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Statistical models with latent structure have a history going back to the1950s and have seen widespread use in the social sciences and, more recently,in computational biology and in machine learning. Here we study the basiclatent class model proposed originally by the sociologist Paul F. Lazarfeld forcategorical variables, and we explain its geometric structure. We drawparallels between the statistical and geometric properties of latent classmodels and we illustrate geometrically the causes of many problems associatedwith maximum likelihood estimation and related statistical inference. Inparticular, we focus on issues of non-identifiability and determination of themodel dimension, of maximization of the likelihood function and on the effectof symmetric data. We illustrate these phenomena with a variety of syntheticand real-life tables, of different dimension and complexity. Much of themotivation for this work stems from the "100 Swiss Francs" problem, which weintroduce and describe in detail.

Maximum Likelihood Estimation in Latent Class Models For Contingency Table Data