Multiple Groups - Modification Indices - lavaan vs MPlus and LISREL

[Diego Tavares]

Hi everyone,

I am learning SEM on my own and using (Whittaker & Schumacker, 2022) as my major reference. However, the book uses Mplus and LISREL for coding and I am using the internet to find the correspondent functions in lavaan in R and I compare the results to assess if I have the right function or not.

Everything has been good until I needed the Modification Indices function modindices() to use with SEM with Multiple Groups. Using the same data to analyze the separate groups and the baseline models for Path Analysis and for CFA, equal results were found. So no problem about that. The problems started to arise when I used the Modification Indices to analyze which parameters I should remove the Invariance Constraints for a better fit. The functions used in MPlus and LISREL offered results significantly different than modindices() in lavaan.

For the sake of learning the procedure, I ignored the recommendations from modindices(), and followed the ones from MPlus and LISREL and the model fit results using lavaan were equal to the ones offered in MPlus and LISREL. From that, my conclusion is that for some reason modindices() is not the best resource for Modification Indices when dealing with Multiple Groups. Maybe they follow different algorithms.

Does anyone (1) know the reason? And (2) can anyone recommend which function to use in this scenario?

I tested with both modindices() and modificationindices() and they offered the same results. Moreover, similar results are found between the three software when analyzing single-group SEM. So this situation occurs only with Multiple Groups.

Here is the code for modindices() I have been using:

lavaan:

modificationindices(fit2, sort = TRUE)
modindices(fit2, sort = TRUE)

MPlus:

OUTPUT: STDYX MODINDICES(3.84);

LISREL:

OPTIONS: SC MI

References:

Whittaker, T. A., & Schumacker, R. E. (2022). A Beginner’s Guide to Structural Equation Modeling. Routledge.

Thank you for your time and availability!

[Terrence Jorgensen]

when I used the Modification Indices to analyze which parameters I should remove the Invariance Constraints for a better fit. The functions used in MPlus and LISREL offered results significantly different than modindices() in lavaan.

That is because lavaan::modindices() only provides score tests (which are only called "modification indices" in the SEM world) for fixed parameters.  The more general lavaan::lavTestScore() function provides score tests for fixed parameters (using the add= argument) as well as for equality-constrained estimated parameters (using the release= argument).  You can search this forum for my previous posts about using lavTestScore() for investigating DIF / partial invariance.

can anyone recommend which function to use in this scenario?

I think lavaan's approach makes more sense because you test a hypothesis about an equality constraint using a single test statistic about that constraint.  Providing separate modification indices (e.g., for the same parameter in each group) seems misleading, and unnecessarily provides 2 statistics to test 1 null hypothesis.

I tested with both modindices() and modificationindices() and they offered the same results. 

Because they are the same function.  Look up the help page.

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen