A framework for the interpretation of first-order interaction in logit modeling

Several suggestions have been tendered for interpreting first-order interaction in log-linear analysis. Occasionally these methods result either in a loss of information or in results that are difficult to grasp on an intuitive level. It is argued that interpreting effect parameters in terms of odds ratios provides an elegant and intuitively appealing conceptual framework that has great generality across models. The interaction term then resembles a cross-product term in linear regression. In both forms of analysis, the partial effect of a given predictor on the response is composed of a constant and a correction that is a function of the other predictor involved in the interaction. This framework is especially appealing for models in which the logit is based on a bifurcation of the dependent variable. Although odds ratios are still useful for summarizing effects on polytomous dependent variables, greater caution must be exercised to avoid misleading interpretations.