Author:

Keywords:

Deviance information criteria, Hierarchical Poisson–Normal model, Hierarchical Poisson–Normal Overdispersion, Overdispersion, Science & Technology, Technology, Physical Sciences, Computer Science, Interdisciplinary Applications, Statistics & Probability, Computer Science, Mathematics, Hierarchical Poisson-Normal model (HPN), Hierarchical Poisson-Normal overdispersed model (HPNOD), MODELS, REGRESSION, 0104 Statistics, 0802 Computation Theory and Mathematics, 1403 Econometrics, 3802 Econometrics, 4905 Statistics

Abstract:

In sets of count data, the sample variance is often considerably larger or smaller than the sample mean, known as a problem of over- or underdispersion. The focus is on hierarchical Bayesian modeling of such longitudinal count data. Two different models are considered. The first one assumes a Poisson distribution for the count data and includes a subjectspecific intercept, which is assumed to follow a normal distribution, to account for subject heterogeneity. However, such a model does not fully address the potential problem of extra-Poisson dispersion. The second model, therefore, includes also random subject and time dependent parameters, assumed to be gamma distributed for reasons of conjugacy. To compare the performance of the two models, a simulation study is conducted in which the mean squared error, relative bias, and variance of the posterior means are compared.