A General Latent Variable Model

Abstract

This chapter shows that, starting from the two-way analysis of variance with random effects, it is possible to arrive at a general latent variable model. It does this, first by enlarging the family of conditional distributions considered and secondly, and more fundamentally, by allowing the random effect associated with the rows of the two-way table to be linear in a set of (unobserved) latent variables. In the case when the observed variables are conditionally normal, the standard model for factor analysis emerges but the framework adopted includes a great many other possibilities, including non-linear models. One advantage of adopting this general framework is that it makes the essential arbitrariness of the distribution of the latent variables transparent. It also paves the way for the following chapter in which we turn to clarifying what can be said about the prediction of the latent variables.