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The Poisson Inverse Gaussian Regression Model in the Analysis of Clustered Counts Data

We explore the possibility of modeling clustered count data using the Poisson Inverse Gaussian distribution. We develop a regression model, which relates the number of mastitis cases in a sample of dairy farms in Ontario, Canada, to various farm level covariates, to illustrate the methodology. Residual plots are constructed to explore the quality of the fit. We compare the results with a negative binomial regression model using maximum likelihood estimation, and to the generalized linear mixed regression model fitted in SAS.