137 0.000 685.404 18.446
## .prob (.p9.) 679.045 1.085 626.045 0.000 679.045 18.508
## .proc (.10.) 694.503 1.344 516.872 0.000 694.503 15.122
## f 6.719 1.590 4.227 0.000 0.198 0.198
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .math 228.586 23.731 9.632 0.000 228.586 0.166
## .prob 416.978 25.698 16.226 0.000 416.978 0.310
## .proc 701.501 41.356 16.962 0.000 701.501 0.333
## f 1152.103 61.736 18.662 0.000 1.000 1.000
##
## R-Square:
## Estimate
## math 0.834
## prob 0.690
## proc 0.667# obtain model-implied (fitted) covariance matrix and mean vector
fitted(SMM.fit) ## $`Group 1`
## $`Group 1`$cov
## math prob proc
## math 1366.271
## prob 995.289 1362.995
## proc 1225.120 1100.158 2101.666
##
## $`Group 1`$mean
## math prob proc
## 685.404 679.045 694.503
##
##
## $`Group 2`
## $`Group 2`$cov
## math prob proc
## math 1380.688
## prob 1034.588 1346.038
## proc 1273.494 1143.597 2109.176
##
## $`Group 2`$mean
## math prob proc
## 692.123 685.079 701.931#obtain unstandardized residuals of a fitted model
resid(SMM.fit)## $`Group 1`
## $`Group 1`$type
## [1] "raw"
##
## $`Group 1`$cov
## math prob proc
## math 8.021
## prob 25.502 29.140
## proc -31.965 -15.333 -69.690
##
## $`Group 1`$mean
## math prob proc
## -0.064 0.055 0.097
##
##
## $`Group 2`
## $`Group 2`$type
## [1] "raw"
##
## $`Group 2`$cov
## math prob proc
## math -7.878
## prob -22.007 -25.311
## proc 29.664 15.936 66.734
##
## $`Group 2`$mean
## math prob proc
## 0.057 -0.049 -0.091#obtain standardized residuals of a fitted model
resid(SMM.fit, type="standardized")## $`Group 1`
## $`Group 1`$type
## [1] "standardized"
##
## $`Group 1`$cov
## math prob proc
## math 0.821
## prob 2.608 1.758
## proc -2.534 -0.888 -2.584
##
## $`Group 1`$mean
## math prob proc
## -0.357 0.176 0.245
##
##
## $`Group 2`
## $`Group 2`$type
## [1] "standardized"
##
## $`Group 2`$cov
## math prob proc
## math -0.974
## prob -2.850 -1.804
## proc 2.808 1.131 2.953
##
## $`Group 2`$mean
## math prob proc
## 0.372 -0.185 -0.2577.2.1 Configural invariance model
SMM.reading.G1.corr <- '
1.00
0.77 1.00
0.63 0.65 1.00'
SMM.reading.G1.SDs <- c(48.21, 40.32, 39.13)
SMM.reading.G1.means <- c(692.36, 680.63, 654.31)
SMM.reading.G2.corr <- '
1.00
0.78 1.00
0.65 0.65 1.00'
SMM.reading.G2.SDs <- c(45.88, 39.69, 38.37)
SMM.reading.G2.means <- c(709.47, 696.67, 669.17)
SMM.reading.G1.cov <- getCov(SMM.reading.G1.corr, sds = SMM.reading.G1.SDs, names = c("voc", "comp", "lang"))
SMM.reading.G2.cov <- getCov(SMM.reading.G2.corr, sds = SMM.reading.G2.SDs, names = c("voc", "comp", "lang"))
SMM.reading.model <- 'f =~ voc + comp + lang'
SMM.reading.configural.fit <- cfa(SMM.reading.model, sample.cov = list(SMM.reading.G1.cov, SMM.reading.G2.cov), sample.mean = list(SMM.reading.G1.means, SMM.reading.G2.means), sample.nobs = c(1000, 1000), std.lv = TRUE)
summary(SMM.reading.configural.fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE, modindices = TRUE)## lavaan 0.6-8 ended normally after 25 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 18
##
## Number of observations per group:
## Group 1 1000
## Group 2 1000
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
## Test statistic for each group:
## Group 1 0.000
## Group 2 0.000
##
## Model Test Baseline Model:
##
## Test statistic 3103.084
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -29352.796
## Loglikelihood unrestricted model (H1) -29352.796
##
## Akaike (AIC) 58741.591
## Bayesian (BIC) 58842.408
## Sample-size adjusted Bayesian (BIC) 58785.221
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value RMSEA <= 0.05 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## 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
## f =~
## voc 41.627 1.312 31.723 0.000 41.627 0.864
## comp 35.920 1.085 33.104 0.000 35.920 0.891
## lang 28.522 1.117 25.531 0.000 28.522 0.729
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 692.360 1.524 454.373 0.000 692.360 14.369
## .comp 680.630 1.274 534.082 0.000 680.630 16.889
## .lang 654.310 1.237 529.043 0.000 654.310 16.730
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 589.043 50.404 11.686 0.000 589.043 0.254
## .comp 333.838 35.308 9.455 0.000 333.838 0.206
## .lang 716.143 37.851 18.920 0.000 716.143 0.468
## f 1.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.746
## comp 0.794
## lang 0.532
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f =~
## voc 40.500 1.229 32.946 0.000 40.500 0.883
## comp 35.036 1.063 32.946 0.000 35.036 0.883
## lang 28.225 1.088 25.947 0.000 28.225 0.736
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 709.470 1.450 489.247 0.000 709.470 15.471
## .comp 696.670 1.254 555.346 0.000 696.670 17.562
## .lang 669.170 1.213 551.775 0.000 669.170 17.449
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 462.631 43.889 10.541 0.000 462.631 0.220
## .comp 346.219 32.845 10.541 0.000 346.219 0.220
## .lang 674.110 35.529 18.974 0.000 674.110 0.458
## f 1.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.780
## comp 0.780
## lang 0.542
##
## Modification Indices:
##
## [1] lhs op rhs block group level mi epc
## [9] sepc.lv sepc.all sepc.nox
## <0 rows> (or 0-length row.names)7.2.2 Metric invariance/factor loading invariance
Note: For the metric and scalar invariance models, the latent factors are identified using the reference indicator approach. The factor variance for group 1 was NOT fixed at 1. The “std.lv = TRUE” argument should not be used because if it is used, all factor variances would be forced to be equal to 1.
