The analysis of repeated ordinal data using latent trends
This thesis presents methodology to analyse repeated ordered categorical data (repeated ordinal data), under the assumption that measurements arise as discrete realisations of an underlying (latent) continuous distribution. Two sets of estimation equations, called quasiestimation equations or QEEs, are presented to estimate the mean structure and the cutoff points which define boundaries between different categories. A series of simulation studies are employed to examine the quality of the estimation processes and of the estimation of the underlying latent correlation structure. Graphical studies and theoretical considerations are also utilised to explore the asymptotic properties of the correlation, mean and cutoff parameter estimates. One important aspect of repeated analysis is the structure of the correlation and simulation studies are used to look at the effect of correlation misspecification, both on the consistency of estimates and their asymptotical stability. To compare the QEEs with current methodology, simulations studies are used to analyse the simple case where the data are binary, so that generalised estimation equations (GEEs) can also be applied to model the latent trend. Again the effect of correlation misspecification will be considered. QEEs are applied to a data set consisting of the pain runners feel in their legs after a long race. Both ordinal and continuous responses are measured and comparisons between QEEs and continuous counterparts are made. Finally, this methodology is extended to the case when there are multivariate repeated ordinal measurements, giving rise to inter-time and intra-time correlations.