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A mixed‐effect model for positive responses augmented by zeros
Author(s) -
RodriguesMotta Mariana,
Galvis Soto Diana Milena,
Lachos Victor H.,
Vilca Filidor,
Baltar Valéria Troncoso,
Junior Eliseu Verly,
Fisberg Regina Mara,
Lobo Marchioni Dirce Maria
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6450
Subject(s) - markov chain monte carlo , skewness , mathematics , statistics , bayesian probability , random effects model , mixture model , computer science , dirichlet process , econometrics , medicine , meta analysis
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.