Spatial Poisson regression : Bayesian approach correcting for measurement error with applications.
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Atkinson, William H., 1980-
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Under and over reporting is a common problem in social science research, adverse events associated with drug use, and many other areas of research. Furthermore, overdispersion is another common problem that plagues count data. McBride (2006) proposed a Bayesian Poisson regression model which accounts for overdispersion in count data. We extend this model by adding parameters to accommodate the problems associated with under and over reporting in the count data. We then study the model's coverage, power, accuracy of point estimates, and credible set widths through simulation using a spatial lattice grid. We find that our proposed model produces reliable point estimates and reasonable credible set widths, coverage, and power. We also provide two examples of the models use: disease mapping of habitat burglary from the city of Waco Texas and an analysis of sports data similar to that of Albert's (1992) analysis of homerun data. Research questions of interest are answered using the subset selection procedure proposed by Bratcher and Bhalla (1974), used by Hamilton, Bratcher, and Stamey (2008) and Stamey, Bratcher, and Young (2007), to demonstrate the ease of use for combining the our model developed here and the subset selection procedure itself, as was also done in McBride (2006).