Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation

Abstract

Longitudinal data is a special type of multivariate data that occur when counts, measurements or categorical responses are obtained from one or more experimental units or subjects through time. A number of various approaches for representing longitudinal data in terms of a statistical model have been developed. The data used in this thesis are from Kenward (1987) that reports an experiment in which cattle were assigned randomly to two treatment groups A and B, and their weights were recorded to study the effect of treatments on intestinal parasites. Thirty animals received treatment A and another 30 received treatment B. They are weighed 11 times over a 133-day period; the first 10 measurements on each animal were made at two-week intervals and the final measurement was made one week later. The measurement times were common across animals and were rescaled to t=1,2,…,10,11. No observation was missing so this is a balanced longitudinal dataset. Our goal is to find which model among these presented in this thesis fits best to the two different groups of our data. We compare among joint mean- covariance models (Pourahmadi, 1999) and mixed effects models.