Interpreting interactions and interaction hierarchies in generalized linear models: Issues and applications. Paper presented at the Annual Meeting of the American Political Science Association

There is substantial confusion in political science and related literatures about the meaning and interpreta-tion of interaction effects in models with non-interval, non-normal outcome variables. Often these terms are casually thrown into the model specification without observing that their presence fundamentally changes the interpretation of the resulting coefficients. This article addresses this lack of clarity and rigor by explaining the conditional nature of reported coefficients and their standard errors in models with interactions, defining the necessarily different interpretation of interactions in generalized linear models, and introducing useful hi-erarchies of interaction effects in these specifications. Unfortunately, there is little written about specifying the uncertainty of these interaction effects through reported standard errors, and much of which is currently reported is actually misleading. This article fills a gap in the methodological literature by providing a general analytical method for correctly calculating coefficient standard errors in models with second-order or higher interactions and complex interaction specifications. The methodology is demonstrated with applications to current work in political science. These examples demonstrate the utility of interaction hierarchy specifications in generalized linear models by providing analyses of data from comparative politics, judicial decision-making, and education public policy