ABSTRACT
This chapter considers continuous mixture models in which a linear model is attached not to the observations themselves but rather to a distribution of observations. It outlines kinds of model, using the common beta-binomial and gamma-Poisson (negative-binomial) models of the type. The chapter explains how to employ multilevel models that estimate both the residuals of each observation and the distribution of those residuals. It also explains how to parameterize a distribution of outcomes on the scale of log-cumulative-odds. Both the beta-binomial and gamma-Poisson models are maximum entropy for the same constraints as the regular binomial and Poisson. A mixture model uses more than one simple probability distribution to model a mixture of causes.
