A General Method for Comparing Probitand Logit-models with Single and Multilevel Data

The paper proposes a method for overcoming the so-called latent scale-problem that prevents nested logistic and probit models from being compared. This allows us to decompose direct and indirect effects for binary outcomes. Our solution is based on an explicit construction of a latent propensity behind a given binary variable. The method is validated based on both simulated and the European Social Survey data. It is more accurate and easier to interpret than the previously available methods. Furthermore, it is the only method allowing us to compare mixed binary models: the so-called ystandardisation method, for instance, is not suitable for multilevel data because there is no global scale parameter applicable to both fixed and random effects. Finally, the paper concludes that the reason why nested binary regression models are not comparable is not related to ‘unobserved heterogeneity’, like Mood (2010) suggested, but it reflects the structure of the observed model.