I have a couple of questions about issues regarding a SEM with latent variables. My model contains 11 latent predictors (measured by categorical indicators), five observed controls, and one latent outcome (measured by categorical indicators). First, Mplus reports that the model estimation terminates normally, and the fit statistics suggest a good to excellent fit; there are no obvious model problems. However, the SEM results differ substantially from OLS with additive scales results: the SEM standard errors are larger (which I expected), and some coefficient’s signs are reversed relative to OLS. I believe the SEM results are more accurate than the OLS, but my co-authors are not entirely convinced and are worried about the reverse sign and lack of significance of two key variables. Could you provide any suggestions/thoughts? Second, I attempted to re-estimate the SEM model with the MLR estimator, but after a long time running an error message appeared reporting that there is not enough memory. I asked my institution’s computer support people, and they told me the computer I was using had almost four gigs available for virtual memory. My sample size is fairly large (N=7600), but is this really not enough memory? Is there another suggestion? Third, the model contains a latent time 1 variable as a control for the latent time 2 outcome. Is the interpretation of the results any different in the SEM framework than it is in the OLS framework? Is there an article towards which you could point me that uses an approach like this?
I assume that by OLS you mean treating the categorical variables as continuous. Regarding such a comparison, please see the 2 articles by Muthen & Kaplan which are listed on our web site under References, Categorical Outcomes.
The MLR estimator with categorical outcomes and 11 latent variables gives rise to 11-dimensional integration which is not computationally feasible even with the best current computers.
Regressions among latent variables are linear regressions so the interpretation is not different depending on the observed indicators.
Professor, Thank you for your quick repsonse. What I meant by "OLS" was creating additive scales of the sets of categorical indicators, and treating these scales as continuous variables. The observed categorical variables that were added together to create the scales were the same as those used to create the factors in the SEM approach. Therefore, by OLS I meant regression using scales, and by SEM I meant regression using factors. I certainly will read the articles you suggest. Thank you again for your time.
The comparisons of using sums of categorical items and using a model with factors depends on the number and quality of the items. For example, having few items and/or items that give a sum with a strong floor or ceiling effect will produce different results than using a model with factors.