Full Contingency Tables, Logits, and Split Contingency Tables

Three methods of fitting log-linear models to multivariate contingency-table data with one dichotomous variable are discussed. Logit analysis is commonly used when a full contingency table of s dimensions is regarded as a table of rates of dimension s -1. The split-table method treats the same data as two separate tables each of dimension s -1. We show that the full contingency-table method can be regarded as a generalized approach: models which can be fitted by it include both the mutually exclusive subsets that can be fitted by the other two methods. Even when the logit method permits the model of choice to be fitted, the full contingency-table method of iterative proportional fitting to the set of sufficient configurations has the advantage of requiring neither matrix inversion nor substitution of an arbitrary value in empty elementary cells.