Much Ado About Not Very Much? Clarifying the Confusion about Models for Categorical Dependent Variables

Models for categorical dependent variables, such as turnout, party choice, or partisanship have eluded scholars for decades. Should the coefficients be reported and interpreted or are marginal effects preferable? Can interaction effects be statistical significant even without of product terms? How make sense of multinomial logit models, if their coefficients depend on the choice of the baseline category? There are several papers concerned with such questions, but not all of them can help with researchers' confusion about how to apply and interpret results of these models. Yet much of this confusion about models for categorical dependent variables can be avoided by not asking too much of them and by keeping in mind the distinction between model specification, model parameters, and quantities of interest. The paper points out that certain aspects of linear regression cannot be generalised without getting into the trouble of paradoxes and ambiguities. Firstly, it shows how identifying causal effects with differences in means leads to paradoxes while marginal effects do not globally describe the properties of a statistical model for categorical dependent variables. Secondly, it shows that the dependence of coefficients on the choice of a baseline category is not a problem unique to multinomial logit models, but also concerns linear regression models with categorical independent variables. Third, it discusses well-established techniques of statistical inference that allow to deal with this situation without incurring ambiguities. Based on this discussion, the paper derives a set of guidelines for sound inference about generalised linear and related models.