Direct and Indirect Effects in a Logit Model

Abstract

This article discusses a method by Erikson et al. (2005) for decomposing a total effect in a logit model into direct and indirect effects. Moreover, this article extends this method in three ways. First, in the original method the variable through which the indirect effect occurs is assumed to be normally distributed. In this article the method is generalized by allowing this variable to have any distribution. Second, the original method did not provide standard errors for the estimates. In this article the bootstrap is proposed as a method of providing those. Third, I show how to include control variables in this decomposition, which was not allowed in the original method. The original method and these extensions are implemented in the ldecomp package.

Chronic medical conditions mediate the association between depression and cardiovascular disease mortality

“…Survival time data for the first 2 years of followup was removed, to reduce the risk of bias from imminent deaths. A logit model in a generalization method was used to determine multiple-adjusted odds ratios with 95% confidence intervals (OR [95% CI]) for CVD mortality according to total, direct and indirect (mediation) effects of depression plus prevalent/incident chronic medical conditions [34]. Logistic regression was used to determine multiple-adjusted ORs for incident depression at the 1982-1984 follow-up associated with prevalent chronic medical conditions at baseline, to explore for evidence of reverse temporal order.…”

“…This study's principal strength is that findings are based on a large, nationally representative, prospective cohort of the US population with several long-term follow-ups, high Table 1 CVD cardiovascular disease, HBP high blood pressure, OR odds ratios with confidence intervals (95% CI) and P values were derived by a logit model in a generalization method [34] participation and successful tracing rates for mortality, and extensive data collection by trained interviewers and medical examiners. This study's principal limitation is that cutoff scores for self-rated symptoms from two psychometric scales were used to define clinically significant depressive symptoms, introducing several potential sources of bias.…”

Decomposing the association between the amount of exposure and the frequency of self-reported involvement in a road crash

“…Analysis: We used the method proposed by Buis,9 a generalisation of the original decomposition method developed by Erikson et al 10 This method decomposes the total association between a categorical, discrete or continuous exposure variable, and an outcome in a direct effect and an indirect effect. In our case, we applied the Buis procedure to a logit model in which the outcome was the log (odds) of reporting involvement in a road crash during the previous year, exposure was the number of kilometres driven in the previous year (stratified in four levels), and the intermediate variable was the number of driving circumstances reported by each driver, included in the model as a continuous variable.…”

“…Bootstrapping (1000 iterations) was used to obtain CIs for the estimated ORs. The Buis method was implemented with the ldecomp package from Stata 12 (StataCorp, 2011) 9 12…”

“…We applied the analytic approach recently proposed by Buis,9 (an extension of the decomposition method described by Eriksson et al 10 for logit models) to a cross-sectional study of university students that explored driving exposure as car drivers (km/year driven), the involvement in risky driving patterns and the frequency of reporting a road crash. Our aim was to decompose the association between the amount of exposure and the frequency of reporting a road crash in a direct path and in an indirect path (mediated through risky driving patterns).…”