Considering the Distributional Form of Zeroes When Calculating Mediation Effects with Zero-Inflated Count Outcomes

Abstract

Recent work has demonstrated how to calculate conditional mediated effects for mediation models with zero-inflated count outcomes in a non-causal framework (O’Rourke & Vazquez, 2019); however, those formulas do not distinguish between logistic and count portions of the data distribution when calculating mediated effects separately for zeroes and counts. When calculating conditional mediated effects for the counts in a zero-inflated count outcome Y, the b path should use the partial derivative of the log-linear regression equation for X and M predicting Y. When calculating conditional mediated effects for the zeroes, the b path should use the partial derivative of the logistic regression equation for X and M predicting Y instead of the log-linear equation. This paper presents adjustments to the analytical formulas of conditional mediated effects for mediation with zero-inflated count outcomes when zeroes and counts are differentially predicted. Using a Monte Carlo simulation, we also empirically show that these adjustments produce different results than when the distributional form of zeroes is ignored.