Bayesian Multilevel Structural Equation Modeling: An Investigation into Robust Prior Distributions for the Doubly Latent Categorical Model

Abstract

Bayesian estimation of multilevel structural equation models (MLSEMs) offers advantages in terms of sample size requirements and computational feasibility, but does require careful specification of the prior distribution especially for the random effects variance parameters. The traditional “non-informative” conjugate choice of an inverse-Gamma prior with small hyperparameters has been shown time and again to be problematic. In this paper, we investigate alternative, more robust prior distributions for the doubly latent categorical multilevel model. In contrast to multilevel models without latent variables, MLSEMs have multiple random effects variance parameters both for the multilevel structure and for the latent variable structure. It is therefore even more important to construct reasonable priors for these parameters. We find that, although the robust priors outperform the traditional inverse-Gamma prior, their hyperparameters do require careful consideration.