TITLE:
Inference Procedures on the Generalized Poisson Distribution from Multiple Samples: Comparisons with Nonparametric Models for Analysis of Covariance (ANCOVA) of Count Data
AUTHORS:
Maha Al-Eid, Mohamed M. Shoukri
KEYWORDS:
Count Regression, Over Dispersion, Generalized Linear Models, Analysis of Covariance, Generalized Additive Models
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.3,
June
25,
2021
ABSTRACT: Count data that exhibit over dispersion (variance of
counts is larger than its mean) are commonly analyzed using discrete
distributions such as negative binomial, Poisson inverse Gaussian and other
models. The Poisson is characterized by the equality of mean and variance
whereas the Negative Binomial and the Poisson inverse Gaussian have variance
larger than the mean and therefore are more appropriate to model over-dispersed
count data. As an alternative to these two models, we shall use the generalized
Poisson distribution for group comparisons in the presence of multiple
covariates. This problem is known as the ANCOVA and is solved for continuous
data. Our objectives were to develop ANCOVA using the generalized Poisson
distribution, and compare its goodness of fit to that of the nonparametric
Generalized Additive Models. We used real life data to show that the model
performs quite satisfactorily when compared to the nonparametric Generalized
Additive Models.