I'm using continuous indicators in a latent profile analysis and finding that I have some odd residuals and a very small class in the model with the best fit statistics. I'd like to use residuals to help decide how to relax assumptions of local independence. I see that using Tech12, I have residual covariances for the mixed model that range from 0% to 77% of the observed sample covariance. However, using RESIDUAL, I see that the residual covariances in the small class range from 1% to 1200% of the observed sample covariance, which doesn't seem very meaningful.
What would be a good way to use the outputs to make decisions about which residual covariances to estimate in the model to test assumptions? Is there a rule of thumb?
Thank you for those suggestions. I found that in my "average" class, most modindices for WITH statements were <5 or 6, but there were also two modindices of 40 and 90. However, in the small class (6% of a sample of 732 males, or 44 males), WITH statement modindices ranged from <1 to 430. Out of 15 potential WITH statements, 5 were >250, 5 were between 15 and 45, and two were <1. For this two class model, the adjusted Lo-Mendell-Rubin test was ~.08. Models with additional classes did not fit either.
I'm not really sure how to interpret those differences in scale. I decided to start with relaxing assumptions for those that were in the 100's; the model with relaxed assumptions gave me an LMR pvalue of .02. However, I'm not sure how to discuss the findings. It seems like it would be correct to say that there is no latent profile solution for this sample unless assumptions of local independence are relaxed. Would it be appropriate to to continue tweaking the model? What is a good way to make decisions about how to use modindices in LCA/LPA? I could also allow variances to be estimated separately, for example. The overarching concern for me is that I would like to have a model I could use to continue looking at associations with covariates, transition over time, etc, but I want the limitations/challenges of the model to be clear.
Why don't you try the setup of UG ex 7.22. That way you can see how many WITH statements were really needed. That approach assumes that the true model has many significant WITH statements, whereas the Modind approach assumes that there are few of them. You should use the approach that you believe starts the closest to the true model.