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Abstract:
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It is of interest to predict spatially correlated count data that follows a Poisson distribution. This will include disease incidence or mortality rates. One such disease that we would like to predict is the incidence West Nile virus. Count data for the number of West Nile virus cases in humans are available at the county level for each state in the U.S, from 2000-2014 as well as counts of infected mosquitos and birds. An environmental predictor of West Nile virus is percent irrigated farmland. To predict a Poisson outcome variable in the presence of an auxiliary variable, we propose a bivariate Generalized Linear Mixed Model (GLMM). A GLMM model is fit with a bivariate distribution containing a Poisson outcome variable and an auxiliary variable; assuming a correlation structure similar to that used in cokriging. These methods are examined in the context of a real data example using the West Nile virus data. The bivariate model is fit using human data as the primary outcome variable and the mosquito, bird and irrigation data as an auxiliary variable. Cross-validation is used to evaluate the prediction, using this method predicted incidence is compared to the actual incidence.
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