Thesis (MComm)--Stellenbosch University, 2011. / 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 binêre en telling data.
Die primêre doel van hierdie tesis is om tegnieke vir verkennende en inferensiële analise
van binêre 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 gebeurlikheidstabelle te analiseer. Hoofstuk 3 bevat tegnieke vir tros analise. In
hierdie hoofstuk verduidelik ons vier gewilde tros analise metodes. Ons bespreek ook die
afstand maatstawwe wat beskikbaar is in die literatuur vir binêre en telling data. Hoofstuk
4 bevat ’n verduideliking van metriese en nie-metriese meerdimensionele skalering.
Hierdie metodes kan gebruik word om binêre of telling data in ‘n lae dimensionele
Euclidiese ruimte voor te stel. In Hoofstuk 5 beskryf ons ’n inferensie metode wat bekend
staan as die analise van afstande. Hierdie metode gebruik ’n soortgelyke redenasie as die
analise van variansie. Die inferensie hier is gebaseer op ’n pseudo F-toetsstatistiek en die
p-waardes word verkry deur gebruik te maak van permutasies van die data. Hoofstuk 6
bevat toepassings van bogenoemde tegnieke op werklike datastelle wat bekend staan as
die Biolog data en die Barents Fish data.
Die sekondêre doel van die tesis is om te demonstreer hoe hierdie tegnieke uitgevoer
word in the R sagteware. Verskeie R pakette en funksies word deurgaans bespreek in die
tesis. Die gebruik van die funksies word gedemonstreer met toepaslike voorbeelde.
Aandag word ook gegee aan die interpretasie van die afvoer en die grafieke. Die tesis
sluit af met algemene gevolgtrekkings en voorstelle vir verdere navorsing.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/17949 |
| Date | 12 1900 |
| Creators | Ntushelo, Nombasa Sheroline |
| Contributors | Lamont, M. M. C., Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | ix, 122 p. : ill. (some col.) |
| Rights | Stellenbosch University |
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