The Poisson Inverse Gaussian Regression Model in the Analysis of Clustered Counts Data
Mohamed M. Shoukri, Musa Hakan Asyalı, R. VanDorp, D.F. Kelton
Abstract
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 method ology. Residual plots are constructed to explore the quality of the fit. We compare the results with a negative binomial regression model using max imum likelihood estimation, and to the generalized linear mixed regression model fitted in SAS.
Topics & Concepts
Poisson regressionStatisticsMathematicsCovariatePoisson distributionNegative binomial distributionCount dataInverse Gaussian distributionRegression analysisGeneralized linear modelRegressionDistribution (mathematics)PopulationSociologyDemographyMathematical analysisBayesian Methods and Mixture ModelsSoil Geostatistics and MappingStatistical Methods and Bayesian Inference