Modeling Interaction Effects in Logistic Regression: Information Analysis
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The Akaike information criterion (AIC) is commonly used to select a logistic regression model for predicting a discrete response variable using available regressors. In practice, finding models with near-minimum AIC estimates is not presented with a well-defined procedure. As an alternative approach to model selection, we propose to formulate a two-step selection scheme of identifying the indispensable regressors as main-effect predictors, followed by inspecting the significant interaction effects between the selected predictors so as to construct the desired logistic model. In this study, the two-step selection scheme is developed based on the analysis of mutual information between the regressors and the response variable. It is proved that the scheme yields the most parsimonious logistic model using the indispensable predictors and the least interaction effects. As a byproduct, it also conveniently locates the minimum AIC model in a neighborhood of the selected model. The scheme is employed to modeling the regression for predicting the acquisition of professional licenses in a survey of employed youth workers.
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