Introduction to Birch (1963) Maximum Likelihood in Three-Way Contingency Tables

During the 1960s, there was an extremely rapid expansion of the literature on categorical data analysis, especially related to the use of loglinear models for multidimensional contingency tables, culminating in a series of papers by Goodman [e.g., see those collected in Goodman (1978)] and the monographs by Bishop et al. (1975) and Haberman (1974). The problems addressed by this literature paralleled for discrete/categorical data those addressed by multiple regression, analysis of variance, and the general linear model for continuous data. Loglinear model methods have had a major impact on the current statistical methodology in use today for the analysis of categorical data, and a crucial paper by Martin Birch that appeared in 1963 provides the underpinnings of the general statistical theory involved.