SEM Homework 2
Omolola A. Odejimi
[Updated] 10/26/2020
Multigroup Invariance Analysis
In this assignment you will test and report on Multigroup Measurement Invariance. Self-Determination is measured by 3 constructs: autonomy, psychological empowerment and self-realization. Each construct has 3 indicators available. Again, the constructs are autonomy [AUTO1-3], psychological empowerment [PSYE1-3] and self-realization [SR1-3].
There are 7 groups in this sample: 1=High_Incidence 2=Sensory 3=Intellectual 4=Orthopedic 5=Cognitive 6=Traumatic_Brain 7 = ASD
Instructions
Note* The model and the syntax for all levels of invariance are given. You will copy and paste this syntax into R. You should not need to write any new syntax, only copy and paste.
The output for the configural model is included in this assignment. You will need to run the metric, scalar and latent means models. The syntax/instructions for these are under the output from the configural model.
YOU WILL BE GRADED ON THE FOLLOWING CRITERIA:
[1] You will be graded on constructing a table like this one using APA 7th edition guidelines. (50 points)
You will use the chi-square value and the DF from the User model, NOT the Baseline model.
[2] You will be graded for drawing an SEM diagram of the model (25 points) Just one model. No need to draw one for each group. *circles, squares, arrows, curved arrows (no need to add values, I just want to see the structure)
*You can use the software at the provided link to draw this diagram <app.diagrams.net>
[3] Based on the guidance from the Multigroup CFA lecture (slides and class recording on blackboard), describe whether the model has reached all levels of invariance: Configural, Metric, Scalar and Latent Means (125).
There will be 4 write-ups, 1 for each stage of invariance testing.
Example Write-Up for Metric Invariance: “Loadings are invariant across 7th and 8th graders. In a comparison of this metric model and the configural model, the change in CFI was .006 which is lower than the .01 threshold. The RMSEA value for this metric model, .04, is within the confidence interval for the configural model’s RMSEA, [.03-.08]. This is evidence that the model has passed metric invariance.” -slide 16 gives this example
Load Data
Your file <NLTS.csv> is in a folder on your computer. Set your directory, with the setwd() function, to that folder. Mine is unique to my computer.
setwd("E:/SEM - TA/HW2") # Make sure to use a forward slash /
dat <- read.csv("NLTS.csv", na.strings = "-99") # Now the software knows where this file livesInvestigate data
names(dat)## [1] "id" "disability" "AUTO1" "AUTO2" "AUTO3"
## [6] "PSYE1" "PSYE2" "PSYE3" "SR1" "SR2"
## [11] "SR3" "group"psych::describe(dat)Level 1: Configural Invariance
Configural invariance describes the situation when the parameters are estimated uniquely in each group but the pattern of free and fixed parameters is the same (or very similar).
Fit a multiple-group model with the same factor structure to two (or more) groups. If the model fits well, configural invariance is supported.
Please judge model fit by the CFI and RMSEA. You can use the fit guidelines from the following page http://davidakenny.net/cm/fit.htm
SD.model <-'
#define the constructs
AUTO =~ AUTO1 + AUTO2 + AUTO3
PSYE =~ PSYE1 + PSYE2 + PSYE3
SR =~ SR1 + SR2 + SR3
#specify correlation
AUTO ~~ PSYE + SR
PSYE ~~ SR'You may need to install Lavaan if this is your first time using it.
