Comparisons of zero‐augmented continuous regression models from a Bayesian perspective

• Published in: Statistics in medicine Vol. 40; no. 5; pp. 1073 - 1100
• Main Authors: Ye, Tairan, Lachos, Victor H., Wang, Xiaojing, Dey, Dipak K.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 28.02.2021
• Subjects: Bayesian analysis; leave‐one‐out cross‐validation; sensitivity analysis for priors; Tweedie model; Watanabe‐Akaike information criterion; zero‐augmented models; Watanabe-Akaike information criterion; Bayesian analysis; Tweedie model; sensitivity analysis for priors; zero-augmented models; leave-one-out cross-validation
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.8795

Summary The two‐part model and the Tweedie model are two essential methods to analyze the positive continuous and zero‐augmented responses. Compared with other continuous zero‐augmented models, the zero‐augmented gamma model (ZAG) demonstrates its performance on the mass zeros data. In this article, we compare the Bayesian model for continuous data of excess zeros by considering the ZAG and Tweedie model. We model the mean of both models in a logarithmic scale and the probability of zero within the zero‐augmented model in a logit scale. As previous researchers employed different priors in Bayesian settings for the Tweedie model, by conducting a sensitivity analysis, we select the optimal priors for Tweedie model. Furthermore, we present a simulation study to evaluate the performance of two models in the comparison and apply them to a dataset about the daily fish intake and blood mercury levels from National Health and Nutrition Examination Survey. According to the Watanabe‐Akaike information criterion and leave‐one‐out cross‐validation criterion, the Tweedie model provides higher predictive accuracy for the positive continuous and zero‐augmented data.