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

ENGLISH ABSTRACT: The analysis of multidimensional (multivariate) data sets is a very important area of research in applied statistics. Over the decades many techniques have been developed to deal with such datasets. The multivariate techniques that have been developed include inferential analysis, regression analysis, discriminant analysis, cluster analysis and many more exploratory methods. Most of these methods deal with cases where the data contain numerical variables. However, there are powerful methods in the literature that also deal with multidimensional binary and count data. The primary purpose of this thesis is to discuss the exploratory and inferential techniques that can be used for binary and count data. In Chapter 2 of this thesis we give the detail of correspondence analysis and canonical correspondence analysis. These methods are used to analyze the data in contingency tables. Chapter 3 is devoted to cluster analysis. In this chapter 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 4 contains an explanation of metric and non-metric multidimensional scaling. These methods can be used to represent binary or count data in a lower dimensional Euclidean space. In Chapter 5 we give a method for inferential analysis called the analysis of distance. This method use a similar reasoning as the analysis of variance, but the inference is based on a pseudo F-statistic with the p-value obtained using permutations of the data. Chapter 6 contains real-world applications of these above methods on two special data sets called the Biolog data and Barents Fish data. The secondary purpose of the thesis is to demonstrate how the above techniques can be performed in the software package R. Several R packages and functions are discussed throughout this thesis. The usage of these functions is also demonstrated with appropriate examples. Attention is also given to the interpretation of the output and graphics. The thesis ends with some general conclusions and ideas for further research.%%%%AFRIKAANSE OPSOMMING: Die analise van meerdimensionele (meerveranderlike) datastelle is ’n belangrike area van navorsing in toegepaste statistiek. Oor die afgelope dekades is daar verskeie tegnieke ontwikkel om sulke data te ontleed. Die meerveranderlike tegnieke wat ontwikkel is sluit in inferensie analise, regressie analise, diskriminant analise, tros analise en vele meer verkennende data analise tegnieke. Die meerderheid van hierdie metodes hanteer gevalle waar die data numeriese veranderlikes bevat. Daar bestaan ook kragtige metodes in die literatuur vir die analise van meerdimensionele binere en telling data. Die primere doel van hierdie tesis is om tegnieke vir verkennende en inferensiele analise van binere en telling data te bespreek. In Hoofstuk 2 van hierdie tesis bespreek ons ooreenkoms analise en kanoniese ooreenkoms analise. Hierdie metodes word gebruik om data in…