library(lavaan)
setwd(mypath) # set working directory to where the data file is stored
data1 <- read.table("causacian.csv", sep=",", header = F)
data2 <- read.table("african-american.csv", sep = ",", header = F)
data1$race <- 1
data2$race <- 2
data <- rbind(data1, data2)
colnames(data) <- c('hand', 'number', 'word',
'gestalt', 'triangle', 'matrix', 'spatial', 'photo','race')
cfa.constrained <- '
SEQUENT =~ hand + number + word
SIMULTAN =~ triangle + matrix + spatial
hand ~ 1
number ~ 1
word ~ 1
triangle ~ 1
matrix ~ 1
spatial ~ 1
'
fit.constrained <- sem(cfa.constrained, data, group = "race", group.equal = c("loadings"))
summary(fit.constrained, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 78 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
## Number of equality constraints 4
##
## Number of observations per group:
## 1 86
## 2 86
##
## Model Test User Model:
##
## Test statistic 31.643
## Degrees of freedom 20
## P-value (Chi-square) 0.047
## Test statistic for each group:
## 1 20.207
## 2 11.436
##
## Model Test Baseline Model:
##
## Test statistic 200.885
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.932
## Tucker-Lewis Index (TLI) 0.898
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2436.281
## Loglikelihood unrestricted model (H1) -2420.459
##
## Akaike (AIC) 4940.561
## Bayesian (BIC) 5047.576
## Sample-size adjusted Bayesian (SABIC) 4939.915
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.009
## 90 Percent confidence interval - upper 0.134
## P-value H_0: RMSEA <= 0.050 0.162
## P-value H_0: RMSEA >= 0.080 0.564
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.082
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT =~
## hand 1.000 1.526 0.552
## number (.p2.) 0.960 0.212 4.531 0.000 1.465 0.718
## word (.p3.) 1.004 0.223 4.508 0.000 1.532 0.761
## SIMULTAN =~
## triangl 1.000 1.589 0.700
## matrix (.p5.) 1.459 0.297 4.918 0.000 2.318 0.678
## spatial (.p6.) 1.434 0.336 4.266 0.000 2.278 0.186
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT ~~
## SIMULTAN 1.412 0.491 2.874 0.004 0.582 0.582
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand -0.001 0.298 -0.003 0.998 -0.001 -0.000
## .number -0.001 0.220 -0.003 0.998 -0.001 -0.000
## .word 0.001 0.217 0.004 0.997 0.001 0.000
## .triangle -0.000 0.245 -0.000 1.000 -0.000 -0.000
## .matrix 0.001 0.368 0.004 0.997 0.001 0.000
## .spatial -0.003 1.318 -0.002 0.998 -0.003 -0.000
## SEQUENT 0.000 0.000 0.000
## SIMULTAN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand 5.306 0.942 5.635 0.000 5.306 0.695
## .number 2.020 0.485 4.162 0.000 2.020 0.485
## .word 1.701 0.481 3.536 0.000 1.701 0.420
## .triangle 2.627 0.712 3.693 0.000 2.627 0.510
## .matrix 6.300 1.581 3.984 0.000 6.300 0.540
## .spatial 144.165 22.248 6.480 0.000 144.165 0.965
## SEQUENT 2.329 0.916 2.544 0.011 1.000 1.000
## SIMULTAN 2.524 0.804 3.137 0.002 1.000 1.000
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT =~
## hand 1.000 1.119 0.263
## number (.p2.) 0.960 0.212 4.531 0.000 1.074 0.566
## word (.p3.) 1.004 0.223 4.508 0.000 1.123 0.727
## SIMULTAN =~
## triangl 1.000 1.249 0.624
## matrix (.p5.) 1.459 0.297 4.918 0.000 1.823 0.543
## spatial (.p6.) 1.434 0.336 4.266 0.000 1.791 0.769
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT ~~
## SIMULTAN 0.752 0.303 2.477 0.013 0.538 0.538
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand -0.002 0.459 -0.004 0.997 -0.002 -0.000
## .number -0.001 0.205 -0.005 0.996 -0.001 -0.001
## .word 0.000 0.167 0.001 0.999 0.000 0.000
## .triangle -0.000 0.216 -0.002 0.998 -0.000 -0.000
## .matrix 0.000 0.362 0.001 0.999 0.000 0.000
## .spatial -0.001 0.251 -0.003 0.998 -0.001 -0.000
## SEQUENT 0.000 0.000 0.000
## SIMULTAN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand 16.881 2.648 6.375 0.000 16.881 0.931
## .number 2.449 0.479 5.115 0.000 2.449 0.680
## .word 1.123 0.360 3.120 0.002 1.123 0.471
## .triangle 2.451 0.507 4.832 0.000 2.451 0.611
## .matrix 7.934 1.437 5.520 0.000 7.934 0.705
## .spatial 2.214 0.771 2.872 0.004 2.214 0.408
## SEQUENT 1.252 0.579 2.164 0.030 1.000 1.000
## SIMULTAN 1.561 0.547 2.853 0.004 1.000 1.000
mod.constrained <- modindices(fit.constrained, sort = T)
mod.constrained[mod.constrained$mi >= 3.841, ]