SMM.reading.metric.fit <- cfa(SMM.reading.model, sample.cov = list(SMM.reading.G1.cov, SMM.reading.G2.cov), sample.mean = list(SMM.reading.G1.means, SMM.reading.G2.means), sample.nobs = c(1000, 1000), group.equal = "loadings")
summary(SMM.reading.metric.fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE, modindices = TRUE)## lavaan 0.6-8 ended normally after 119 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 18
## Number of equality constraints 2
##
## Number of observations per group:
## Group 1 1000
## Group 2 1000
##
## Model Test User Model:
##
## Test statistic 0.105
## Degrees of freedom 2
## P-value (Chi-square) 0.949
## Test statistic for each group:
## Group 1 0.053
## Group 2 0.052
##
## Model Test Baseline Model:
##
## Test statistic 3103.084
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -29352.848
## Loglikelihood unrestricted model (H1) -29352.796
##
## Akaike (AIC) 58737.696
## Bayesian (BIC) 58827.311
## Sample-size adjusted Bayesian (BIC) 58776.478
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.005
## P-value RMSEA <= 0.05 0.996
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.003
##
## 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
## f =~
## voc 1.000 41.545 0.863
## comp (.p2.) 0.864 0.020 42.989 0.000 35.897 0.891
## lang (.p3.) 0.691 0.019 36.630 0.000 28.713 0.732
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 692.360 1.522 454.880 0.000 692.360 14.385
## .comp 680.630 1.274 534.310 0.000 680.630 16.896
## .lang 654.310 1.241 527.453 0.000 654.310 16.680
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 590.690 46.241 12.774 0.000 590.690 0.255
## .comp 334.089 31.891 10.476 0.000 334.089 0.206
## .lang 714.401 37.411 19.096 0.000 714.401 0.464
## f 1726.008 98.323 17.555 0.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.745
## comp 0.794
## lang 0.536
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f =~
## voc 1.000 40.571 0.884
## comp (.p2.) 0.864 0.020 42.989 0.000 35.056 0.883
## lang (.p3.) 0.691 0.019 36.630 0.000 28.040 0.733
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 709.470 1.452 488.777 0.000 709.470 15.456
## .comp 696.670 1.255 555.092 0.000 696.670 17.554
## .lang 669.170 1.209 553.421 0.000 669.170 17.501
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 460.883 40.602 11.351 0.000 460.883 0.219
## .comp 346.272 30.361 11.405 0.000 346.272 0.220
## .lang 675.787 35.137 19.233 0.000 675.787 0.462
## f 1646.030 92.054 17.881 0.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.781
## comp 0.780
## lang 0.538
##
## Modification Indices:
##
## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 1 f =~ voc 1 1 1 0.034 0.008 0.324 0.007 0.007
## 12 f =~ voc 2 2 1 0.034 -0.008 -0.316 -0.007 -0.007
## 25 voc ~~ comp 1 1 1 0.102 23.484 23.484 0.053 0.053
## 26 voc ~~ lang 1 1 1 0.008 -4.389 -4.389 -0.007 -0.007
## 27 comp ~~ lang 1 1 1 0.034 -8.030 -8.030 -0.016 -0.016
## 28 voc ~~ comp 2 2 1 0.102 -22.396 -22.396 -0.056 -0.056
## 29 voc ~~ lang 2 2 1 0.008 4.186 4.186 0.007 0.007
## 30 comp ~~ lang 2 2 1 0.034 7.658 7.658 0.016 0.0167.2.3 Scalar invariance/intercept invariance model
SMM.reading.scalar.fit <- cfa(SMM.reading.model, sample.cov = list(SMM.reading.G1.cov, SMM.reading.G2.cov), sample.mean = list(SMM.reading.G1.means, SMM.reading.G2.means), sample.nobs = c(1000, 1000), group.equal = c("loadings", "intercepts"))
summary(SMM.reading.scalar.fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE, modindices = TRUE)## lavaan 0.6-8 ended normally after 226 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
## Number of equality constraints 5
##
## Number of observations per group:
## Group 1 1000
## Group 2 1000
##
## Model Test User Model:
##
## Test statistic 4.706
## Degrees of freedom 4
## P-value (Chi-square) 0.319
## Test statistic for each group:
## Group 1 2.635
## Group 2 2.071
##
## Model Test Baseline Model:
##
## Test statistic 3103.084
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -29355.149
## Loglikelihood unrestricted model (H1) -29352.796
##
## Akaike (AIC) 58738.297
## Bayesian (BIC) 58816.710
## Sample-size adjusted Bayesian (BIC) 58772.231
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.013
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.051
## P-value RMSEA <= 0.05 0.943
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.011
##
## 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
## f =~
## voc 1.000 41.316 0.861
## comp (.p2.) 0.870 0.019 44.973 0.000 35.946 0.892
## lang (.p3.) 0.701 0.018 37.995 0.000 28.971 0.735
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc (.p8.) 691.678 1.455 475.458 0.000 691.678 14.407
## .comp (.p9.) 680.677 1.242 547.898 0.000 680.677 16.895
## .lang (.10.) 655.343 1.122 584.297 0.000 655.343 16.629
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 598.097 45.727 13.080 0.000 598.097 0.259
## .comp 331.125 31.561 10.491 0.000 331.125 0.204
## .lang 713.796 37.496 19.037 0.000 713.796 0.460
## f 1706.971 96.584 17.673 0.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.741
## comp 0.796
## lang 0.540
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f =~
## voc 1.000 40.362 0.881
## comp (.p2.) 0.870 0.019 44.973 0.000 35.116 0.885
## lang (.p3.) 0.701 0.018 37.995 0.000 28.302 0.737
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc (.p8.) 691.678 1.455 475.458 0.000 691.678 15.104
## .comp (.p9.) 680.677 1.242 547.898 0.000 680.677 17.145
## .lang (.10.) 655.343 1.122 584.297 0.000 655.343 17.060
## f 18.325 1.950 9.398 0.000 0.454 0.454
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 468.055 40.053 11.686 0.000 468.055 0.223
## .comp 342.990 30.035 11.420 0.000 342.990 0.218
## .lang 674.667 35.193 19.170 0.000 674.667 0.457
## f 1629.068 90.587 17.984 0.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.777
## comp 0.782
## lang 0.543
##
## Modification Indices:
##
## lhs op rhs block group level mi epc sepc.lv sepc.all sepc.nox
## 1 f =~ voc 1 1 1 0.344 0.024 0.985 0.021 0.021
## 12 f =~ voc 2 2 1 0.344 -0.024 -0.962 -0.021 -0.021
## 28 voc ~~ comp 1 1 1 0.561 53.066 53.066 0.119 0.119
## 29 voc ~~ lang 1 1 1 0.003 -2.452 -2.452 -0.004 -0.004
## 30 comp ~~ lang 1 1 1 0.344 -24.832 -24.832 -0.051 -0.051
## 31 voc ~~ comp 2 2 1 0.019 9.360 9.360 0.023 0.023
## 32 voc ~~ lang 2 2 1 0.020 6.540 6.540 0.012 0.012
## 33 comp ~~ lang 2 2 1 0.068 -10.460 -10.460 -0.022 -0.0227.2.4 Partial invariance model
SMM.reading.scalar.fit.partial <- cfa(SMM.reading.model, sample.cov = list(SMM.reading.G1.cov, SMM.reading.G2.cov), sample.mean = list(SMM.reading.G1.means, SMM.reading.G2.means), sample.nobs = c(1000, 1000), group.equal = c("loadings", "intercepts"), group.partial = c("f=~comp", "comp~1"))
