Correlated Populations with Fixed and Non-normal Latent Variables

Latent variable or structural equation modeling (SEM) is used widely in applications, especially in social and behavioral sciences. Since the normality based model fitting procedures are simple and broadly available, and since such procedures are often applied to non-normal data or non-random samples, it is important to investigate the appropriateness of such practice and to suggest simple remedies. This paper addresses these issues for the analysis of multiple populations. For a very general class of latent variable models, a particular parameterization is proposed for meaningful and interpretable analysis of several populations. It is shown that under this parameterization the large-sample statistical inferences based on the assumption of normal and independent populations are valid for non-normal and dependent populations. This result is also shown to be valid when some latent variables are treated as fixed instead of random, or when a group of individuals is measured over several time points longitudinally. More precisely, the paper shows how to get robust asymptotic standard errors (a.s.e's) and overall-fit measures. The proposed a.s.e's are shown to have less variability than the robust a.s.e's computed by the so-called sandwich estimator. Simulation studies are conducted to verify the theoretical results, assess the use of asymptotic results in finite samples, show the robustness of the power for tests, and demonstrate the efficiency of the method relative to the full-likelihood estimation method that includes all the covariances of the variables over populations.