ABSTRACT
In this chapter, we introduce finite mixture models designed specifically for discrete data, including categorical data (nominal or ordinal), counts (univariate or multivariate), rankings and so on. Both univariate and multivariate cases are considered. In fact, the finite mixture models for discrete data are similar to those designed for continuous data, since many types of discrete data can be considered as discretized versions of some continuous latent data. Therefore, the idea of the EM algorithm can be readily applied to this chapter for model estimation. However, oppositely, as the dimension of the data increases, it becomes much more difficult to model discrete multivariate data than continuous data. For example, even for the Poisson distribution, which is the most widely used distribution to model counting data, it is far more difficult to generalize from the univariate to even the bivariate case than to generalize the univariate Gaussian to the multivariate Gaussian. As a result, finite mixture models for discrete data are not as plentiful as for continuous data
