Comparing Regression Coefficients Between Models using Logit and Probit: A New Method

Abstract

Logit and probit models are widely used in empirical sociological research. However, the widespread practice of comparing the coefficients of a given variable across differently specified models does not warrant the same interpretation in logits and probits as in linear regression. Unlike in linear models, the change in the coefficient of the variable of interest cannot be straightforwardly attributed to the inclusion of confounding variables. The reason for this is that the variance of the underlying latent variable is not identified and will differ between models. We refer to this as the problem of rescaling. We propose a solution that allows researchers to assess the influence of confounding relative to the influence of rescaling, and we develop a test statistic that allows researchers to assess the statistical significance of both confounding and rescaling. We also show why y-standardized coefficients and average partial effects are not suitable for comparing coefficients across models. We present examples of the application of our method using simulated data and data from the National Educational Longitudinal Survey.

Keywords: logit, probit, logistic regression, scaling, confounding, statistical control, mediation

JEL Classification: C25