Statistics and Its Interface

Volume 14 (2021)

Number 2

Bayesian zero-inflated growth mixture models with application to health risk behavior data

Pages: 151 – 163

DOI: https://dx.doi.org/10.4310/20-SII623

Authors

Si Yang (Department of Computer Science and Statistics, University of Rhode Island, Kingston, R.I., U.S.A.)

Gavino Puggioni (Department of Computer Science and Statistics, University of Rhode Island, Kingston, R.I., U.S.A.)

Abstract

This paper focuses on developing latent class models for longitudinal data with zero-inflated count response variables. The goals are to model discrete longitudinal patterns of rare events counts (for instance, health-risky behavior), and to identify individual-specific covariates associated with latent class probabilities. Two discrete latent structures are present in this type of model: a latent categorical variable that classifies subgroups with distinct developmental trajectories and a latent binary variable that identifies whether an observation is from a zero-inflation process or a regular count process. Within each class, two sets of covariates are used to separately model the probability of structural zeros and the mean trajectories of the count process. The estimation of the latent variables and regression parameters are carried jointly in a hierarchical Bayesian framework. Our methods are validated through a simulation study and then applied to cigarette smoking data, obtained from the National Longitudinal Study of Adolescent Health.

Keywords

latent class models, finite mixtures, longitudinal methods, adolescent smoking, behavioral sciences, hierarchical models

2010 Mathematics Subject Classification

Primary 62C10, 62P15. Secondary 62C12.

Received 15 November 2016

Accepted 9 June 2020

Published 22 December 2020