Modellvergleich und Ergebnisinterpretation in Logit- und Probit-Regressionen

In the social sciences logit and probit models are often used multivariate data analysis procedures for binary dependent variables. Both procedures can be thought of as resting on a linear model for an unobserved variable y* from which a nonlinear model for the probability of y?=?1 is derived. We first show that compared to linear models this nonlinearity leads to problems of interpreting results from such analysis. In particular odds ratios (exponentiated logit coefficients) often used in logistic regression are problematic in this respect. Instead we recommend using graphical procedures and reporting (corrected) average marginal effects (AME). Based on a series of Monte-Carlo simulations we next demonstrate that the regression coefficients from logit and probit models should not be compared between nested models. Because model building in the social sciences often employs a stepwise procedure a method allowing valid comparisons of effect sizes between models would be advantageous. Results from our simulation study show that average marginal effects and regression coefficients corrected by a method proposed by Karlson et al. (Sociological Methodology 42, 2012) lead to satisfactory results in many different scenarios. In contrast, y*-standardized coefficients are of limited utility and coefficients from a linear probability model should only be used with normally distributed variables.