Data Simulation
> set.seed(1992)
> N<-runif(1,500,1000)
> bA1<-runif(1,1,5)
> bA2<-runif(1,1,5)
> bA3<-runif(1,1,5)
> bA4<-runif(1,1,5)
> cA1<-runif(1,1,5)
> cA2<-runif(1,1,5)
> cA3<-runif(1,1,5)
> cA4<-runif(1,1,5)
> eb<-runif(1,10,20)*sample(c(-1,1),1)
> ec<-runif(1,10,20)*sample(c(-1,1),1)
>
> ## Random Variables ####
> A1<-rnorm(N,1,10)
> A2<-rnorm(N,1,10)
> A3<-rnorm(N,1,10)
> A4<-rnorm(N,1,10)
> eB<-rnorm(N,1,10)
> eC<-rnorm(N,1,10)
> ## Directed Equations ####
> B_C<-(bA1*A1)+(bA2*A2)+(bA3*A3)+(bA4*A4)+(eb*eB)
> summary(B_C)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-636.65158031 -136.24443920 -10.56683713 -1.56843134 137.18856826 632.45821131
> B_n<-((B_C)-min(B_C-100))/((max(B_C+100))-min(B_C-100))
> summary(B_n)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.068068432 0.408687727 0.494234500 0.500359574 0.594809288 0.931931568
> B<-rbinom(N,1,prob=B_n)
> table(B)
B
0 1
417 395
> C<-0*B+(cA1*A1)+(cA2*A2)+(cA3*A3)+(cA4*A4)+(ec*eC)
>
> DF<-data.frame(A1,A2,A3,A4,B,C)
> DF$C<-DF$C*.01
DWLS estimator without specifying B as ordered
>
> F1<-'
+ # Latent Factor ####
+ B~A1
+ C~B
+
+ '
> M<-sem(F1,orthogonal = T, data=DF, estimator = "DWLS")
> summary(M, fit.measures= TRUE, standardized = TRUE, ci = TRUE, rsquare = T)
lavaan 0.6-9 ended normally after 14 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 5
Number of observations 812
Model Test User Model:
Test statistic 45.349
Degrees of freedom 1
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 45.352
Degrees of freedom 3
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.000
Tucker-Lewis Index (TLI) -2.141
Root Mean Square Error of Approximation:
RMSEA 0.234
90 Percent confidence interval - lower 0.179
90 Percent confidence interval - upper 0.294
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.094
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Unstructured
Regressions:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
B ~
A1 -0.000 0.002 -0.032 0.975 -0.004 0.003 -0.000 -0.001
C ~
B 0.003 0.086 0.038 0.970 -0.166 0.172 0.003 0.001
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.B 0.250 0.000 525.565 0.000 0.249 0.251 0.250 1.000
.C 1.511 0.076 19.938 0.000 1.363 1.660 1.511 1.000
A1 95.802 4.333 22.108 0.000 87.308 104.295 95.802 1.000
R-Square:
Estimate
B 0.000
C 0.000
DWLS estimator with specifying B as ordered
> F2<-'
+ # Latent Factor ####
+ B~A1
+ C~B
+
+ '
> M2<-sem(F2, orthogonal = T, data=DF, estimator = "DWLS", ordered = "B")
> summary(M2, fit.measures= TRUE, standardized = TRUE, ci = TRUE, rsquare = T)
lavaan 0.6-9 ended normally after 11 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 5
Number of observations 812
Model Test User Model:
Test statistic 40.935
Degrees of freedom 1
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 0.003
Degrees of freedom 1
P-value 0.955
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.000
Tucker-Lewis Index (TLI) 41.061
Root Mean Square Error of Approximation:
RMSEA 0.222
90 Percent confidence interval - lower 0.167
90 Percent confidence interval - upper 0.282
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Unstructured
Regressions:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
B ~
A1 -0.000 0.005 -0.025 0.980 -0.009 0.009 -0.000 -0.001
C ~
B 0.003 0.053 0.048 0.962 -0.101 0.106 0.003 0.002
Intercepts:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.B 0.000 0.000 0.000 0.000 0.000
.C 0.226 0.042 5.323 0.000 0.142 0.309 0.226 0.189
Thresholds:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
B|t1 0.034 0.044 0.765 0.444 -0.053 0.120 0.034 0.034
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.B 1.000 1.000 1.000 1.000 1.000
.C 1.429 0.069 20.859 0.000 1.295 1.564 1.429 1.000
Scales y*:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
B 1.000 1.000 1.000 1.000 1.000
R-Square:
Estimate
B 0.000
C 0.000
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