Variational approximations for categorical causal modeling with latent variables

Latent class models in the social and behavioral sciences have remained structurally simple. One reason for this is that inference in statistical models can be computationally difficult. Methods for approximate inference, known as variational approximations, which have been developed in the machine teaming, graphical modeling and statistical physics literatures, can be used to alleviate the computational difficulties of inference for latent variable models. The aim of the present article is to set these methods alongside some social and behavioral science literature to which they are relevant, and in particular to consider their potential for "categorical causal modeling", using latent class analysis. We have collated a number of popular categorical-data models with latent variables and causal structure, typically incorporating a Markovian structure. The efficacy of the approximation methods has been demonstrated through simulations related to an important behavioral science model.