summary(SMM.reading.scalar.fit.partial, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)## lavaan 0.6-8 ended normally after 273 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
## Number of equality constraints 3
##
## Number of observations per group:
## Group 1 1000
## Group 2 1000
##
## Model Test User Model:
##
## Test statistic 4.668
## Degrees of freedom 2
## P-value (Chi-square) 0.097
## Test statistic for each group:
## Group 1 2.612
## Group 2 2.055
##
## Model Test Baseline Model:
##
## Test statistic 3103.084
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999
## Tucker-Lewis Index (TLI) 0.997
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -29355.130
## Loglikelihood unrestricted model (H1) -29352.796
##
## Akaike (AIC) 58742.259
## Bayesian (BIC) 58831.874
## Sample-size adjusted Bayesian (BIC) 58781.041
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.037
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.081
## P-value RMSEA <= 0.05 0.623
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.011
##
## 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
## f =~
## voc 1.000 41.298 0.860
## comp 0.871 0.028 31.506 0.000 35.967 0.892
## lang (.p3.) 0.701 0.018 37.967 0.000 28.951 0.735
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc (.p8.) 691.731 1.489 464.517 0.000 691.731 14.410
## .comp 680.630 1.274 534.082 0.000 680.630 16.889
## .lang (.10.) 655.380 1.141 574.509 0.000 655.380 16.634
## f 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 598.666 48.809 12.265 0.000 598.666 0.260
## .comp 330.450 34.976 9.448 0.000 330.450 0.203
## .lang 714.134 37.712 18.936 0.000 714.134 0.460
## f 1705.548 102.981 16.562 0.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.740
## comp 0.797
## lang 0.540
##
##
## Group 2 [Group 2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## f =~
## voc 1.000 40.418 0.882
## comp 0.867 0.027 32.558 0.000 35.055 0.884
## lang (.p3.) 0.701 0.018 37.967 0.000 28.334 0.737
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc (.p8.) 691.731 1.489 464.517 0.000 691.731 15.097
## .comp 680.861 1.557 437.325 0.000 680.861 17.163
## .lang (.10.) 655.380 1.141 574.509 0.000 655.380 17.051
## f 18.228 2.032 8.970 0.000 0.451 0.451
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .voc 465.700 42.660 10.916 0.000 465.700 0.222
## .comp 344.898 32.607 10.577 0.000 344.898 0.219
## .lang 674.462 35.279 19.118 0.000 674.462 0.457
## f 1633.619 95.439 17.117 0.000 1.000 1.000
##
## R-Square:
## Estimate
## voc 0.778
## comp 0.781
## lang 0.543semPaths(SMM.reading.scalar.fit.partial, intercepts = FALSE)
7.3 Syntax - Mplus - MIMIC model
TITLE: MIMIC approach to latent means models
DATA: FILE IS "data\MATHSINGLEGROUP.txt";
TYPE IS CORRELATION STDEVIATIONS;
NOBSERVATIONS ARE 2000;
VARIABLE: NAMES ARE math prob proc dummy;
ANALYSIS: ESTIMATOR=ML;
MODEL: f BY math prob proc;
f ON dummy;
dummy*;
OUTPUT: SAMP STAND MOD;## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE: MIMIC approach to latent means models
## DATA: FILE IS "data\MATHSINGLEGROUP.txt";
## TYPE IS CORRELATION STDEVIATIONS;
## NOBSERVATIONS ARE 2000;
## VARIABLE: NAMES ARE math prob proc dummy;
## ANALYSIS: ESTIMATOR=ML;
## MODEL: f BY math prob proc;
## f ON dummy;
## dummy*;
## OUTPUT: SAMP STAND MOD;
##
##
##
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
## MIMIC approach to latent means models
##
## SUMMARY OF ANALYSIS
##
## Number of groups 1
## Number of observations 2000
##
## Number of dependent variables 3
## Number of independent variables 1
## Number of continuous latent variables 1
##
## Observed dependent variables
##
## Continuous
## MATH PROB PROC
##
## Observed independent variables
## DUMMY
##
## Continuous latent variables
## F
##
##
## Estimator ML
## Information matrix EXPECTED
## Maximum number of iterations 1000
## Convergence criterion 0.500D-04
## Maximum number of steepest descent iterations 20
##
## Input data file(s)
## data\MATHSINGLEGROUP.txt
##
## Input data format FREE
##
##
## SAMPLE STATISTICS
##
##
## SAMPLE STATISTICS
##
##
## Covariances/Correlations/Residual Correlations
## MATH PROB PROC DUMMY
## ________ ________ ________ ________
## MATH 1386.818
## PROB 1028.442 1366.781
## PROC 1261.620 1133.352 2118.761
## DUMMY 1.713 1.479 1.818 0.250
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 8
##
## Loglikelihood
##
## H0 Value -30402.179
## H1 Value -30402.146
##
## Information Criteria
##
## Akaike (AIC) 60820.357
## Bayesian (BIC) 60865.164
## Sample-Size Adjusted BIC 60839.748
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 0.064
## Degrees of Freedom 2
## P-Value 0.9683
##
## RMSEA (Root Mean Square Error Of Approximation)
##
## Estimate 0.000
## 90 Percent C.I. 0.000 0.000
## Probability RMSEA <= .05 1.000
##
## CFI/TLI
##
## CFI 1.000
## TLI 1.000
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 3349.268
## Degrees of Freedom 6
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value 0.001
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## F BY
## MATH 1.000 0.000 999.000 999.000
## PROB 0.898 0.021 43.629 0.000
## PROC 1.102 0.026 42.915 0.000
##
## F ON
## DUMMY 6.736 1.592 4.232 0.000
##
## Variances
## DUMMY 0.250 0.008 31.623 0.000
##
## Residual Variances
## MATH 241.506 18.975 12.727 0.000
## PROB 442.909 19.819 22.347 0.000
## PROC 728.356 31.241 23.314 0.000
## F 1133.296 46.117 24.574 0.000
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## F BY
## MATH 0.909 0.008 114.741 0.000
## PROB 0.822 0.010 85.922 0.000
## PROC 0.810 0.010 82.236 0.000
##
## F ON
## DUMMY 0.100 0.023 4.256 0.000
##
## Variances
## DUMMY 1.000 0.000 999.000 999.000
##
## Residual Variances
## MATH 0.174 0.014 12.105 0.000
## PROB 0.324 0.016 20.611 0.000
## PROC 0.344 0.016 21.557 0.000
## F 0.990 0.005 212.696 0.000
##
##
## STDY Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## F BY
## MATH 0.909 0.008 114.741 0.000
## PROB 0.822 0.010 85.922 0.000
## PROC 0.810 0.010 82.236 0.000
##
## F ON
## DUMMY 0.100 0.023 4.256 0.000
##
## Variances
## DUMMY 1.000 0.000 999.000 999.000
##
## Residual Variances
## MATH 0.174 0.014 12.105 0.000
## PROB 0.324 0.016 20.611 0.000
## PROC 0.344 0.016 21.557 0.000
## F 0.990 0.005 212.696 0.000
##
##
## STD Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## F BY
## MATH 33.832 0.688 49.203 0.000
## PROB 30.384 0.711 42.735 0.000
## PROC 37.273 0.890 41.891 0.000
##
## F ON
## DUMMY 0.199 0.047 4.265 0.000
##
## Variances
## DUMMY 0.250 0.008 31.623 0.000
##
## Residual Variances
## MATH 241.506 18.975 12.727 0.000
## PROB 442.909 19.819 22.347 0.000
## PROC 728.356 31.241 23.314 0.000
## F 0.990 0.005 212.696 0.000
##
##
## R-SQUARE
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## MATH 0.826 0.014 57.370 0.000
