Mixed Interaction Models

Abstract

This chapter describes graphical models for mixed data, that is to say, with both discrete and continuous variables. Such data are frequently met in practice. The models are based on the conditional Gaussian distribution: that is, conditional on the discrete variables, the continuous variables are Gaussian with mean depending on the discrete variables. These models combine and generalize hierarchical log-linear models and Gaussian graphical models described in Chaps. 2 and 4. We start by describing some example datasets that are used as illustration. We then give a concise exposition of the theory of homogeneous mixed interaction models, illustrating using the gRim package. This exposition includes accounts of model formulae, important model subclasses such as graphical and decomposable models, maximum likelihood estimation using the IPS algorithm, and hypothesis testing. The final sections illustrate stepwise model selection and the construction of a mixed chain graph model.