install.packages(“lavaan”)
library(lavaan) ## This is lavaan 0.6-7## lavaan is BETA software! Please report any bugs.conf <- cfa(model = SD.model,
data = dat,
group = "group",
missing = "fiml")
options(max.print = 100000) #this line extends the output in the console
summary(conf,
standardized=TRUE,
fit.measures=TRUE,
rsquare=TRUE)## lavaan 0.6-7 ended normally after 339 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 210
##
## Number of observations per group:
## 1 4162
## 3 758
## 6 204
## 2 586
## 5 495
## 7 637
## 4 297
## Number of missing patterns per group:
## 1 29
## 3 21
## 6 10
## 2 14
## 5 13
## 7 19
## 4 7
##
## Model Test User Model:
##
## Test statistic 513.977
## Degrees of freedom 168
## P-value (Chi-square) 0.000
## Test statistic for each group:
## 1 226.822
## 3 40.211
## 6 35.299
## 2 54.914
## 5 33.024
## 7 73.438
## 4 50.270
##
## Model Test Baseline Model:
##
## Test statistic 12407.613
## Degrees of freedom 252
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.972
## Tucker-Lewis Index (TLI) 0.957
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -10175.921
## Loglikelihood unrestricted model (H1) -9918.933
##
## Akaike (AIC) 20771.843
## Bayesian (BIC) 22215.242
## Sample-size adjusted Bayesian (BIC) 21547.909
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.045
## 90 Percent confidence interval - lower 0.041
## 90 Percent confidence interval - upper 0.049
## P-value RMSEA <= 0.05 0.969
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.571 0.717
## AUTO2 1.038 0.029 36.226 0.000 0.592 0.716
## AUTO3 0.925 0.025 36.808 0.000 0.528 0.776
## PSYE =~
## PSYE1 1.000 0.114 0.537
## PSYE2 1.227 0.050 24.509 0.000 0.140 0.628
## PSYE3 0.745 0.039 19.162 0.000 0.085 0.459
## SR =~
## SR1 1.000 0.100 0.559
## SR2 0.970 0.039 24.710 0.000 0.097 0.572
## SR3 1.181 0.051 23.377 0.000 0.118 0.618
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.016 0.002 9.562 0.000 0.240 0.240
## SR 0.011 0.001 8.528 0.000 0.200 0.200
## PSYE ~~
## SR 0.010 0.000 20.149 0.000 0.871 0.871
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.825 0.012 228.708 0.000 2.825 3.549
## .AUTO2 2.409 0.013 187.573 0.000 2.409 2.910
## .AUTO3 2.701 0.011 255.556 0.000 2.701 3.969
## .PSYE1 1.908 0.003 577.886 0.000 1.908 8.979
## .PSYE2 1.899 0.003 549.287 0.000 1.899 8.523
## .PSYE3 1.923 0.003 667.984 0.000 1.923 10.385
## .SR1 1.940 0.003 701.252 0.000 1.940 10.886
## .SR2 1.951 0.003 745.609 0.000 1.951 11.571
## .SR3 1.915 0.003 645.736 0.000 1.915 10.061
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.308 0.010 30.904 0.000 0.308 0.486
## .AUTO2 0.334 0.011 30.941 0.000 0.334 0.488
## .AUTO3 0.184 0.007 24.800 0.000 0.184 0.398
## .PSYE1 0.032 0.001 36.126 0.000 0.032 0.712
## .PSYE2 0.030 0.001 29.809 0.000 0.030 0.606
## .PSYE3 0.027 0.001 39.613 0.000 0.027 0.789
## .SR1 0.022 0.001 35.524 0.000 0.022 0.688
## .SR2 0.019 0.001 34.780 0.000 0.019 0.672
## .SR3 0.022 0.001 32.364 0.000 0.022 0.618
## AUTO 0.326 0.014 22.953 0.000 1.000 1.000
## PSYE 0.013 0.001 14.730 0.000 1.000 1.000
## SR 0.010 0.001 15.545 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.514
## AUTO2 0.512
## AUTO3 0.602
## PSYE1 0.288
## PSYE2 0.394
## PSYE3 0.211
## SR1 0.312
## SR2 0.328
## SR3 0.382
##
##
## Group 2 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.636 0.738
## AUTO2 0.958 0.062 15.460 0.000 0.609 0.707
## AUTO3 0.901 0.057 15.678 0.000 0.573 0.763
## PSYE =~
## PSYE1 1.000 0.154 0.591
## PSYE2 0.940 0.105 8.942 0.000 0.144 0.629
## PSYE3 0.482 0.065 7.393 0.000 0.074 0.410
## SR =~
## SR1 1.000 0.166 0.690
## SR2 0.536 0.053 10.082 0.000 0.089 0.521
## SR3 0.846 0.080 10.518 0.000 0.141 0.654
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.026 0.006 4.526 0.000 0.267 0.267
