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A Bayesian approach for analyzing zero‐inflated clustered count data with dispersion
Author(s) -
ChooWosoba Hyoyoung,
Gaskins Jeremy,
Levy Steven,
Datta Somnath
Publication year - 2017
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.7541
Subject(s) - overdispersion , poisson distribution , count data , zero inflated model , markov chain monte carlo , cluster analysis , statistics , bayesian probability , mathematics , bayesian inference , random effects model , computer science , inference , population , econometrics , poisson regression , artificial intelligence , medicine , meta analysis , demography , sociology
In practice, count data may exhibit varying dispersion patterns and excessive zero values; additionally, they may appear in groups or clusters sharing a common source of variation. We present a novel Bayesian approach for analyzing such data. To model these features, we combine the Conway‐Maxwell‐Poisson distribution, which allows both overdispersion and underdispersion, with a hurdle component for the zeros and random effects for clustering. We propose an efficient Markov chain Monte Carlo sampling scheme to obtain posterior inference from our model. Through simulation studies, we compare our hurdle Conway‐Maxwell‐Poisson model with a hurdle Poisson model to demonstrate the effectiveness of our Conway‐Maxwell‐Poisson approach. Furthermore, we apply our model to analyze an illustrative dataset containing information on the number and types of carious lesions on each tooth in a population of 9‐year‐olds from the Iowa Fluoride Study, which is an ongoing longitudinal study on a cohort of Iowa children that began in 1991.