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Título

A MIXED-EFFECT MODEL FOR POSITIVE RESPONSES AUGMENTED BY ZEROS

Resumo

In this research article, we propose a class of models for positive and zero responses by means of a zero-augmented mixed regression model. Under this class, we are particularly interested in studying positive responses whose dis- tribution accommodates skewness. At the same time, responses can be zero, and therefore, we justify the use of a zero-augmented mixture model. We model the mean of the positive response in a logarithmic scale and the mix- ture probability in a logit scale, both as a function of fixed and random effects. Moreover, the random effects link the two random components through their joint distribution and incorporate within-subject correlation because of the repeated measurements and between-subject heterogeneity. A Markov chain Monte Carlo algorithm is tai- lored to obtain Bayesian posterior distributions of the unknown quantities of interest, and Bayesian case-deletion influence diagnostics based on the q-divergence measure is performed. We apply the proposed method to a dataset from a 24 hour dietary recall study conducted in the city of São Paulo and present a simulation study to evaluate the performance of the proposed methods.

Palavras-chave

Bayesian inference; gamma distribution; log-normal distribution; mixed models; random effects; usual intake; zero-augmented distributions