Mapping the mind with broken theodolites : contributions to multidimensional scaling methodology, with special application to triadic data, and the sorting and hierarchical sorting methods : a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Human Development Studies at Massey University
This thesis focuses on the psychological applications of Multidimensional Scaling (MDS) theory and methodology. The results are investigated of treating certain kinds of dissimilarity data (triadic data, to begin with) as comparisons between dissimilarities. This is a familiar idea but many of its implications are unexplored. First, when data are available from more than one subject, it becomes possible to apply models of individual variation, in non-metric form. The Weighted Euclidean (or INDSCAL) model is the one used most often in this thesis, but the more general IDIOSCAL model is used to investigate individual differences in the case of colour vision. The data sets need not be complete. This is important when the size of the stimulus set means that there are too many comparisons for a single subject to respond to them all. Second, Maximum Likelihood Estimation (MLE) becomes a straightforward generalisation of the standard hill-descent algorithm for minimising Stress. Third, data collected with the sorting and hierarchical sorting methods can also be regarded as dissimilarity comparisons. The convenience of the sorting method and the lesser demands it makes on subjects when the number of stimuli is large have led to its widespread use, but the best way of analysing such data is uncertain. A 'reconstructed dyad' analysis is described and shown to be better than the usual co-occurence approach in a number of examples in which evidence about the true perceptual or conceptual space is available independently. Finally, when the data are interpreted as dissimilarity comparisons, an interactive method of scaling large stimulus sets becomes possible, in which one selectively acquires incomplete data, concentrating on comparisons which are expected to contain most information about the configuration. This approach has been applied twice, with the stimuli being simple synthesised sounds in one example, and complex natural sounds (canine heartbeats) in the second, working well in both cases. The potential applications for training people to recognise sounds are briefly considered. Some possibilities for future research arising from this work are described.