Log-Linear Models for Contingency Table Analysis

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Abstract
This paper is concerned with the interpretation of fitted log-linear models in contingency table analysis. The two most commonly used alternatives are the direct interpretation of the estimated coefficients of the fitted model and the interpretation of statistics, such as odds ratios, based upon the expected cell frequencies under the fitted model. There are strong reasons for preferring the latter since the statistics will be the same whatever computer program is used to fit the model whereas the estimated parameter coefficients will depend upon the set of constraints used to solve the normal equations. Thus, different computer programs can (correctly) provide different parameter estimates from the same data whereas statistics such as odds ratios based upon the expected cell frequencies will be unaffected. Interpretation based upon the estimated parameters of the fitted model is therefore potentially misleading. These problems are not unique to log-linear analysis but occur in analyses involving the generalized linear model.