Robust methods of analysing repeated measurements data in a longitudinal setting.

Two longitudinal data sets were individually analysed within this thesis. Data set A was a vital signs data set and data set B was a data set of dietary response. Initially, an exploratory data analysis approach was used to analyse the data at each univariate time point. Missing data were observed and an approach was suggested of estimating some of these missing records. It was found that this missing data only affected multivariate test results when the proportion of individuals with missing records was large. While using the conventional methods of analysis of the data set as a whole, some authors suggest using restrictive covariance structures corresponding to the data, following the assumption of normality. An issue that can cause problems with matrix calculations for any multivariate method and therefore invalidates the multivariate procedures is if the number of repeated measures is greater than the number of individual profiles per group. In this situation there is the problem in assuming a normal distribution for the data, which is a major assumption for any multivariate analysis, when this assumption does not really hold. The main aim of our research was to devise methods of analysing the whole data set when the data is of the form mentioned above and when the assumption of normality fails. Various data reduction approaches were suggested for analysing the data in a multivariate manner for this situation. The following three approaches were suggested to reduce the number of repeated measurements: (a) multivariate summary measures, (b) principal components and (c) averaging the data over groups of time points.Both the principal components and summary measures approaches do not retain the time element and so firm conclusions can not be made. Our main contribution, within this thesis, is to illustrate that there are ways of reducing the data by still retaining the element of time in some manner. This is by using the method of averaging the data over groups of time points. The suggested procedures, of averaging data over segments of time, allows the use of the usual multivariate tests and modelling procedures without having to meet the assumption of normality or having any constraints on the covariance structure. This reduction method leads to more robust tests. Most analysis of variance tests become reduced to Chi-squared tests following this type of data reduction approach.Any statistical analyses were conducted with the aid of SAS 6.10 on VAX and later on 6.12 on UNIX. Data set A was the primary data set for analysis purposes.