Beyond Linearity by Default: Generalized Additive Models

Abstract

Social scientists almost always use statistical models positing the dependent variable as a global, linear function of X, despite suspicions that the social and political world is not so simple, or that our theories are so strong. Generalized additive models (GAMs) let researchers fit each independent variable with arbitrary nonparametric functions, but subject to the constraint that the nonparametric effects combine additively. In this way GAMs strike a sensible balance between the flexibility of nonparametric techniques and the ease of interpretation and familiarity of linear regression. GAMs thus offer social scientists a practical methodology for improving on the extant practice of global linearity by default. We reanalyze published work from several subfields of political science, highlighting the strengths (and limitations) of GAMs. We estimate non-linear marginal effects in a regression analysis of incumbent reelection, nonparametric duration dependence in an analysis of cabinet duration, and within-dyad interaction effects in a reconsideration of the democratic peace hypothesis. We conclude with a more general consideration of the circumstances in which GAMs are likely to be of use to political scientists, as well as some apparent limitations of the technique.