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

Abstract

This article 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 muchdiscussed 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 always performs 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 article with an application of our method to data from the National Educational Longitudinal Study of 1988.

To what degree is the association between educational inequality and laryngeal cancer explained by smoking, alcohol consumption, and occupational exposure?

“…According to Karlson et al, in logistic regression the coefficients from different nested models are not measured on the same scale. Therefore their change across the models reflects both the confounding due to other covariates and the rescaling (4,25). Their basic idea is to substitute the covariates of the fully adjusted model with the residuals of a reduced model from a regression on the covariates of interest.…”

The health knowledge mechanism: evidence on the link between education and health lifestyle in the Philippines

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Less inequality through universal access? Socioeconomic background of tertiary entrants in Australia after the expansion of university participation

“…To estimate coefficients, I applied the Karlson-Holm-Breen (khb) method (Kohler et al 2011;Breen et al 2013). khb allows one to conduct a path analysis in non-linear probability models and hence, to decompose the total effects of independent variables into direct effects and indirect effects.…”