## PROB 0.676 0.016 42.961 0.000
## PROC 0.656 0.016 41.118 0.000
##
## Latent Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## F 0.010 0.005 2.128 0.033
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.280E-03
## (ratio of smallest to largest eigenvalue)
##
##
## MODEL MODIFICATION INDICES
##
## NOTE: Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included. To include these, request
## MODINDICES (ALL).
##
## Minimum M.I. value for printing the modification index 10.000
##
## M.I. E.P.C. Std E.P.C. StdYX E.P.C.
##
## No modification indices above the minimum value.
##
##
##
## Beginning Time: 12:20:08
## Ending Time: 12:20:08
## Elapsed Time: 00:00:00
##
##
##
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA 90066
##
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
##
## Copyright (c) 1998-2019 Muthen & Muthen7.4 Syntax - Mplus - Structured Means Modeling
TITLE: Structural Means Modeling
DATA: FILE IS "data\MATHBOTHGROUPS.txt";
TYPE IS CORRELATION MEANS STDEVIATIONS;
NOBSERVATIONS ARE 1000 1000;
NGROUPS IS 2;
VARIABLE: NAMES ARE math prob proc;
ANALYSIS: ESTIMATOR=ML;
MODEL: f BY math prob proc;
OUTPUT: SAMP STDYX RES MOD;## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE: Structural Means Modeling
## DATA: FILE IS "data\MATHBOTHGROUPS.txt";
## TYPE IS CORRELATION MEANS STDEVIATIONS;
## NOBSERVATIONS ARE 1000 1000;
## NGROUPS IS 2;
## VARIABLE: NAMES ARE math prob proc;
## ANALYSIS: ESTIMATOR=ML;
## MODEL: f BY math prob proc;
## OUTPUT: SAMP STDYX RES MOD;
##
##
##
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
## Structural Means Modeling
##
## SUMMARY OF ANALYSIS
##
## Number of groups 2
## Number of observations
## Group G1 1000
## Group G2 1000
## Total sample size 2000
##
## Number of dependent variables 3
## Number of independent variables 0
## Number of continuous latent variables 1
##
## Observed dependent variables
##
## Continuous
## MATH PROB PROC
##
## Continuous latent variables
## F
##
##
## Estimator ML
## Information matrix EXPECTED
## Maximum number of iterations 1000
## Convergence criterion 0.500D-04
## Maximum number of steepest descent iterations 20
##
## Input data file(s)
## data\MATHBOTHGROUPS.txt
##
## Input data format FREE
##
##
## SAMPLE STATISTICS
##
##
## SAMPLE STATISTICS FOR G1
##
##
## Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 685.340 679.100 694.600
##
##
## Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH 1375.668
## PROB 1021.812 1393.529
## PROC 1194.350 1085.911 2034.010
##
##
## SAMPLE STATISTICS FOR G2
##
##
## Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 692.180 685.030 701.840
##
##
## Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH 1374.185
## PROB 1013.595 1322.050
## PROC 1304.463 1160.694 2178.089
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 14
##
## Loglikelihood
##
## H0 Value -28947.160
## H1 Value -28945.037
##
## Information Criteria
##
## Akaike (AIC) 57922.320
## Bayesian (BIC) 58000.732
## Sample-Size Adjusted BIC 57956.254
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 4.246
## Degrees of Freedom 4
## P-Value 0.3737
##
## Chi-Square Contribution From Each Group
##
## G1 2.231
## G2 2.015
##
## RMSEA (Root Mean Square Error Of Approximation)
##
## Estimate 0.008
## 90 Percent C.I. 0.000 0.049
## Probability RMSEA <= .05 0.956
##
## CFI/TLI
##
## CFI 1.000
## TLI 1.000
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 3313.997
## Degrees of Freedom 6
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value 0.016
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## MATH 1.000 0.000 999.000 999.000
## PROB 0.898 0.021 43.711 0.000
## PROC 1.105 0.026 43.059 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## MATH 685.404 1.142 600.135 0.000
## PROB 679.045 1.085 626.044 0.000
## PROC 694.503 1.344 516.871 0.000
##
## Variances
## F 1108.350 60.377 18.357 0.000
##
## Residual Variances
## MATH 257.928 25.677 10.045 0.000
## PROB 469.220 28.390 16.528 0.000
## PROC 747.455 44.332 16.860 0.000
##
## Group G2
##
## F BY
## MATH 1.000 0.000 999.000 999.000
## PROB 0.898 0.021 43.711 0.000
## PROC 1.105 0.026 43.059 0.000
##
## Means
## F 6.719 1.590 4.227 0.000
##
## Intercepts
## MATH 685.404 1.142 600.135 0.000
## PROB 679.045 1.085 626.044 0.000
## PROC 694.503 1.344 516.871 0.000
##
## Variances
## F 1152.107 61.736 18.662 0.000
##
## Residual Variances
## MATH 228.591 23.731 9.632 0.000
## PROB 416.979 25.698 16.226 0.000
## PROC 701.506 41.356 16.962 0.000
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## MATH 0.901 0.011 85.148 0.000
## PROB 0.810 0.013 64.575 0.000
## PROC 0.803 0.013 62.955 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## MATH 18.543 0.406 45.642 0.000
## PROB 18.393 0.384 47.955 0.000
## PROC 15.149 0.315 48.018 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## MATH 0.189 0.019 9.908 0.000
## PROB 0.344 0.020 16.951 0.000
## PROC 0.356 0.020 17.374 0.000
##
## Group G2
##
## F BY
## MATH 0.913 0.010 94.614 0.000
## PROB 0.831 0.012 71.285 0.000
## PROC 0.817 0.012 67.803 0.000
##
## Means
## F 0.198 0.047 4.207 0.000
##
## Intercepts
## MATH 18.446 0.406 45.394 0.000
## PROB 18.508 0.392 47.259 0.000
## PROC 15.122 0.318 47.537 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## MATH 0.166 0.018 9.386 0.000
## PROB 0.310 0.019 15.997 0.000
## PROC 0.333 0.020 16.894 0.000
##
##
## R-SQUARE
##
## Group G1
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## MATH 0.811 0.019 42.574 0.000
## PROB 0.656 0.020 32.288 0.000
## PROC 0.644 0.020 31.478 0.000
##
## Group G2
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## MATH 0.834 0.018 47.307 0.000