## SR 0.026 0.006 4.523 0.000 0.247 0.247
## PSYE ~~
## SR 0.015 0.002 7.497 0.000 0.592 0.592
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.704 0.031 86.175 0.000 2.704 3.136
## .AUTO2 2.357 0.031 75.125 0.000 2.357 2.736
## .AUTO3 2.638 0.027 96.113 0.000 2.638 3.508
## .PSYE1 1.871 0.010 196.862 0.000 1.871 7.190
## .PSYE2 1.895 0.008 226.663 0.000 1.895 8.247
## .PSYE3 1.924 0.007 290.540 0.000 1.924 10.649
## .SR1 1.892 0.009 214.839 0.000 1.892 7.839
## .SR2 1.944 0.006 311.528 0.000 1.944 11.341
## .SR3 1.887 0.008 239.456 0.000 1.887 8.760
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.339 0.028 12.272 0.000 0.339 0.456
## .AUTO2 0.371 0.027 13.574 0.000 0.371 0.500
## .AUTO3 0.236 0.021 11.205 0.000 0.236 0.418
## .PSYE1 0.044 0.003 12.881 0.000 0.044 0.651
## .PSYE2 0.032 0.003 11.439 0.000 0.032 0.605
## .PSYE3 0.027 0.002 16.869 0.000 0.027 0.832
## .SR1 0.031 0.003 10.837 0.000 0.031 0.524
## .SR2 0.021 0.001 16.095 0.000 0.021 0.729
## .SR3 0.027 0.002 12.043 0.000 0.027 0.573
## AUTO 0.405 0.040 10.057 0.000 1.000 1.000
## PSYE 0.024 0.004 6.407 0.000 1.000 1.000
## SR 0.028 0.003 7.982 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.544
## AUTO2 0.500
## AUTO3 0.582
## PSYE1 0.349
## PSYE2 0.395
## PSYE3 0.168
## SR1 0.476
## SR2 0.271
## SR3 0.427
##
##
## Group 3 [6]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.585 0.700
## AUTO2 1.018 0.114 8.951 0.000 0.595 0.764
## AUTO3 0.980 0.111 8.853 0.000 0.573 0.826
## PSYE =~
## PSYE1 1.000 0.141 0.608
## PSYE2 1.082 0.202 5.358 0.000 0.152 0.652
## PSYE3 0.600 0.132 4.526 0.000 0.084 0.457
## SR =~
## SR1 1.000 0.117 0.687
## SR2 0.952 0.136 6.979 0.000 0.111 0.672
## SR3 1.250 0.205 6.092 0.000 0.146 0.644
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.028 0.009 3.148 0.002 0.344 0.344
## SR 0.002 0.006 0.309 0.757 0.029 0.029
## PSYE ~~
## SR 0.010 0.002 4.246 0.000 0.585 0.585
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.813 0.059 47.969 0.000 2.813 3.370
## .AUTO2 2.429 0.055 44.548 0.000 2.429 3.119
## .AUTO3 2.741 0.049 56.226 0.000 2.741 3.948
## .PSYE1 1.896 0.016 116.214 0.000 1.896 8.186
## .PSYE2 1.874 0.016 114.093 0.000 1.874 8.021
## .PSYE3 1.923 0.013 147.399 0.000 1.923 10.411
## .SR1 1.946 0.012 162.784 0.000 1.946 11.417
## .SR2 1.944 0.012 167.526 0.000 1.944 11.729
## .SR3 1.896 0.016 118.044 0.000 1.896 8.340
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.355 0.046 7.688 0.000 0.355 0.510
