Mplus does not include residual variances for Poisson regression with a dependent variable that is a count variable - this is in line with regular Poisson regression analysis where such a residual is absent. The Theta parameterization is not in effect for count outcomes. You can, however, in Mplus define a residual by defining a factor that influences the dependent count variable, e.g. when regressing y on a covariate x,
I am estimating a parallel process latent growth model with four outcomes, over three timepoints. Three outcomes are continuous and the fourth is a count of conduct problems (from 0 to 7). This is my input:
You could try using only 1 factor for each of the 3 time points and let the different loadings capture the different sizes of the residual correlations among the 3 processes. So 3 dimensions instead of 9. Make sure the 3 factors are uncorrelated with each other.
I am running a negative binomial model with 2 count predictors, 2 continuous mediators, 2 count outcomes (y1, y2), and 1 dichotomous covariate.
I tried to estimate the residual covariance between y1 and y2 (study hypotheses expect significant covariance) by defining a factor that influences both outcomes:
fy2 by y2@0; fy2@1; fy1 by y1@0; fy1@1; y2 on fy2@1; y1 on fy1@1; fy2 with fy1;
However, there were several issues: (a) estimated residual covariance was very high (.96), (b) non-trustworthy standard error estimates and fixing several parameters to avoid singularity of the information matrix, and (c) significant indirect effects emerged that were not present before defining the residual.
Is this the correct way to estimate the residual covariance? Are these indirect effects interpretable? Or, is it not appropriate to estimate the residual covariance in this model?