group.equal() argument does not work for the "residuals" key word

[Patrick Yang]

Hi all:

I was fitting a CFA model in lavaan. There are eight likert scale indicators loading on one factor and the likert items have been declared to be categorical. I attempted to run a measurement invariance analysis between two groups/countries. I used the group.equal argument. I added four key words, "loadings", "intercepts", "lv.variance" and "residuals". The first three were successful with regard to unstandardized estimates. Loading estimates were equal, intercept estimates were equal and latent variable variance estimates were also equal. However, the last one did not work. The indicator error variance estimates continued to be UNequal across the two groups. Did I do anything incorrectly?

Also, regarding the three sets of parameters which were constrained and also estimated to be equal across the two groups (loadings, intercepts and latent variable variance), only unstandardized estimates were equal across the two groups. For each type of parameter, the two sets of standardized estimates under Std.lv and Std.all were not equal. Is it normal?

fit.strict2.inv <- cfa(model = model.str, data = respdata, estimator="DWLS", group = "CNT", group.equal=c("loadings", "intercepts", "lv.variances", "residuals"), 

                            ordered=c("ST37Q01",

                                      "ST37Q02",

                                      "ST37Q03",

                                      "ST37Q04",

                                      "ST37Q05",

                                      "ST37Q06",

                                      "ST37Q07",

                                      "ST37Q08"

                            ));

[Terrence Jorgensen]

I added four key words, "loadings", "intercepts", "lv.variance" and "residuals". Loading estimates were equal, intercept estimates were equal and latent variable variance estimates were also equal.

Intercepts are already assumed equal by default with ordered indicators, because they are all fixed to zero.  

However, the last one did not work. The indicator error variance estimates continued to be UNequal across the two groups. Did I do anything incorrectly?

I'm not sure how you are drawing your conclusions, because the residual variances are not even model parameters under the default "delta" parameterization.

https://www.statmodel.com/download/webnotes/CatMGLong.pdf

 

Try installing the semTools package and looking at the ?measEq.syntax help page to get help with specifying invariance models for categorical indicators.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[hongwei.pa...@gmail.com]

Hi Terrence:

 

Thank you for your response.

 

I could be very wrong on this. In one of the lavaan output items, I found.

 

Variances:

                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all

   .ST37Q01           0.144                               0.144    0.135

   .ST37Q02           0.108                               0.108    0.101

   .ST37Q03           0.100                               0.100    0.097

   .ST37Q04           0.100                               0.100    0.102

   .ST37Q05           0.025                               0.025    0.026

   .ST37Q06           0.146                               0.146    0.140

   .ST37Q07           0.090                               0.090    0.089

   .ST37Q08           0.143                               0.143    0.141

 

Aren’t these estimates the error variance estimates for observed variables ST37Q01 through ST37Q08 in this CFA?

 

Hongwei Yang

 

Hongwei “Patrick” Yang, Ph.D.

Assistant Professor

Educational Research and Administration

College of Education and Professional Studies

The University of West Florida

Pensacola, FL 32514

E-mail (business): py...@uwf.edu

Office Phone: 850-474-2843

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[Terrence Jorgensen]

Aren’t these estimates the error variance estimates for observed variables ST37Q01 through ST37Q08 in this CFA?

No, they don't have SEs because they are not estimates.  And with delta parameterization, they aren't specifiable as parameters, only implied by the latent scales.  The answers to your questions are in the link I sent you to read.