This thesis has three sections. Section one contains two chapters, the first describing those techniques used later, principally multidimensional scaling, procrustes fitting and cluster analysis. Least squares scaling, preprocessing the dissimilarity matrix and clustering by maximum likelihood partition are less known. The second chapter reviews simulation studies previously published in multidimensional scaling literature. Section two contains one chapter detailing four simulation studies in multidimensional scaling. The first considers the robustness of classical scaling in the presence of error in the dissimilarity matrix. Four probabilistic models generating euclidean-distance-like dissimilarity functions are proposed, which reflect some of the ways dissimilarities actually arise, and allow dependence between dissimilarities to be studied. Next we compare how well various scaling methods reconstruct specific configurations, given the same dissimilarity matrix. Properties of preprocessing the matrix and least squares scaling are demonstrated. Thirdly we describe a study, designed to measure the redundancy in a dissimilarity matrix, which justifies subsequent use of scaling with missing data. Finally we determine the robustness of approximations to procrustes statistics obtained from perturbational analysis of classical scaling by Sibson (1979). Section three contains four applications chapters. Firstly multidimensional scaling is applied to data concerning the voting behaviour of M.P.s in 1861. This large data set requires special handling, some dissimilarity values being best treated as unknown. The results identify both unusual and regular voting behaviour. The second application is in ethnology. Dissimilarity values derived from phonetic differences between languages are used to derive their genetic origin. The techniques, especially clustering by maximum likelihood partition, reproduce known relationships satisfactorily and suggest others. The third example uses morphological and meristic parameters to generate dissimilarities between specimens of the fish species Colisa. Here the aim is taxonomic. Finally we consider dietary changes across Britain through time to identify regional and temporal differences.
|Date of Award||1982|