I'm new to all things SEM, but I'm attempting to use OpenMx for a Cross-lagged Panel Model (with random intercepts) on longitudinal data in youth. I have two measured variables at two timepoints, equally spaced apart. I have gone through John Flournoy's tutorials (http://johnflournoy.science/2018/09/26/riclpm-openmx-demo/) as well as several other resources on this topic, but I have a few questions I was hoping I could get some input on from the experts here!

The main question I have concerns covariates. I have both time-dependent (e.g., pubertal status) and time-independent (e.g., race, sex) covariates that I'd like to include. Would I simply add these to my model as observed variables, or do I need to also include latent factors representing random intercepts for these as well? Maybe this is a silly question, but given that RI-CLPM separates within- from between-person variance, are covariates already accounted for in some way by these models?

I also have one other question that I hope is okay to include here as well. When I provide my model with the raw data I receive this error message: "The Hessian at the solution does not appear to be convex. See ?mxCheckIdentification for possible diagnosis (Mx status RED)." However, scaling the X and Y variables (x1, x2, y1, y2) seems to resolve this error, but I'm not sure whether it is appropriate to scale data for SEM. Is there a reason not to scale? The scales that my X and Y variables are on are quite different.

Thank you in advance for the help!

Dear mxruby,

a RI-CLPM with fewer than 3 timepoints is not identified, so this is not an appropriate model for your data!

Regarding your other question: It is a reasonable assumption that effects of time-invariant covariates are absorbed by the random intercepts in a RI-CLPM, unless for some reason the covariate would have a different impact at different timepoints.

For instance, in most cases SES is invariant, and effects on the random intercept are sufficient. But if family SES has a different effect on children pre- and post puberty, that would be a reason to allow effects of SES on the within-wave residuals, in addition to effects on the random intercept.