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Abstract:
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The Poisson-gamma mixture model is often used in modeling over-dispersed count data. This model is computationally tractable and is included in many generalized linear model packages. In many cases a more natural model for the variation in the random Poisson mean is the lognormal distribution. Since the mean and variance functions for both models are identical, mis-specification of the model can have little impact on statistical inference. However, for certain model properties, for example, the probability of nonzero counts, misspecification bias can exceed 50%. The implications of these results for bioassay and environmental monitoring are explored. Also, an efficient numerical integration method for the Poisson-lognormal is presented.
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