On the comparison of regression coefficients across multiple logistic models with binary predictors

In many applied contexts, it is of interest to identify the extent to which a given association measure changes its value as different sets of variables are included in the analysis. We consider logistic regression models where the interest is for the effect of a focal binary explanatory variable on a specific response, and a further collection of binary covariates is available. We provide a methodological framework for the joint analysis of the full set of coefficients of the focal variable computed across all the models obtained by adding or removing predictors from the set of covariates. The result is obtained by applying a specific log-hybrid linear expansion of the joint distribution of the variables that implicitly comprises all the regression coefficients of interest. In this way, we obtain a method that allows one to verify, in a flexible way, a wide range of scientific hypotheses involving the comparison of multiple logistic regression coefficients both in nested and in non-nested models. The proposed methodology is illustrated through a test bed example and an empirical application.