Multilevel Latent Class Modelling

Abstract

In Chap. 5 we introduced multilevel modelling, where a continuous latent variable represents variation across the levels of a natural hierarchy, yielding random effects. In Chap. 6, we introduced latent class analysis, where using a binary latent variable gave rise to a mixture model of count data to accommodate an excess of zeros relative to standard count distributions. In this chapter, we combine and develop these concepts further. By employing discrete latent variables for upper levels of a hierarchy, a richer mixture model can be represented, with mixtures at the lower level only, the higher level only, or at both levels. Where the upper level mixture has many latent classes, this model can be viewed as similar to the traditional multilevel model, though with a discrete (opposed to continuous) distribution and thereby foregoing any parametric assumptions: for instance, the normal distribution at the upper level is replaced by a number of discrete components, and for many components, this can be viewed as a semi-parametric approximation of the continuous latent variable.