## PROB 0.690 0.019 35.643 0.000
## PROC 0.667 0.020 33.901 0.000
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.632E-05
## (ratio of smallest to largest eigenvalue)
##
##
## RESIDUAL OUTPUT
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G1
##
##
## Model Estimated Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 685.404 679.045 694.503
##
##
## Residuals for Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## -0.064 0.055 0.097
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## -0.242 0.119 0.203
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## -0.055 0.047 0.068
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH 1366.278
## PROB 995.296 1362.994
## PROC 1225.131 1100.165 2101.672
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH 8.015
## PROB 25.495 29.141
## PROC -31.975 -15.340 -69.696
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## MATH PROB PROC
## ________ ________ ________
## MATH 0.544
## PROB 1.543 1.124
## PROC -2.809 -0.708 -2.661
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH 0.130
## PROB 0.469 0.468
## PROC -0.492 -0.242 -0.767
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G2
##
##
## Model Estimated Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 692.123 685.079 701.931
##
##
## Residuals for Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 0.057 -0.049 -0.091
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 0.281 -0.140 -0.159
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## MATH PROB PROC
## ________ ________ ________
## 0.048 -0.043 -0.062
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH 1380.699
## PROB 1034.590 1346.039
## PROC 1273.499 1143.599 2109.187
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH -7.888
## PROB -22.009 -25.311
## PROC 29.660 15.934 66.724
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## MATH PROB PROC
## ________ ________ ________
## MATH -0.817
## PROB -3.610 -1.538
## PROC 1.503 0.722 1.624
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## MATH PROB PROC
## ________ ________ ________
## MATH -0.128
## PROB -0.413 -0.429
## PROC 0.433 0.245 0.686
##
##
## MODEL MODIFICATION INDICES
##
## NOTE: Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included. To include these, request
## MODINDICES (ALL).
##
## Minimum M.I. value for printing the modification index 10.000
##
## M.I. E.P.C. Std E.P.C. StdYX E.P.C.
## Group G1
##
##
## No modification indices above the minimum value.
##
## Group G2
##
##
## No modification indices above the minimum value.
##
##
##
## Beginning Time: 12:20:08
## Ending Time: 12:20:08
## Elapsed Time: 00:00:00
##
##
##
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA 90066
##
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
##
## Copyright (c) 1998-2019 Muthen & Muthen7.4.1 Configural invariance model
TITLE: Structural Means Modeling -
configural invariance
DATA: FILE IS "data\READINGBOTHGROUPS.txt";
TYPE IS CORRELATION MEANS STDEVIATIONS;
NOBSERVATIONS ARE 1000 1000;
NGROUPS IS 2;
VARIABLE: NAMES ARE voc comp lang;
ANALYSIS: ESTIMATOR=ML;
MODEL: f BY voc* comp lang;
[voc*]; [comp*]; [lang*];
[f@0]; f@1;
MODEL G2: f BY voc* comp lang;
[voc*]; [comp*]; [lang*];
[f@0]; f@1;
OUTPUT: SAMP STDYX RES MOD(0);## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE: Structural Means Modeling -
## configural invariance
## DATA: FILE IS "data\READINGBOTHGROUPS.txt";
## TYPE IS CORRELATION MEANS STDEVIATIONS;
## NOBSERVATIONS ARE 1000 1000;
## NGROUPS IS 2;
## VARIABLE: NAMES ARE voc comp lang;
## ANALYSIS: ESTIMATOR=ML;
## MODEL: f BY voc* comp lang;
## [voc*]; [comp*]; [lang*];
## [f@0]; f@1;
## MODEL G2: f BY voc* comp lang;
## [voc*]; [comp*]; [lang*];
## [f@0]; f@1;
## OUTPUT: SAMP STDYX RES MOD(0);
##
##
##
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
## Structural Means Modeling -
## configural invariance
##
## SUMMARY OF ANALYSIS
##
## Number of groups 2
## Number of observations
## Group G1 1000
## Group G2 1000
## Total sample size 2000
##
## Number of dependent variables 3
## Number of independent variables 0
## Number of continuous latent variables 1
##
## Observed dependent variables
##
## Continuous
## VOC COMP LANG
##
## Continuous latent variables
## F
##
##
## Estimator ML
## Information matrix EXPECTED
## Maximum number of iterations 1000
## Convergence criterion 0.500D-04
## Maximum number of steepest descent iterations 20
##
## Input data file(s)
## data\READINGBOTHGROUPS.txt
##
## Input data format FREE
##
##
## SAMPLE STATISTICS
##
##
## SAMPLE STATISTICS FOR G1
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 692.360 680.630 654.310
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2324.204
## COMP 1496.747 1625.702
## LANG 1188.468 1025.519 1531.157
##
##
## SAMPLE STATISTICS FOR G2
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.470 696.670 669.170
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2104.974
## COMP 1420.362 1575.296
## LANG 1144.270 989.888 1472.257
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 18
##
## Loglikelihood
##
## H0 Value -29352.796
## H1 Value -29352.796
##
## Information Criteria
##
## Akaike (AIC) 58741.591
## Bayesian (BIC) 58842.408
## Sample-Size Adjusted BIC 58785.221
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 0.000
## Degrees of Freedom 0
## P-Value 0.0000
##
## Chi-Square Contribution From Each Group
##
## G1 0.000
## G2 0.000
##
## RMSEA (Root Mean Square Error Of Approximation)
##
## Estimate 0.000
## 90 Percent C.I. 0.000 0.000
## Probability RMSEA <= .05 0.000
##
## CFI/TLI
##
## CFI 1.000
## TLI 1.000
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 3103.084
## Degrees of Freedom 6
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value 0.000
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 41.629 1.312 31.724 0.000
## COMP 35.921 1.085 33.105 0.000
## LANG 28.523 1.117 25.533 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 692.360 1.524 454.360 0.000
## COMP 680.630 1.274 534.066 0.000
## LANG 654.310 1.237 529.030 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 589.034 50.403 11.687 0.000
## COMP 333.843 35.307 9.455 0.000
## LANG 716.113 37.850 18.920 0.000
##
## Group G2
##
## F BY
## VOC 40.500 1.229 32.946 0.000
## COMP 35.036 1.063 32.946 0.000
## LANG 28.225 1.088 25.947 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 709.470 1.450 489.247 0.000
## COMP 696.670 1.255 555.337 0.000
## LANG 669.170 1.213 551.775 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 462.621 43.889 10.541 0.000
## COMP 346.237 32.846 10.541 0.000
## LANG 674.117 35.529 18.974 0.000
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 0.864 0.013 64.558 0.000
## COMP 0.891 0.013 69.523 0.000
## LANG 0.729 0.017 42.042 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 14.368 0.323 44.506 0.000
## COMP 16.889 0.379 44.565 0.000
## LANG 16.729 0.375 44.562 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.254 0.023 10.972 0.000
## COMP 0.206 0.023 8.994 0.000
## LANG 0.468 0.025 18.502 0.000
##
## Group G2
##
## F BY
## VOC 0.883 0.013 70.488 0.000
## COMP 0.883 0.013 70.487 0.000
## LANG 0.736 0.017 43.559 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 15.471 0.347 44.536 0.000
## COMP 17.561 0.394 44.577 0.000
## LANG 17.449 0.391 44.575 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.220 0.022 9.940 0.000
## COMP 0.220 0.022 9.941 0.000
## LANG 0.458 0.025 18.429 0.000
##
##
## R-SQUARE
##
## Group G1
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.746 0.023 32.279 0.000
## COMP 0.794 0.023 34.761 0.000
## LANG 0.532 0.025 21.021 0.000
##
## Group G2
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.780 0.022 35.244 0.000
## COMP 0.780 0.022 35.243 0.000
## LANG 0.542 0.025 21.779 0.000
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.536E-04
## (ratio of smallest to largest eigenvalue)
##
##
## RESIDUAL OUTPUT
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G1
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 692.360 680.630 654.310
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2322.008
## COMP 1495.361 1624.170
## LANG 1187.403 1024.594 1529.700
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC -0.128
## COMP -0.111 -0.093
## LANG -0.123 -0.101 -0.075
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 999.000
## COMP 999.000 999.000
## LANG 999.000 999.000 999.000
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC -0.001
## COMP -0.001 -0.001
## LANG -0.002 -0.002 -0.001
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G2
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.470 696.670 669.170
