Exploratory and inferential multivariate statistical techniques for multidimensional count and binary data with applications in R

[摘要] ENGLISH ABSTRACT: The analysis of multidimensional (multivariate) data sets is a very important area ofresearch in applied statistics. Over the decades many techniques have been developed todeal with such datasets. The multivariate techniques that have been developed includeinferential analysis, regression analysis, discriminant analysis, cluster analysis and manymore exploratory methods. Most of these methods deal with cases where the data containnumerical variables. However, there are powerful methods in the literature that also dealwith multidimensional binary and count data.The primary purpose of this thesis is to discuss the exploratory and inferential techniquesthat can be used for binary and count data. In Chapter 2 of this thesis we give the detail ofcorrespondence analysis and canonical correspondence analysis. These methods are usedto analyze the data in contingency tables. Chapter 3 is devoted to cluster analysis. In thischapter we explain four well-known clustering methods and we also discuss the distance(dissimilarity) measures available in the literature for binary and count data. Chapter 4contains an explanation of metric and non-metric multidimensional scaling. Thesemethods can be used to represent binary or count data in a lower dimensional Euclideanspace. In Chapter 5 we give a method for inferential analysis called the analysis ofdistance. This method use a similar reasoning as the analysis of variance, but theinference is based on a pseudo F-statistic with the p-value obtained using permutations ofthe data. Chapter 6 contains real-world applications of these above methods on twospecial data sets called the Biolog data and Barents Fish data.The secondary purpose of the thesis is to demonstrate how the above techniques can beperformed in the software package R. Several R packages and functions are discussedthroughout this thesis. The usage of these functions is also demonstrated with appropriateexamples. Attention is also given to the interpretation of the output and graphics. Thethesis ends with some general conclusions and ideas for further research.

[发布机构] Stellenbosch University