## .AUTO2 0.253 0.039 6.474 0.000 0.253 0.417
## .AUTO3 0.154 0.032 4.822 0.000 0.154 0.319
## .PSYE1 0.034 0.005 6.934 0.000 0.034 0.631
## .PSYE2 0.031 0.005 6.231 0.000 0.031 0.575
## .PSYE3 0.027 0.003 8.667 0.000 0.027 0.791
## .SR1 0.015 0.002 6.427 0.000 0.015 0.528
## .SR2 0.015 0.002 6.731 0.000 0.015 0.548
## .SR3 0.030 0.004 6.836 0.000 0.030 0.585
## AUTO 0.342 0.067 5.122 0.000 1.000 1.000
## PSYE 0.020 0.005 3.651 0.000 1.000 1.000
## SR 0.014 0.003 4.484 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.490
## AUTO2 0.583
## AUTO3 0.681
## PSYE1 0.369
## PSYE2 0.425
## PSYE3 0.209
## SR1 0.472
## SR2 0.452
## SR3 0.415
##
##
## Group 4 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.505 0.655
## AUTO2 0.969 0.083 11.677 0.000 0.489 0.631
## AUTO3 1.070 0.092 11.592 0.000 0.540 0.816
## PSYE =~
## PSYE1 1.000 0.145 0.681
## PSYE2 0.922 0.105 8.763 0.000 0.134 0.593
## PSYE3 0.490 0.072 6.831 0.000 0.071 0.433
## SR =~
## SR1 1.000 0.094 0.532
## SR2 0.955 0.123 7.753 0.000 0.090 0.598
## SR3 0.988 0.148 6.656 0.000 0.093 0.521
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.019 0.005 4.032 0.000 0.260 0.260
## SR 0.012 0.003 3.637 0.000 0.249 0.249
## PSYE ~~
## SR 0.008 0.001 6.520 0.000 0.598 0.598
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.851 0.032 89.534 0.000 2.851 3.702
## .AUTO2 2.383 0.032 74.224 0.000 2.383 3.071
## .AUTO3 2.718 0.027 98.879 0.000 2.718 4.103
## .PSYE1 1.904 0.009 215.309 0.000 1.904 8.925
## .PSYE2 1.889 0.009 201.914 0.000 1.889 8.371
## .PSYE3 1.940 0.007 284.426 0.000 1.940 11.804
## .SR1 1.937 0.007 265.190 0.000 1.937 10.979
## .SR2 1.956 0.006 315.564 0.000 1.956 13.046
## .SR3 1.925 0.007 260.000 0.000 1.925 10.822
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.338 0.027 12.361 0.000 0.338 0.570
## .AUTO2 0.363 0.028 13.107 0.000 0.363 0.602
## .AUTO3 0.147 0.023 6.388 0.000 0.147 0.335
## .PSYE1 0.024 0.003 8.686 0.000 0.024 0.537
## .PSYE2 0.033 0.003 11.827 0.000 0.033 0.648
## .PSYE3 0.022 0.002 14.565 0.000 0.022 0.813
## .SR1 0.022 0.002 12.586 0.000 0.022 0.717
## .SR2 0.014 0.001 10.777 0.000 0.014 0.643
## .SR3 0.023 0.002 12.619 0.000 0.023 0.729
## AUTO 0.255 0.034 7.453 0.000 1.000 1.000
## PSYE 0.021 0.003 6.379 0.000 1.000 1.000
## SR 0.009 0.002 5.052 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.430
## AUTO2 0.398
## AUTO3 0.665
## PSYE1 0.463
## PSYE2 0.352
## PSYE3 0.187
## SR1 0.283
## SR2 0.357
## SR3 0.271
##
##
## Group 5 [5]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.594 0.710
## AUTO2 1.114 0.085 13.090 0.000 0.661 0.750
## AUTO3 0.952 0.072 13.184 0.000 0.566 0.777
## PSYE =~
## PSYE1 1.000 0.134 0.574
## PSYE2 0.979 0.115 8.544 0.000 0.131 0.560
## PSYE3 0.791 0.100 7.947 0.000 0.106 0.523
## SR =~
## SR1 1.000 0.155 0.655
## SR2 0.655 0.073 8.991 0.000 0.101 0.544
## SR3 0.752 0.082 9.178 0.000 0.116 0.598
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.029 0.006 4.794 0.000 0.363 0.363
## SR 0.028 0.006 4.551 0.000 0.309 0.309
## PSYE ~~
## SR 0.019 0.002 7.959 0.000 0.912 0.912
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.769 0.038 73.571 0.000 2.769 3.309
## .AUTO2 2.356 0.040 59.348 0.000 2.356 2.672
## .AUTO3 2.671 0.033 81.328 0.000 2.671 3.668
## .PSYE1 1.893 0.011 180.084 0.000 1.893 8.114
## .PSYE2 1.880 0.011 178.487 0.000 1.880 8.029
## .PSYE3 1.909 0.009 207.780 0.000 1.909 9.418
## .SR1 1.905 0.011 179.194 0.000 1.905 8.079
## .SR2 1.942 0.008 232.453 0.000 1.942 10.448
## .SR3 1.910 0.009 217.757 0.000 1.910 9.834
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.348 0.031 11.240 0.000 0.348 0.496
## .AUTO2 0.339 0.034 9.947 0.000 0.339 0.437
## .AUTO3 0.210 0.023 8.969 0.000 0.210 0.396
## .PSYE1 0.036 0.003 12.249 0.000 0.036 0.670
## .PSYE2 0.038 0.003 12.571 0.000 0.038 0.686
## .PSYE3 0.030 0.002 13.113 0.000 0.030 0.727
## .SR1 0.032 0.003 10.859 0.000 0.032 0.571
## .SR2 0.024 0.002 13.041 0.000 0.024 0.704
## .SR3 0.024 0.002 12.098 0.000 0.024 0.643
## AUTO 0.353 0.044 7.967 0.000 1.000 1.000
## PSYE 0.018 0.003 5.658 0.000 1.000 1.000
## SR 0.024 0.004 6.651 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.504
## AUTO2 0.563
## AUTO3 0.604
## PSYE1 0.330
## PSYE2 0.314
## PSYE3 0.273
## SR1 0.429
## SR2 0.296
## SR3 0.357
##
##
## Group 6 [7]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.598 0.734
## AUTO2 0.867 0.069 12.552 0.000 0.518 0.647
## AUTO3 0.865 0.067 12.893 0.000 0.517 0.741
## PSYE =~
## PSYE1 1.000 0.166 0.575
## PSYE2 0.947 0.115 8.261 0.000 0.157 0.578
## PSYE3 0.383 0.068 5.623 0.000 0.063 0.343
## SR =~
## SR1 1.000 0.121 0.596
## SR2 0.948 0.099 9.558 0.000 0.114 0.595
## SR3 1.046 0.136 7.695 0.000 0.126 0.544
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.033 0.007 4.643 0.000 0.335 0.335
## SR 0.018 0.004 4.076 0.000 0.253 0.253
## PSYE ~~
## SR 0.015 0.002 7.514 0.000 0.763 0.763
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.503 0.032 77.407 0.000 2.503 3.071
## .AUTO2 2.215 0.032 69.757 0.000 2.215 2.768
## .AUTO3 2.568 0.028 92.743 0.000 2.568 3.679
## .PSYE1 1.792 0.012 155.436 0.000 1.792 6.216
## .PSYE2 1.818 0.011 167.771 0.000 1.818 6.696
## .PSYE3 1.919 0.007 260.095 0.000 1.919 10.382
## .SR1 1.919 0.008 238.211 0.000 1.919 9.483
## .SR2 1.933 0.008 253.194 0.000 1.933 10.066
## .SR3 1.874 0.009 201.093 0.000 1.874 8.081
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.307 0.029 10.428 0.000 0.307 0.462
## .AUTO2 0.372 0.028 13.452 0.000 0.372 0.581
## .AUTO3 0.219 0.022 10.158 0.000 0.219 0.450
## .PSYE1 0.056 0.005 12.187 0.000 0.056 0.670
## .PSYE2 0.049 0.004 11.896 0.000 0.049 0.666
## .PSYE3 0.030 0.002 16.174 0.000 0.030 0.883
## .SR1 0.026 0.002 11.946 0.000 0.026 0.645
## .SR2 0.024 0.002 12.083 0.000 0.024 0.646
## .SR3 0.038 0.003 13.008 0.000 0.038 0.704
## AUTO 0.357 0.041 8.770 0.000 1.000 1.000
## PSYE 0.027 0.005 5.708 0.000 1.000 1.000
## SR 0.015 0.002 6.011 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.538
## AUTO2 0.419
## AUTO3 0.550
## PSYE1 0.330
## PSYE2 0.334
## PSYE3 0.117
## SR1 0.355
## SR2 0.354
## SR3 0.296
##
##
## Group 7 [4]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO =~
## AUTO1 1.000 0.619 0.731
## AUTO2 1.123 0.103 10.910 0.000 0.696 0.806
## AUTO3 0.896 0.083 10.807 0.000 0.555 0.757
## PSYE =~
## PSYE1 1.000 0.100 0.490
## PSYE2 1.145 0.198 5.771 0.000 0.114 0.551
## PSYE3 1.007 0.198 5.094 0.000 0.100 0.522
## SR =~
## SR1 1.000 0.129 0.703
## SR2 0.778 0.107 7.299 0.000 0.100 0.603
## SR3 0.454 0.094 4.801 0.000 0.058 0.407
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AUTO ~~
## PSYE 0.017 0.006 2.812 0.005 0.274 0.274
## SR 0.015 0.007 2.209 0.027 0.184 0.184
## PSYE ~~
## SR 0.011 0.002 5.742 0.000 0.858 0.858
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 2.850 0.049 57.945 0.000 2.850 3.366