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 999.000 999.000 999.000
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2102.870
## COMP 1418.965 1573.771
## LANG 1143.125 988.908 1470.786
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.000
## COMP -0.023 -0.050
## LANG 0.000 -0.009 -0.001
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 999.000
## COMP 999.000 999.000
## LANG 999.000 999.000 999.000
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.000
## COMP 0.000 -0.001
## LANG 0.000 0.000 0.000
##
##
## MODEL MODIFICATION INDICES
##
## NOTE: Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included. To include these, request
## MODINDICES (ALL).
##
## Minimum M.I. value for printing the modification index 0.000
##
## M.I. E.P.C. Std E.P.C. StdYX E.P.C.
## Group G1
##
##
## No modification indices above the minimum value.
##
## Group G2
##
##
## No modification indices above the minimum value.
##
##
##
## Beginning Time: 12:20:09
## Ending Time: 12:20:09
## Elapsed Time: 00:00:00
##
##
##
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA 90066
##
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
##
## Copyright (c) 1998-2019 Muthen & Muthen7.4.2 Metric invariance/factor loading invariance
TITLE: Structural Means Modeling -
factor loading invariance
DATA: FILE IS "data\READINGBOTHGROUPS.txt";
TYPE IS CORRELATION MEANS STDEVIATIONS;
NOBSERVATIONS ARE 1000 1000;
NGROUPS IS 2;
VARIABLE: NAMES ARE voc comp lang;
ANALYSIS: ESTIMATOR=ML;
MODEL: f BY voc* (1)
comp (2)
lang (3);
[voc*]; [comp*]; [lang*];
[f@0]; f@1;
MODEL G2:
[voc*]; [comp*]; [lang*];
[f@0]; f*; ! factor variance in G2 is freed
OUTPUT: SAMP STDYX RES MOD(0);## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE: Structural Means Modeling -
## factor loading invariance
## DATA: FILE IS "data\READINGBOTHGROUPS.txt";
## TYPE IS CORRELATION MEANS STDEVIATIONS;
## NOBSERVATIONS ARE 1000 1000;
## NGROUPS IS 2;
## VARIABLE: NAMES ARE voc comp lang;
## ANALYSIS: ESTIMATOR=ML;
## MODEL: f BY voc* (1)
## comp (2)
## lang (3);
## [voc*]; [comp*]; [lang*];
## [f@0]; f@1;
## MODEL G2:
## [voc*]; [comp*]; [lang*];
## [f@0]; f*; ! factor variance in G2 is freed
## OUTPUT: SAMP STDYX RES MOD(0);
##
##
##
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
## Structural Means Modeling -
## factor loading invariance
##
## SUMMARY OF ANALYSIS
##
## Number of groups 2
## Number of observations
## Group G1 1000
## Group G2 1000
## Total sample size 2000
##
## Number of dependent variables 3
## Number of independent variables 0
## Number of continuous latent variables 1
##
## Observed dependent variables
##
## Continuous
## VOC COMP LANG
##
## Continuous latent variables
## F
##
##
## Estimator ML
## Information matrix EXPECTED
## Maximum number of iterations 1000
## Convergence criterion 0.500D-04
## Maximum number of steepest descent iterations 20
##
## Input data file(s)
## data\READINGBOTHGROUPS.txt
##
## Input data format FREE
##
##
## SAMPLE STATISTICS
##
##
## SAMPLE STATISTICS FOR G1
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 692.360 680.630 654.310
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2324.204
## COMP 1496.747 1625.702
## LANG 1188.468 1025.519 1531.157
##
##
## SAMPLE STATISTICS FOR G2
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.470 696.670 669.170
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2104.974
## COMP 1420.362 1575.296
## LANG 1144.270 989.888 1472.257
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 16
##
## Loglikelihood
##
## H0 Value -29352.848
## H1 Value -29352.796
##
## Information Criteria
##
## Akaike (AIC) 58737.696
## Bayesian (BIC) 58827.311
## Sample-Size Adjusted BIC 58776.478
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 0.105
## Degrees of Freedom 2
## P-Value 0.9489
##
## Chi-Square Contribution From Each Group
##
## G1 0.054
## G2 0.051
##
## RMSEA (Root Mean Square Error Of Approximation)
##
## Estimate 0.000
## 90 Percent C.I. 0.000 0.005
## Probability RMSEA <= .05 0.996
##
## CFI/TLI
##
## CFI 1.000
## TLI 1.000
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 3103.084
## Degrees of Freedom 6
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value 0.003
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 41.548 1.183 35.110 0.000
## COMP 35.899 0.997 35.998 0.000
## LANG 28.716 0.941 30.526 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 692.360 1.522 454.863 0.000
## COMP 680.630 1.274 534.284 0.000
## LANG 654.310 1.241 527.419 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 590.610 46.239 12.773 0.000
## COMP 334.092 31.891 10.476 0.000
## LANG 714.433 37.413 19.096 0.000
##
## Group G2
##
## F BY
## VOC 41.548 1.183 35.110 0.000
## COMP 35.899 0.997 35.998 0.000
## LANG 28.716 0.941 30.526 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 709.470 1.451 488.784 0.000
## COMP 696.670 1.255 555.090 0.000
## LANG 669.170 1.209 553.406 0.000
##
## Variances
## F 0.953 0.068 14.006 0.000
##
## Residual Variances
## VOC 460.862 40.603 11.351 0.000
## COMP 346.347 30.363 11.407 0.000
## LANG 675.852 35.140 19.233 0.000
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 0.863 0.012 74.148 0.000
## COMP 0.891 0.011 79.802 0.000
## LANG 0.732 0.015 48.949 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 14.384 0.311 46.213 0.000
## COMP 16.896 0.370 45.665 0.000
## LANG 16.678 0.340 49.081 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.255 0.020 12.684 0.000
## COMP 0.206 0.020 10.344 0.000
## LANG 0.464 0.022 21.204 0.000
##
## Group G2
##
## F BY
## VOC 0.884 0.011 79.700 0.000
## COMP 0.883 0.011 79.583 0.000
## LANG 0.733 0.015 49.377 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 15.457 0.338 45.775 0.000
## COMP 17.553 0.383 45.839 0.000
## LANG 17.500 0.357 49.057 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.219 0.020 11.158 0.000
## COMP 0.220 0.020 11.215 0.000
## LANG 0.462 0.022 21.221 0.000
##
##
## R-SQUARE
##
## Group G1
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.745 0.020 37.074 0.000
## COMP 0.794 0.020 39.901 0.000
## LANG 0.536 0.022 24.475 0.000
##
## Group G2
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.781 0.020 39.850 0.000
## COMP 0.780 0.020 39.792 0.000
## LANG 0.538 0.022 24.689 0.000
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.552E-04
## (ratio of smallest to largest eigenvalue)
##
##
## RESIDUAL OUTPUT
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G1
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 692.360 680.630 654.310
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2316.880
## COMP 1491.557 1622.849
## LANG 1193.117 1030.895 1539.060
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 5.000
## COMP 3.693 1.227
## LANG -5.838 -6.401 -9.434
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 0.173
## COMP 0.285 0.076
## LANG -0.228 -0.319 -0.338
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.048
## COMP 0.048 0.017
## LANG -0.083 -0.108 -0.138
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G2
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.470 696.670 669.170
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 999.000 0.000 0.000
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.000 0.000 0.000
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2106.849
## COMP 1422.191 1575.169
## LANG 1137.630 982.952 1462.128
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC -3.979
## COMP -3.249 -1.448
## LANG 5.496 5.947 8.656
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC -0.189
## COMP -0.344 -0.089
## LANG 0.232 0.289 0.306
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC -0.042
## COMP -0.045 -0.021
## LANG 0.083 0.104 0.132
##
##
## MODEL MODIFICATION INDICES
##
## NOTE: Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included. To include these, request
## MODINDICES (ALL).
##
## Minimum M.I. value for printing the modification index 0.000
##
## M.I. E.P.C. Std E.P.C. StdYX E.P.C.
## Group G1
##
##
## BY Statements
##
## F BY VOC 0.034 0.103 0.103 0.002
## F BY COMP 0.007 0.036 0.036 0.001
## F BY LANG 0.104 -0.195 -0.195 -0.005
##
## WITH Statements
##
## LANG WITH VOC 0.008 -4.472 -4.472 -0.007
## LANG WITH COMP 0.034 -7.983 -7.983 -0.016
##
## Group G2
##
##
## BY Statements
##
## F BY VOC 0.033 -0.218 -0.213 -0.005
## F BY COMP 0.008 -0.095 -0.093 -0.002
## F BY LANG 0.101 0.258 0.252 0.007
##
## WITH Statements
##
## LANG WITH VOC 0.007 4.138 4.138 0.007
## LANG WITH COMP 0.036 7.830 7.830 0.016
##
##
##
## Beginning Time: 12:20:09
## Ending Time: 12:20:09
## Elapsed Time: 00:00:00
##
##
##
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA 90066
