Point and Interval Estimators of an Indirect Effect for a Binary Outcome

Abstract

Conventional estimators for indirect effects using a difference in coefficients and product of coefficients produce the same results for continuous outcomes. However, for binary outcomes, the difference in coefficient estimator systematically underestimates the indirect effects because of a scaling problem. One solution is to standardize regression coefficients. The residual from a regression of a predictor on a mediator, which we call the residualized variable in this paper, was used to address the scaling problem. In simulation study 1, different point estimators of indirect effects for binary outcomes are compared in terms of the means of the estimated indirect effects to demonstrate the scaling problem and the effects of its remedies. In simulation study 2, confidence and credible intervals of indirect effects for binary outcomes were compared in terms of powers, coverage rates, and type I error rates. The bias-corrected (BC) bootstrap confidence intervals performed better than did other intervals.

Keywords

• Indirect effects
• Binary outcome
• Confidence intervals
• Bootstrap
• Delta

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