Copula-based joint regression models for longitudinal data

A popular approach to modelling longitudinal observations is using mixed models with random effects for subjects. Recent developments in joint regression modelling presents an alternative approach to longitudinal analysis which utilises copulas to flexibly model dependence structures for correlated data. The performance of copula-based regression models has, to date, not been quantified in comparison to random effect based models and other popular methods. This thesis provides a preliminary analysis of some of the situations in which copula-based joint regression models may be more appropriate than mixed models for longitudinal regression analysis. The models are compared across a range of simulated longitudinal datasets generated from a flexible bivariate distribution, and applied to three real-world datasets. The results of the analysis indicate that in cases where the outcome variables marginal distributions are skewed and there is rank correlation between regression outcome variables, measured by Kendall’s tau, mixed models provide biased parameter estimates while copula-based joint regression models provide unbiased estimates with generally lower standard errors than other alternative methods such as generalised linear models or generalised estimating equations.