A mixed-effect model for positive responses augmented by zeros

• Published in: Statistics in medicine Vol. 34; no. 10; pp. 1761 - 1778
• Main Authors: Rodrigues-Motta, Mariana, Galvis Soto, Diana Milena, Lachos, Victor H., Vilca, Filidor, Baltar, Valéria Troncoso, Junior, Eliseu Verly, Fisberg, Regina Mara, Lobo Marchioni, Dirce Maria
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 10-05-2015; Wiley Subscription Services, Inc
• Subjects: Algorithms; Bayes Theorem; Bayesian analysis; Bayesian inference; Brazil; Computer Simulation; Diet - statistics & numerical data; gamma distribution; Humans; Likelihood Functions; Linear Models; log-normal distribution; Markov analysis; Markov Chains; Mathematical models; Mental Recall; mixed models; Models, Statistical; Monte Carlo Method; Monte Carlo simulation; Poisson Distribution; Probability distribution; random effects; Regression analysis; usual intake; zero-augmented distributions; Brazil; Sao Paulo Brazil; random effects; gamma distribution; usual intake; mixed models; zero-augmented distributions; Bayesian inference; log-normal distribution
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.6450

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 distribution 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 mixture 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 tailored 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 24hour dietary recall study conducted in the city of São Paulo and present a simulation study to evaluate the performance of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.