Inference for structural equation modelling on dependent populations

Latent variable modelling is used widely in applications to economics, social and behavioural 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 parameterisation is used for meaningful and interpretable analysis of several populations. It turns out that under this parameterisation the large sample statistical inferences based on the assumption of normal and independent populations are valid for virtually any non-normal and dependent populations. This result is also 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.