Multi-group comparison for RI-CLPM

[Brandon E Gibb]

Hi all,

I am hoping someone can help with a question I have.  I’m running a RI-CLPM in which two variables were assessed at 5 occasions over time in each of two distinct groups of subjects and we want to see if the model parameters differ across groups.  It’s pretty straightforward to set up a multi-group comparison to test whether the groups differ in the magnitudes of the cross-lagged paths.  However, we also would also like to see if the groups differ in their random intercepts for each variable (mean levels of each variable over time).  Typically, I would just include Group as a predictor of each random intercept, but I’d prefer to test both forms of moderation (values of the random intercept and magnitudes of the cross-paths) in the same model.  I assume there is a straightforward way to accomplish this that I am just missing.  Any help would be greatly appreciated.

Thanks,

Brandon

Brandon E. Gibb, Ph.D.

Professor

Director, Mood Disorders Institute

Department of Psychology

Binghamton University (SUNY)

Binghamton, NY

Phone: 607-777-2511

Fax: 607-777-3665

[Terrence Jorgensen]

we also would also like to see if the groups differ in their random intercepts for each variable (mean levels of each variable over time). 

Do you mean testing whether the average random-intercept (latent mean) differs across groups?  Measurement invariance is imposed by virtue of equal loadings across groups (all loadings are 1, to give the latent intercept its interpretation).  But the latent means are fixed to zero for identification.  I think in this case you could hypothetically use effects-coding constraints on the intercepts over time to estimate the random intercept's mean.  The problem is that the first occasion's intercept doesn't have the same interpretation as the remaining occasions' intercepts, because you aren't regressing the first occasion on a previous occasion.  

What I would recommend instead is labelling all of your intercepts (unique labels across groups), then defining group-difference parameters, which will have delta-method SEs and tests in your summary() output.  You can use lavTestWald() to obtain a single omnibus test statistic that all 5 group differences == 0, and the individual tests on each occasion would be follow-up tests if the omnibus H0 is rejected.

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

[Michael Zyphur]

Hi Brandon

In case it's of interest you can also conceptualize the interactions you're describing in a single-group framework as latent interactions. This is described in details here, along with the different WxW, BxB, and WxB interaction types allowed in these types of longitudinal models (as if they were multilevel):

Ozkok, O., Vaulont, M. J., Zyphur, M. J., Zhang, Z., Preacher, K. J., Koval, P., & Zheng, Y. (2021). Interaction Effects in Cross-Lagged Panel Models: SEM with Latent Interactions Applied to Work-Family Conflict, Job Satisfaction, and Gender. Organizational Research Methods, 10944281211043733.

https://journals.sagepub.com/doi/abs/10.1177/10944281211043733

Best wishes

Mike