## lhs op rhs block group level mi epc sepc.lv sepc.all
## 62 number ~~ word 1 1 1 8.130 2.023 2.023 1.091
## 87 word ~~ triangle 2 2 1 5.747 -0.649 -0.649 -0.391
## 69 triangle ~~ matrix 1 1 1 4.679 -5.443 -5.443 -1.338
## 73 SEQUENT =~ matrix 2 2 1 4.173 0.933 1.043 0.311
## 60 hand ~~ matrix 1 1 1 4.108 1.603 1.603 0.277
## sepc.nox
## 62 1.091
## 87 -0.391
## 69 -1.338
## 73 0.311
## 60 0.277
### different from the Mplus output
### Release the constraints
## free the loading based on the modification indices obtained in Mplus (to be consistent with your practice in class)
cfa.unconstrained <- '
SEQUENT =~ hand + number + word
SIMULTAN =~ triangle + matrix + c(a,b)*spatial
hand~1
number~1
word~1
triangle~1
matrix ~ 1
spatial~1
'
fit.unconstrained <- sem(cfa.unconstrained, data, group="race", group.equal=c("loadings"))
summary(fit.unconstrained, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 79 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
## Number of equality constraints 3
##
## Number of observations per group:
## 1 86
## 2 86
##
## Model Test User Model:
##
## Test statistic 23.515
## Degrees of freedom 19
## P-value (Chi-square) 0.215
## Test statistic for each group:
## 1 12.784
## 2 10.731
##
## Model Test Baseline Model:
##
## Test statistic 200.885
## Degrees of freedom 30
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.974
## Tucker-Lewis Index (TLI) 0.958
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2432.216
## Loglikelihood unrestricted model (H1) -2420.459
##
## Akaike (AIC) 4934.433
## Bayesian (BIC) 5044.595
## Sample-size adjusted Bayesian (SABIC) 4933.768
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.053
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.436
## P-value H_0: RMSEA >= 0.080 0.270
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT =~
## hand 1.000 1.536 0.556
## number (.p2.) 0.949 0.209 4.549 0.000 1.458 0.713
## word (.p3.) 0.998 0.220 4.530 0.000 1.533 0.763
## SIMULTAN =~
## triangl 1.000 1.526 0.684
## matrix (.p5.) 1.449 0.267 5.428 0.000 2.212 0.650
## spatial (a) 4.264 1.186 3.595 0.000 6.508 0.512
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT ~~
## SIMULTAN 1.371 0.473 2.901 0.004 0.585 0.585
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand -0.001 0.298 -0.003 0.998 -0.001 -0.000
## .number -0.001 0.221 -0.003 0.998 -0.001 -0.000
## .word 0.001 0.217 0.004 0.997 0.001 0.000
## .triangle -0.000 0.241 -0.000 1.000 -0.000 -0.000
## .matrix 0.001 0.367 0.004 0.997 0.001 0.000
## .spatial -0.003 1.372 -0.002 0.998 -0.003 -0.000
## SEQUENT 0.000 0.000 0.000
## SIMULTAN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand 5.278 0.939 5.618 0.000 5.278 0.691
## .number 2.060 0.486 4.238 0.000 2.060 0.492
## .word 1.683 0.478 3.517 0.000 1.683 0.417
## .triangle 2.649 0.635 4.170 0.000 2.649 0.532
## .matrix 6.670 1.457 4.577 0.000 6.670 0.577
## .spatial 119.507 21.702 5.507 0.000 119.507 0.738
## SEQUENT 2.359 0.921 2.560 0.010 1.000 1.000
## SIMULTAN 2.329 0.734 3.175 0.002 1.000 1.000
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT =~
## hand 1.000 1.125 0.264
## number (.p2.) 0.949 0.209 4.549 0.000 1.068 0.564
## word (.p3.) 0.998 0.220 4.530 0.000 1.123 0.725
## SIMULTAN =~
## triangl 1.000 1.369 0.671
## matrix (.p5.) 1.449 0.267 5.428 0.000 1.984 0.586
## spatial (b) 1.190 0.274 4.345 0.000 1.629 0.712
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SEQUENT ~~
## SIMULTAN 0.833 0.328 2.543 0.011 0.541 0.541
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand -0.002 0.459 -0.004 0.997 -0.002 -0.000
## .number -0.001 0.204 -0.005 0.996 -0.001 -0.001
## .word 0.000 0.167 0.001 0.999 0.000 0.000
## .triangle -0.000 0.220 -0.002 0.998 -0.000 -0.000
## .matrix 0.000 0.365 0.001 0.999 0.000 0.000
## .spatial -0.001 0.247 -0.003 0.998 -0.001 -0.000
## SEQUENT 0.000 0.000 0.000
## SIMULTAN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .hand 16.860 2.646 6.372 0.000 16.860 0.930
## .number 2.439 0.476 5.120 0.000 2.439 0.681
## .word 1.135 0.362 3.138 0.002 1.135 0.474
## .triangle 2.289 0.518 4.416 0.000 2.289 0.550
## .matrix 7.515 1.424 5.277 0.000 7.515 0.656
## .spatial 2.578 0.691 3.733 0.000 2.578 0.493
## SEQUENT 1.266 0.583 2.171 0.030 1.000 1.000
## SIMULTAN 1.874 0.606 3.094 0.002 1.000 1.000
mod.constrained <- modindices(fit.constrained, sort = T)
mod.constrained[mod.constrained$mi >= 3.841, ]
## lhs op rhs block group level mi epc sepc.lv sepc.all
## 62 number ~~ word 1 1 1 8.130 2.023 2.023 1.091
## 87 word ~~ triangle 2 2 1 5.747 -0.649 -0.649 -0.391
## 69 triangle ~~ matrix 1 1 1 4.679 -5.443 -5.443 -1.338
## 73 SEQUENT =~ matrix 2 2 1 4.173 0.933 1.043 0.311
## 60 hand ~~ matrix 1 1 1 4.108 1.603 1.603 0.277
## sepc.nox
## 62 1.091
## 87 -0.391
## 69 -1.338
## 73 0.311
## 60 0.277
© Copyright 2024
@Yi Feng
and
@Gregory R. Hancock.