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Mixed regression models for discrete data

University of British Columbia

The dissertation consists of two parts. In the first part we introduce and investigate a class of mixed Poisson regression models that include covariates in both mixing probabilities and Poisson rates. The proposed models generalize the usual Poisson regression in several ways, and can be used to adjust for extra-Poisson variation. The features of the models, identifiability, estimation methods based on the EM and quasi-Newton algorithms, properties of these estimates, model selection criteria and residual analysis are discussed. A Monte Carlo study investigates implementation and model choice issues. Several applications of this approach are analyzed. This analysis is compared to quasi-likelihood approaches. In the second part we introduce and investigate a class of mixed logistic regression models that include covariates in both mixing probabilities and binomial parameters with the logit link. The proposed models generalize the usual logistic regression in several ways, and can be used to adjust for extra-binomial variation. The features of the models, identifiability, estimation methods based on the EM and quasi-Newton algorithms, properties of these estimates, model selection criteria and residual analysis are discussed. A Monte Carlo study investigates implementation and model choice issues. An applications of this approach is analyzed and results compared to those by quasi-likelihood approaches. The dissertation also discusses future research in the areas and provides FORTRAN codes for all computations required to apply the models.

Thesis/Dissertation

application/pdf

2009-04-15

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http://hdl.handle.net/2429/7176

Business Administration

University of British Columbia

UBCV

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