Tsai, Tsung-Han, and Jeff Gill. “Interactions in Generalized Linear Models: Theoretical Issues and an Application to Personal Vote-Earning Attributes.” Social Sciences 2, no. 2 (2013): 91-113.
Abstract:There is some confusion in political science, and the social sciences in general, about the meaning and interpretation of
interaction effects in models with non-interval, non-normal outcome variables. Often these terms are casually thrown into a model
specification without observing that their presence fundamentally changes the interpretation of the resulting coefficients. The
work here explains the conditional nature of reported coefficients and their standard errors in models with interactions, defining
the necessarily different interpretation required by generalized linear models, and providing a general analytical method for
correctly calculating coefficient standard errors in models with second-order or higher interactions. Methodological issues are
illustrated with an application of generalized linear models with interactions applied to voter information structured by
electoral systems and resulting legislative representation in comparative politics.