Generalized Poisson regression models with applications.

摘要

The focus of this dissertation was generalized Poisson regression (GPR) methods and models. The study addresses the following questions: (i) What are the statistical assumptions and properties of GPR models? (ii) What are some characteristics of maximum likelihood and moments estimators for GPR models? (iii) What are the properties of asymptotic distribution of GPR estimators? (iv) How different are GPR estimates from those of Poisson regression (PR) and negative binomial regression (NBR) when applied to similar count data problems? (v) How to perform conditional inference on mixture distribution involving Poisson distribution (PD), negative binomial distribution (NBD), or generalized Poisson distribution (GPD)? (vi) What are some applications of GPR models?; The GPR model is based on the family of GPD defined by Consul and Jain (1973). It has been found to be useful in many different areas such as biology, genetics, forestry, ecology, medicine, cancer research, queuing theory, and engineering.; For the first time, GPR, NBR, and PR models are applied simultaneously to the following data sets: hospital discharge, farm injury and safety, sexual behavior, household trips, colon cancer and melanoma, and elderly automobile driver accidents. Relationships between selected response variables (discrete) and covariates are assessed from various data sets. Additionally, the study discusses conditional inference on mixture of distributions with related assumptions and properties.; In conclusion, the GPR model has statistical advantages over PR and NBR models in the event of fitting count data that may be under-, over- or equi-dispersed. A possible explanation is due to results indicating slightly higher information loss incurred in conditioning for NBD than that of GPD. GPR models have similar parameter estimates and standard errors using the method of maximum likelihood (ML) or method of moments (MM) procedure for relatively large samples. Moreover, a concise outline of unsolved problems needing further research work and derivations of GPR-related distributions is presented.