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This thesis considers extensions of Generalized Linear Models (Nelder and Wedderburn, 1972) to incorporate correlated count data. Of particular interest is the Poisson random effects model which is commonly solved by approximate methods due to the complexity of calculations in maximum likelihood estimation (Diggle, Liang and Zeger, 1994, pl73-5). The methods considered fall into 4 categories; 1. quasi-likelihood techniques, (Schall, 1991), (Breslow and Clayton, 1993), 2. overdispersion models, (Van de Ven and Weber, 1995) 3. generalized estimating equations, (Liang and Zeger, 1986), and 4. Markov Chain Monte Carlo techniques, (Zeger and Karim, 1991). |
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