A General Method for Comparing Probitand Logit-models with Single and Multilevel Data - Antti Veilahti (Turku Centre for Welfare Research, 2022)
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.