title: The Gamma-Poisson model as a statistical method to determine if micro-organisms are randomly distributed in a food matrix.
abstract: The Gamma-Poisson model, i.e., a Poisson distribution where the parameter lambda is Gamma distributed, has been suggested as a statistical method for determining whether or not micro-organisms are randomly distributed in a food matrix. In this study, we analyse the Gamma-Poisson model to explore some of the properties of the Gamma-Poisson model left unexplored by the previous study. The conclusion of our analysis is that the Gamma-Poisson model distinguishes poorly between variation at the Poisson level and the Gamma level. Estimated parameter values from simulated data-sets showed large variation around the true values, even for moderate sample sizes (n=100). Furthermore, at these sample sizes the likelihood ratio is not a good test statistic for discriminating between the Gamma-Poisson distribution and the Poisson distribution. Hence, to determine if data are randomly distributed, i.e., Poisson distributed, the Gamma-Poisson distribution is not a good choice. However, the ratio between variation at the Poisson level and the Gamma level does provide a measure of the amount of overdispersion.
authors.affiliation: Department of Large Animal Sciences, The Royal Veterinary and Agricultural University, Grønnegårdsvej 8, DK-1870 Frederiksberg C, Denmark. nt@dina.kvl.dk
authors.forename: Nils
authors.initials: N
authors.lastname: Toft
authors.forename: Giles T
authors.initials: GT
authors.lastname: Innocent
authors.forename: Dominic J
authors.initials: DJ
authors.lastname: Mellor
authors.forename: Stuart W J
authors.initials: SW
authors.lastname: Reid
mesh_terms: D003198:Computer Simulation; D003257:Consumer Product Safety; D003627:Data Interpretation, Statistical; D005516:Food Microbiology; D008954:Models, Biological; D015233:Models, Statistical; D016012:Poisson Distribution; D011237:Predictive Value of Tests