## .AUTO2 2.455 0.050 49.023 0.000 2.455 2.845
## .AUTO3 2.832 0.043 66.342 0.000 2.832 3.861
## .PSYE1 1.922 0.012 162.394 0.000 1.922 9.450
## .PSYE2 1.912 0.012 159.235 0.000 1.912 9.240
## .PSYE3 1.931 0.011 172.947 0.000 1.931 10.050
## .SR1 1.934 0.011 181.948 0.000 1.934 10.558
## .SR2 1.958 0.010 202.774 0.000 1.958 11.766
## .SR3 1.951 0.008 232.367 0.000 1.951 13.587
## AUTO 0.000 0.000 0.000
## PSYE 0.000 0.000 0.000
## SR 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .AUTO1 0.334 0.039 8.530 0.000 0.334 0.465
## .AUTO2 0.261 0.040 6.476 0.000 0.261 0.350
## .AUTO3 0.230 0.029 8.021 0.000 0.230 0.427
## .PSYE1 0.031 0.003 9.840 0.000 0.031 0.760
## .PSYE2 0.030 0.003 9.137 0.000 0.030 0.696
## .PSYE3 0.027 0.003 9.775 0.000 0.027 0.727
## .SR1 0.017 0.003 6.531 0.000 0.017 0.505
## .SR2 0.018 0.002 8.949 0.000 0.018 0.637
## .SR3 0.017 0.002 10.839 0.000 0.017 0.834
## AUTO 0.383 0.059 6.474 0.000 1.000 1.000
## PSYE 0.010 0.003 3.428 0.001 1.000 1.000
## SR 0.017 0.003 5.135 0.000 1.000 1.000
##
## R-Square:
## Estimate
## AUTO1 0.535
## AUTO2 0.650
## AUTO3 0.573
## PSYE1 0.240
## PSYE2 0.304
## PSYE3 0.273
## SR1 0.495
## SR2 0.363
## SR3 0.166Level 2: Metric Invariance
Metric invariance describes the situation when the values of the factor loadingsare equal between the groups.
It also suggests that the observed variables have the same unit of measurement.
Constrain the values of the factor loadings to be equal between the groups. If the model fits well, and the fit is not significantly worsethan the fit of the configural invariance model (Level 1), metric invariance is supported.
Please judge model fit by the change in CFI between this model and the configural model. Change should not be greater than .01 from the configural model.
metric <- cfa(model = SD.model,
data = dat,
group = "group",
missing = "fiml",
group.equal = "loadings")+Enter this into R to get model results
summary(metric, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE)
Level 3: Scalar Invariance
Scalar invariance describes the situation when the values of the factor loadings as well as the intercepts are equal between groups.
It also suggests that the variables have the same unit of measurement as well as the same origin.
Scalar invariance is a “prerequisite” for comparing factor means between groups.
Please judge model fit by the change in CFI between this model and the metric model. Change should not be greater than .01 from the metric model.
scalar <- cfa(model = SD.model,
data = dat,
group = "group",
missing = "fiml",
group.equal = c("loadings", "intercepts"))+Enter this into R to get model results
summary(scalar, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE)
Level 4: Invariance of Factor Means
Invariance of factor means suggests that the values of the factor means are equal across groups
lvmean <- cfa(SD.model,
data = dat,
group = "group",
missing = "fiml",
group.equal=c("loadings", "intercepts", "means"))+Enter this into R to get model results
summary(lvmean, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE)
To compare the latent means model with the scalar model we use the anova test for the difference in chi square values (instead of the change in CFI and RMSEA). If this value is significant, then we can say the values of the factor means are equal across groups.
+Enter this into R to get the anova test results
anova(scalar, lvmean)