Non-Linear models for Multivariate Repeated Ordinal Data

Abstract

Ordinal data have always been present in many different fields of research. The current worldwide trend to accumulate information has revealed the importance of categorical and more specifically ordinal responses. In parallel, the design of studies has become more complex in order to understand better the relationships among variables or factors influencing certain outcomes. This can for instance clearly be seen in the pharmaceutical sector where there is a growing concern for assessing patients’ quality of life. In most cases, patients will be followed over time and have their state measured repeatedly. Hence, there is a growing need for elaborate analysis methods to take into account the dependence among observations recorded on the same individual. Much work has been done for continuous responses. Although a number of distributions were available, the Gaussian distribution had the most success due to its very tractable mathematical properties. Due to the growth in computer power, various other methods have started to be investigated over the last decade. Unfortunately, few statisticians have been attracted to ordinal data leaving many topics to be investigated compared to other statistical fields. This thesis will primarily be concerned with the analysis of dependent ordinal responses.