I have a "3-level" Growth Model (2 level in MPLUS I believe) with time points nested in individuals and individuals nested in organizations. The DVs are manifest, and I am running separate models for each DV. To achieve convergence and a positive definite solution, I have to constrain the random variances associated with intercept and slope (on the individual and/or organization level) to zero in different case. I also have time varying covariates and have to sometimes set their random effects to zero in different cases on different levels to converge and/or get a positve definite solution. In a perfect situation, of course, I would like to estimate the random effect for everything (intercept, slope, and time varying covariates) in every case on every level.
My question - is it permissible to "explain variance" using a covariate on a random effect that has been constrained to zero? It seems counter-intuitive that it would be, but I have at least one stat-book type reference where it seems that this is done, and I have until recently assumed it was appropriate. For example if my random slope variance has been constrained to zero, can I still do a Slope x Covariate interaction to test for slope differences? Any help would be appreciated. Thanks.
In a conditional model, it is the residual variance of a random slope or growth factor that is fixed to zero not the variance. It is fine to regress such a random effect on a covariate. Also, when covariates are added to the model, it can make random effects have non-zero variances whereas without covariates they have zero variances.