Generalised linear models with clustered data

Abstract: In situations where a large data set is partitioned into many relativelysmall clusters, and where the members within a cluster have some common unmeasured characteristics, the number of parameters requiring estimation tends to increase with sample size if a fixed effects model is applied. This fact causes the assumptions underlying asymptotic results to be violated. The first paper in this thesis considers two possible solutions to this problem, a random intercepts model and a fixed effects model, where asymptoticsare replaced by a simple form of bootstrapping. A profiling approach is introduced in the fixed effects case, which makes it computationally efficient even with a huge number of clusters. The grouping effect is mainly seen as a nuisance in this paper.In the second paper the effect of misspecifying the distribution of the random effects in a generalised linear mixed model for binary data is studied. One problem with mixed effects models is that the distributional assumptions about the random effects are not easily checked from real data. Models with Gaussian, logistic and Cauchy distributional assumptions are used for parameter estimation on data simulated using the same three distributions. The effect of these assumptions on parameter estimation is presented. Two criteria for model selection are investigated, the Akaike information criterion and a criterion based on a chi-square statistic. The estimators for fixed effects parameters are quite robust against misspecification of the random effects distribution, at least with the distributions used in this paper. Even when the true random effects distribution is Cauchy, models assuming a Gaussian or a logistic distribution regularly produce estimates with less bias.