Abstract

Using the advancements of Arellano-Valle et al. [2005], which characterize the likelihood function of a linear mixed model (LMM) under a skew-normal distribution for the random effects, this thesis attempt to construct a copula-driven generalized linear mixed model (GLMM). Assuming a multivariate distribution from the exponential family for the response variable and a skew-normal copula, we drive a complete characterization of the general likelihood function. For estimation, we apply a Monte Carlo expectation maximization (MC-EM) algorithm. Some special cases are discussed, in particular, the exponential and gamma distributions. Simulations with multiple link functions are shown alongside a real data example from the Framingham Heart
Study.