Measurement Invariance group.equal not constraining residuals

[AJ1430]

Hello, 

I'm running into an odd issue where I cannot get the residuals to constrain using the group.equal command.

I am doing a classic measurement invariance  procedure. Everything is working well until I get to comparing scalar invariance to strict invariance (which is including constraining the residuals across the two groups). 

# Model syntax                                 
model2 <- 'RGPTSA =~ A1 + A2 + A3 + A4 + A5 + A6 + A7 + A8
          RGPTSB =~ B1 + B2 + B3 + B4 + B5 + B6 + B7 + B8 + B9 + B10
          RGPTSA ~~ RGPTSB'

# scalar models

cfa.scalar <- cfa(model2, data = Passed_df, estimator = "WLSMV", group = "DEM_race", group.equal = c("loadings","intercepts"))

# strict model

cfa.strict <- cfa(model2, data = Passed_df, estimator = "WLSMV", group = "DEM_race", group.equal = c("loadings","intercepts", "residuals"))

This code is resulting in  identical models. I'm confused why the residuals being added to the group.equal is not constraining those parameters.

Any thoughts would be greatly appreciated.

[Stijn Debrouwere]

When you say identical, that includes the number of model parameters and the X2 statistic?

Best, 

Stijn

[J Wolny]

Hi Stijn,

I am also working on the project described above. To answer your question - yes, the model parameters and X2 statistic are exactly the same. Have you run into this before?

Thanks,

J 

[AJ1430]

Hello,

As J mentioned they are identical in terms of fit and number of parameters. It also is clear from the summary output that the residuals are not being fixed across groups (i.e., I can see the labels in the summary indicating that the loadings and intercepts are being constrained, but not the residuals). 

I also did not have success when trying to constrain the residuals "manually" in the model syntax.

Thanks so much for the help.

Best,

Allen

[Terrence Jorgensen]

the residuals are not being fixed across groups

I also did not have success when trying to constrain the residuals "manually" in the model syntax.

You set estimator = "WLSMV" without specifying the ordered= argument, so I assume you have variables of class "ordered" in the Passed_df object (WLSMV is not appropriate for all continuous indicators).   Because you did not specify parameterization = "theta", the residual variances are not model parameters.  And you are equating intercepts, which are already equated by being fixed to zero for ordinal indicators.  They (and residual variances) can only be freed when thresholds are constrained to equality.  You can find many previous posts on this forum about categorical measurement invariance, but the semTools::measEq.syntax() function is designed to be helpful in this context (and the help-page references are enlightening).

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