Marginal effects for zero-inflated semi-continuous data

Zero-inflated semi-continuous data are common in various fields such as medicine, economics, and social sciences, where the outcome distribution consists of a point mass at zero and a positive continuous distribution. This work employs marginalized zero inflated gamma regression and marginalized zero inflated Log-normal regression models to analyze semi-continuous data with zero inflation. These models allow for a direct interpretation of covariate effects on the marginal mean while accounting for distinct mechanisms that generate structural zeros and continuous positive outcomes. The proposed approach is validated through simulation studies and the analysis of real datasets, demonstrating a substantial improvement in both the interpretability and accuracy of estimates. This paper introduces two novel marginalized regression models, marginalized zero inflated gamma regression and marginalized zero inflated Log-normal regression, that address key limitations of existing methods by providing a clear interpretation of covariate effects on the marginal mean and robust statistical properties. This work fills a significant gap in the literature by offering a comprehensive framework for the estimation and interpretation of these models.