title: A mixed-effect model for positive responses augmented by zeros.
abstract: 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 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.
authors: Department of Statistics, State University of Campinas, São Paulo, Brazil.
authors: Mariana
authors: M
authors: Rodrigues-Motta
authors: Diana Milena
authors: DM
authors: Galvis Soto
authors: Victor H
authors: VH
authors: Lachos
authors: Filidor
authors: F
authors: Vilca
authors: Valéria Troncoso
authors: VT
authors: Baltar
authors: Eliseu Verly
authors: EV
authors: Junior
authors: Regina Mara
authors: RM
authors: Fisberg
authors: Dirce Maria
authors: DM
authors: Lobo Marchioni
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001938:Brazil; D003198:Computer Simulation; D004032:Diet / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008390:Markov Chains; D011939:Mental Recall; D015233:Models, Statistical; D009010:Monte Carlo Method; D016012:Poisson Distribution
keywords: Bayesian inference; gamma distribution; log-normal distribution; mixed models; random effects; usual intake; zero-augmented distributions