Total, Direct, and Indirect Effects in Logit and Probit Models

This paper presents a method for estimating and interpreting total, direct, and indirect effects in logit or probit models. The method extends the decomposition properties of linear models to these models; it closes the much-discussed gap between results based on the "difference in coefficients" method and the "product of coefficients" method in mediation analysis involving nonlinear probability models models; it reports effects measured on both the logit or probit scale and the probability scale; and it identifies causal mediation effects under the sequential ignorability assumption. We also show that while our method is computationally simpler than other methods, it performs always as well as or better than these methods. Further derivations suggest a hitherto unrecognized issue in identifying heterogeneous mediation effects in nonlinear probability models. We conclude the paper with an application of our method to data from the National Educational Longitudinal Study of 1988.