Abstract
In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that excess of dispersion in the data may be partially caused from the possible spatial dependence existing among the different spatial units. Thus, specific regression structures are then proposed both for the conditional mean and for the dispersion parameter in the models, including covariates, as well as an assumed spatial neighborhood structure. We focus on the case of response variables following a Poisson distribution, specifically concentrating on the spatial generalized conditional normal overdispersion Poisson model. Models were fitted by making use of the Markov Chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA) algorithms in the specific context of Bayesian estimation methods.
Highlights
Generalized linear models (GLM) are commonly used to model the response variable when working with count data
Watanabe-Akaike Information Criterion (WAIC) values, for the spatial conditional normal Poisson model in the analysis of the Colombian infant mortality rates data set with different prior distributions for the precision parameter of the random effects
We would like to emphasize the importance of taking into account the overdispersion, as well as the dependence that can arise from the correlation among the values of the response variable in neighboring locations
Summary
Generalized linear models (GLM) are commonly used to model the response variable when working with count data (see [1]). Count data regression models commonly exhibit overdispersion, a phenomenon generated when the data show a larger variance than the one that would be expected from the specification of the model itself (see [2]) This situation is known as extra-Poisson or extra-binomial variation when the response variable is assumed to follow either a Poisson or a binomial distribution, respectively. One of the possible causes for overdispersion is the presence of correlation among the values of the variable under study for the different units considered in the specific data set being analyzed (see [3]) This is specially common with spatial data, where observations in locations that are closer in space tend to show similar values, a phenomenon known as spatial autocorrelation (see [4]). These issues must be taken into account in order to obtain reliable inference processes for the estimated parameters in the proposed model
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