Over-dispersed Poisson Model Research Articles

Two-Stage Negative Binomial and Overdispersed Poisson Models for Clustered Developmental Toxicity Data with Random Cluster Size

Through theory, simulation, and analyses of developmental toxicity data, we evaluate two-stage log-linear negative binomial and overdispersed Poisson models that accommodate random cluster-size inference for clustered binary response data. The issue of random cluster size has especially been of concern for animal developmental toxicity studies of teratogenic chemicals where litter sizes vary. Such an application of these twostage models has not been reported previously but is theoretically justified. This unique application of these models is based upon an extension of a little known result that the marginal distribution for cluster-level counts of binary responses is Poisson under a firststage binomial distribution for such counts and a second-stage Poisson distribution for cluster size. The proposed models are compared with generalized estimating equations (GEE) estimation of a logistic model that treats cluster size as fixed. The simulations and data analyses suggest that both the negative binomial and GEE logistic models consistently lead to correct inference when cluster size is a Poisson random variable, although there are some exceptions when cluster size is underdispersed or when it depends upon a covariate.

Corrections: Bayesian Analysis of Two Overdispersed Poisson Models

Corrections: Bayesian Analysis of Two Overdispersed Poisson Models

Bayesian Analysis of Two Overdispersed Poisson Models

In this paper, we consider the Bayesian analysis of two overdispersed Poisson models. The first is an overdispersed generalized Poisson model. The second is an ordinary Poisson and overdispersed generalized Poisson mixture model. Shoukri and Consul (1989, Comimintiicationis inz Statistics: Simnllationi anzd Comiiptutationi 18, 1465-1480) have previously considered a limited form of approximate Bayesian analysis for the first of these two models requiring the use of Pearson curves and the assumption that a certain model parameter has support on a finite number of values. By way of comparison, this paper demonstrates how a full Bayesian analysis of either model may proceed by making use of the Gibbs sampler and adaptive rejection sampling methods for log-concave densities. The methodology is illustrated with an application to a biological data set.