##
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
##
## Copyright (c) 1998-2019 Muthen & Muthen7.4.3 Scalar invariance/intercept invariance model
TITLE: Structural Means Modeling -
factor loading & intercept invariance
DATA: FILE IS "data\READINGBOTHGROUPS.txt";
TYPE IS CORRELATION MEANS STDEVIATIONS;
NOBSERVATIONS ARE 1000 1000;
NGROUPS IS 2;
VARIABLE: NAMES ARE voc comp lang;
ANALYSIS: ESTIMATOR=ML;
MODEL: f BY voc* (1)
comp (2)
lang (3);
[voc*] (i1);
[comp*] (i2);
[lang*] (i3);
[f@0]; f@1;
MODEL G2:
[f*]; ! factor mean in G2 is freed
f*; ! factor variance in G2 is freed
OUTPUT: SAMP STDYX RES MOD(0);## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE: Structural Means Modeling -
## factor loading & intercept invariance
## DATA: FILE IS "data\READINGBOTHGROUPS.txt";
## TYPE IS CORRELATION MEANS STDEVIATIONS;
## NOBSERVATIONS ARE 1000 1000;
## NGROUPS IS 2;
## VARIABLE: NAMES ARE voc comp lang;
## ANALYSIS: ESTIMATOR=ML;
## MODEL: f BY voc* (1)
## comp (2)
## lang (3);
## [voc*] (i1);
## [comp*] (i2);
## [lang*] (i3);
## [f@0]; f@1;
## MODEL G2:
## [f*]; ! factor mean in G2 is freed
## f*; ! factor variance in G2 is freed
## OUTPUT: SAMP STDYX RES MOD(0);
##
##
##
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
## Structural Means Modeling -
## factor loading & intercept invariance
##
## SUMMARY OF ANALYSIS
##
## Number of groups 2
## Number of observations
## Group G1 1000
## Group G2 1000
## Total sample size 2000
##
## Number of dependent variables 3
## Number of independent variables 0
## Number of continuous latent variables 1
##
## Observed dependent variables
##
## Continuous
## VOC COMP LANG
##
## Continuous latent variables
## F
##
##
## Estimator ML
## Information matrix EXPECTED
## Maximum number of iterations 1000
## Convergence criterion 0.500D-04
## Maximum number of steepest descent iterations 20
##
## Input data file(s)
## data\READINGBOTHGROUPS.txt
##
## Input data format FREE
##
##
## SAMPLE STATISTICS
##
##
## SAMPLE STATISTICS FOR G1
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 692.360 680.630 654.310
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2324.204
## COMP 1496.747 1625.702
## LANG 1188.468 1025.519 1531.157
##
##
## SAMPLE STATISTICS FOR G2
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.470 696.670 669.170
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2104.974
## COMP 1420.362 1575.296
## LANG 1144.270 989.888 1472.257
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 14
##
## Loglikelihood
##
## H0 Value -29355.149
## H1 Value -29352.796
##
## Information Criteria
##
## Akaike (AIC) 58738.297
## Bayesian (BIC) 58816.710
## Sample-Size Adjusted BIC 58772.231
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 4.706
## Degrees of Freedom 4
## P-Value 0.3188
##
## Chi-Square Contribution From Each Group
##
## G1 2.635
## G2 2.071
##
## RMSEA (Root Mean Square Error Of Approximation)
##
## Estimate 0.013
## 90 Percent C.I. 0.000 0.051
## Probability RMSEA <= .05 0.943
##
## CFI/TLI
##
## CFI 1.000
## TLI 1.000
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 3103.084
## Degrees of Freedom 6
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value 0.011
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 41.315 1.169 35.347 0.000
## COMP 35.946 0.990 36.298 0.000
## LANG 28.971 0.934 31.008 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 691.678 1.455 475.459 0.000
## COMP 680.677 1.242 547.899 0.000
## LANG 655.344 1.122 584.300 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 598.097 45.727 13.080 0.000
## COMP 331.124 31.561 10.491 0.000
## LANG 713.795 37.496 19.037 0.000
##
## Group G2
##
## F BY
## VOC 41.315 1.169 35.347 0.000
## COMP 35.946 0.990 36.298 0.000
## LANG 28.971 0.934 31.008 0.000
##
## Means
## F 0.444 0.048 9.203 0.000
##
## Intercepts
## VOC 691.678 1.455 475.459 0.000
## COMP 680.677 1.242 547.899 0.000
## LANG 655.344 1.122 584.300 0.000
##
## Variances
## F 0.954 0.068 14.004 0.000
##
## Residual Variances
## VOC 468.055 40.053 11.686 0.000
## COMP 342.990 30.035 11.420 0.000
## LANG 674.666 35.193 19.170 0.000
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 0.861 0.012 74.613 0.000
## COMP 0.892 0.011 81.126 0.000
## LANG 0.735 0.015 49.919 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 14.407 0.311 46.337 0.000
## COMP 16.895 0.370 45.690 0.000
## LANG 16.629 0.338 49.158 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.259 0.020 13.072 0.000
## COMP 0.204 0.020 10.395 0.000
## LANG 0.460 0.022 21.227 0.000
##
## Group G2
##
## F BY
## VOC 0.881 0.011 80.314 0.000
## COMP 0.885 0.011 81.060 0.000
## LANG 0.737 0.015 50.402 0.000
##
## Means
## F 0.454 0.049 9.205 0.000
##
## Intercepts
## VOC 15.104 0.329 45.841 0.000
## COMP 17.145 0.374 45.864 0.000
## LANG 17.060 0.347 49.114 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.223 0.019 11.538 0.000
## COMP 0.218 0.019 11.273 0.000
## LANG 0.457 0.022 21.227 0.000
##
##
## R-SQUARE
##
## Group G1
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.741 0.020 37.306 0.000
## COMP 0.796 0.020 40.563 0.000
## LANG 0.540 0.022 24.959 0.000
##
## Group G2
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.777 0.019 40.157 0.000
## COMP 0.782 0.019 40.530 0.000
## LANG 0.543 0.022 25.201 0.000
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.318E-04
## (ratio of smallest to largest eigenvalue)
##
##
## RESIDUAL OUTPUT
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G1
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 691.678 680.677 655.344
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.682 -0.047 -1.034
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 1.503 -0.167 -1.983
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.447 -0.037 -0.836
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2305.056
## COMP 1485.124 1623.242
## LANG 1196.927 1041.375 1553.086
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 16.824
## COMP 10.127 0.835
## LANG -9.648 -16.882 -23.460
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 0.526
## COMP 0.685 0.050
## LANG -0.370 -0.870 -0.856
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.162
## COMP 0.131 0.011
## LANG -0.137 -0.284 -0.343
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G2
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 710.004 696.621 668.193
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## -0.534 0.049 0.977
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## -1.532 0.170 1.920
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## -0.368 0.039 0.805
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2097.123
## COMP 1417.355 1576.147
## LANG 1142.310 993.856 1475.659
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 5.747
## COMP 1.587 -2.426
## LANG 0.816 -4.957 -4.874
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 0.238
## COMP 0.142 -0.146
## LANG 0.034 -0.248 -0.175
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.061
## COMP 0.022 -0.034
## LANG 0.012 -0.086 -0.074
##
##
## MODEL MODIFICATION INDICES
##
## NOTE: Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included. To include these, request
## MODINDICES (ALL).
##
## Minimum M.I. value for printing the modification index 0.000
##
## M.I. E.P.C. Std E.P.C. StdYX E.P.C.
## Group G1
##
##
## BY Statements
##
## F BY VOC 0.344 0.341 0.341 0.007
## F BY COMP 0.003 0.022 0.022 0.001
## F BY LANG 0.560 -0.466 -0.466 -0.012
##
## WITH Statements
##
## LANG WITH VOC 0.003 -2.450 -2.450 -0.004
## LANG WITH COMP 0.344 -24.830 -24.830 -0.051
##
## Means/Intercepts/Thresholds
##
## [ VOC ] 2.462 0.682 0.682 0.014
## [ COMP ] 0.028 -0.047 -0.047 -0.001
## [ LANG ] 3.619 -1.034 -1.034 -0.026
##
## Group G2
##
##
## BY Statements
##
## F BY VOC 0.344 -0.644 -0.630 -0.014
## F BY COMP 0.003 -0.052 -0.050 -0.001
## F BY LANG 0.561 0.569 0.556 0.014
##
## WITH Statements
##
## LANG WITH VOC 0.020 6.543 6.543 0.012
## LANG WITH COMP 0.068 -10.459 -10.459 -0.022
##
## Means/Intercepts/Thresholds
##
## [ VOC ] 2.462 -1.478 -1.478 -0.032
## [ COMP ] 0.028 0.149 0.149 0.004
## [ LANG ] 3.619 1.466 1.466 0.038
##
##
##
## Beginning Time: 12:20:09
## Ending Time: 12:20:10
## Elapsed Time: 00:00:01
##
##
##
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA 90066
##
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
##
## Copyright (c) 1998-2019 Muthen & Muthen7.4.4 Partial invariance model
TITLE: Structural Means Modeling -
partial invariance
DATA: FILE IS "data\READINGBOTHGROUPS.txt";
TYPE IS CORRELATION MEANS STDEVIATIONS;
NOBSERVATIONS ARE 1000 1000;
