01whole.pdf (914.61 kB)
Download file

Copula-based joint regression models for longitudinal data

Download (914.61 kB)
thesis
posted on 28.03.2022, 19:45 by Aydin Hibbert
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.

History

Table of Contents

1. Introduction -- 2. Simulation -- 3. Applications -- 4. Conclusion -- 5. Discussion -- References -- Supplementary materials.

Notes

Empirical thesis. Bibliography: pages 45-52

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics and Statistics

Department, Centre or School

Department of Mathematics and Statistics

Year of Award

2019

Principal Supervisor

Gillian Heller

Rights

Copyright Aydin Hibbert 2019. Copyright disclaimer: http://mq.edu.au/library/copyright

Language

English

Extent

1 online resource (vi, 61 pages) graphs, tables

Former Identifiers

mq:71071 http://hdl.handle.net/1959.14/1270566