Interactions in Generalized Linear Models: Theoretical Issues and an Application to Personal Vote-Earning Attributes
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
There is some confusion in political science, and the social sciences in general, about the meaning and interpretation ofinteraction effects in models with non-interval, non-normal outcome variables. Often these terms are casually thrown into a modelspecification without observing that their presence fundamentally changes the interpretation of the resulting coefficients. Thework here explains the conditional nature of reported coefficients and their standard errors in models with interactions, definingthe necessarily different interpretation required by generalized linear models, and providing a general analytical method forcorrectly calculating coefficient standard errors in models with second-order or higher interactions. Methodological issues areillustrated with an application of generalized linear models with interactions applied to voter information structured byelectoral systems and resulting legislative representation in comparative politics.