NGROUPS IS 2;
VARIABLE: NAMES ARE voc comp lang;
ANALYSIS: ESTIMATOR=ML;
MODEL: f BY voc* (1)
comp (2)
lang (3);
[voc*] (i1);
[comp*] (i2);
[lang*] (i3);
[f@0]; f@1;
MODEL G2:
f BY comp*;
[comp*];
[f*]; ! factor mean in G2 is freed
f*; ! factor variance in G2 is freed
OUTPUT: SAMP STDYX RES MOD(0);## Mplus VERSION 8.4
## MUTHEN & MUTHEN
## 06/10/2021 12:20 PM
##
## INPUT INSTRUCTIONS
##
## TITLE: Structural Means Modeling -
## partial invariance
## DATA: FILE IS "data\READINGBOTHGROUPS.txt";
## TYPE IS CORRELATION MEANS STDEVIATIONS;
## NOBSERVATIONS ARE 1000 1000;
## NGROUPS IS 2;
## VARIABLE: NAMES ARE voc comp lang;
## ANALYSIS: ESTIMATOR=ML;
## MODEL: f BY voc* (1)
## comp (2)
## lang (3);
## [voc*] (i1);
## [comp*] (i2);
## [lang*] (i3);
## [f@0]; f@1;
## MODEL G2:
## f BY comp*;
## [comp*];
## [f*]; ! factor mean in G2 is freed
## f*; ! factor variance in G2 is freed
## OUTPUT: SAMP STDYX RES MOD(0);
##
##
##
## 1 ERROR(S) FOUND IN THE INPUT INSTRUCTIONS
##
##
##
## Structural Means Modeling -
## partial invariance
##
## SUMMARY OF ANALYSIS
##
## Number of groups 2
## Number of observations
## Group G1 1000
## Group G2 1000
## Total sample size 2000
##
## Number of dependent variables 3
## Number of independent variables 0
## Number of continuous latent variables 1
##
## Observed dependent variables
##
## Continuous
## VOC COMP LANG
##
## Continuous latent variables
## F
##
##
## Estimator ML
## Information matrix EXPECTED
## Maximum number of iterations 1000
## Convergence criterion 0.500D-04
## Maximum number of steepest descent iterations 20
##
## Input data file(s)
## data\READINGBOTHGROUPS.txt
##
## Input data format FREE
##
##
## SAMPLE STATISTICS
##
##
## SAMPLE STATISTICS FOR G1
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 692.360 680.630 654.310
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2324.204
## COMP 1496.747 1625.702
## LANG 1188.468 1025.519 1531.157
##
##
## SAMPLE STATISTICS FOR G2
##
##
## Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.470 696.670 669.170
##
##
## Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2104.974
## COMP 1420.362 1575.296
## LANG 1144.270 989.888 1472.257
##
##
## THE MODEL ESTIMATION TERMINATED NORMALLY
##
##
##
## MODEL FIT INFORMATION
##
## Number of Free Parameters 16
##
## Loglikelihood
##
## H0 Value -29355.130
## H1 Value -29352.796
##
## Information Criteria
##
## Akaike (AIC) 58742.259
## Bayesian (BIC) 58831.874
## Sample-Size Adjusted BIC 58781.041
## (n* = (n + 2) / 24)
##
## Chi-Square Test of Model Fit
##
## Value 4.668
## Degrees of Freedom 2
## P-Value 0.0969
##
## Chi-Square Contribution From Each Group
##
## G1 2.612
## G2 2.056
##
## RMSEA (Root Mean Square Error Of Approximation)
##
## Estimate 0.037
## 90 Percent C.I. 0.000 0.081
## Probability RMSEA <= .05 0.623
##
## CFI/TLI
##
## CFI 0.999
## TLI 0.997
##
## Chi-Square Test of Model Fit for the Baseline Model
##
## Value 3103.084
## Degrees of Freedom 6
## P-Value 0.0000
##
## SRMR (Standardized Root Mean Square Residual)
##
## Value 0.011
##
##
##
## MODEL RESULTS
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 41.298 1.247 33.124 0.000
## COMP 35.967 1.082 33.231 0.000
## LANG 28.951 0.978 29.597 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 691.731 1.489 464.517 0.000
## COMP 680.630 1.274 534.082 0.000
## LANG 655.380 1.141 574.509 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 598.664 48.809 12.265 0.000
## COMP 330.451 34.976 9.448 0.000
## LANG 714.134 37.712 18.936 0.000
##
## Group G2
##
## F BY
## VOC 41.298 1.247 33.124 0.000
## COMP 35.818 1.471 24.345 0.000
## LANG 28.951 0.978 29.597 0.000
##
## Means
## F 0.441 0.051 8.700 0.000
##
## Intercepts
## VOC 691.731 1.489 464.517 0.000
## COMP 680.860 1.557 437.325 0.000
## LANG 655.380 1.141 574.509 0.000
##
## Variances
## F 0.958 0.077 12.414 0.000
##
## Residual Variances
## VOC 465.700 42.660 10.916 0.000
## COMP 344.898 32.607 10.577 0.000
## LANG 674.463 35.279 19.118 0.000
##
##
## STANDARDIZED MODEL RESULTS
##
##
## STDYX Standardization
##
## Two-Tailed
## Estimate S.E. Est./S.E. P-Value
##
## Group G1
##
## F BY
## VOC 0.860 0.013 67.218 0.000
## COMP 0.892 0.013 70.342 0.000
## LANG 0.735 0.015 47.838 0.000
##
## Means
## F 0.000 0.000 999.000 999.000
##
## Intercepts
## VOC 14.410 0.316 45.575 0.000
## COMP 16.889 0.379 44.565 0.000
## LANG 16.634 0.345 48.205 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.260 0.022 11.797 0.000
## COMP 0.203 0.023 8.984 0.000
## LANG 0.460 0.023 20.379 0.000
##
## Group G2
##
## F BY
## VOC 0.882 0.012 73.628 0.000
## COMP 0.884 0.012 71.039 0.000
## LANG 0.737 0.015 48.978 0.000
##
## Means
## F 0.451 0.052 8.716 0.000
##
## Intercepts
## VOC 15.097 0.333 45.278 0.000
## COMP 17.163 0.390 44.048 0.000
## LANG 17.051 0.354 48.156 0.000
##
## Variances
## F 1.000 0.000 999.000 999.000
##
## Residual Variances
## VOC 0.222 0.021 10.495 0.000
## COMP 0.219 0.022 9.969 0.000
## LANG 0.457 0.022 20.573 0.000
##
##
## R-SQUARE
##
## Group G1
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.740 0.022 33.609 0.000
## COMP 0.797 0.023 35.171 0.000
## LANG 0.540 0.023 23.919 0.000
##
## Group G2
##
## Observed Two-Tailed
## Variable Estimate S.E. Est./S.E. P-Value
##
## VOC 0.778 0.021 36.814 0.000
## COMP 0.781 0.022 35.520 0.000
## LANG 0.543 0.022 24.489 0.000
##
##
## QUALITY OF NUMERICAL RESULTS
##
## Condition Number for the Information Matrix 0.421E-04
## (ratio of smallest to largest eigenvalue)
##
##
## RESIDUAL OUTPUT
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G1
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 691.731 680.630 655.380
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.629 0.000 -1.070
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 1.947 0.005 -2.240
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 0.413 0.000 -0.865
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2304.212
## COMP 1485.375 1624.076
## LANG 1195.641 1041.293 1552.315
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 17.668
## COMP 9.875 0.001
## LANG -8.361 -16.799 -22.689
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 0.679
## COMP 0.679 0.013
## LANG -0.916 -0.870 -0.934
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.170
## COMP 0.127 0.000
## LANG -0.119 -0.283 -0.332
##
##
## ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) FOR G2
##
##
## Model Estimated Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## 709.959 696.670 668.159
##
##
## Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## -0.489 0.000 1.011
##
##
## Standardized Residuals (z-scores) for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## -2.068 -0.031 2.168
##
##
## Normalized Residuals for Means/Intercepts/Thresholds
## VOC COMP LANG
## ________ ________ ________
## -0.338 0.000 0.834
##
##
## Model Estimated Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 2099.319
## COMP 1416.837 1573.720
## LANG 1145.216 993.245 1477.294
##
##
## Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 3.551
## COMP 2.105 0.001
## LANG -2.090 -4.347 -6.509
##
##
## Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr
## VOC COMP LANG
## ________ ________ ________
## VOC 0.192
## COMP 0.203 0.010
## LANG -0.182 -0.220 -0.262
##
##
## Normalized Residuals for Covariances/Correlations/Residual Correlations
## VOC COMP LANG
## ________ ________ ________
## VOC 0.038
## COMP 0.029 0.000
## LANG -0.032 -0.076 -0.099
##
##
## MODEL MODIFICATION INDICES
##
## NOTE: Modification indices for direct effects of observed dependent variables
## regressed on covariates may not be included. To include these, request
## MODINDICES (ALL).
##
## Minimum M.I. value for printing the modification index 0.000
##
## M.I. E.P.C. Std E.P.C. StdYX E.P.C.
## Group G1
##
##
## BY Statements
##
## F BY VOC 0.636 0.314 0.314 0.007
## F BY LANG 0.636 -0.439 -0.439 -0.011
##
## WITH Statements
##
## LANG WITH COMP 0.635 -43.871 -43.871 -0.090
##
## Means/Intercepts/Thresholds
##
## [ VOC ] 4.565 0.629 0.629 0.013
## [ LANG ] 4.565 -1.070 -1.070 -0.027
##
## Group G2
##
##
## BY Statements
##
## F BY VOC 0.636 -1.426 -1.396 -0.030
## F BY LANG 0.636 0.781 0.764 0.020
##
## WITH Statements
##
## LANG WITH COMP 0.046 -11.228 -11.228 -0.023
##
## Means/Intercepts/Thresholds
##
## [ VOC ] 4.566 -3.716 -3.716 -0.081
## [ LANG ] 4.566 1.976 1.976 0.051
##
##
##
## Beginning Time: 12:20:10
## Ending Time: 12:20:10
## Elapsed Time: 00:00:00
##
##
##
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA 90066
##
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
##
## Copyright (c) 1998-2019 Muthen & Muthen