Sampling designs for exploratory multivariate analysis.

This thesis is concerned with problems of variable selection, influence of sample size and
related issues in the applications of various techniques of exploratory multivariate
analysis (in particular, correspondence analysis, biplots and canonical correspondence
analysis) to archaeology and ecology. Data sets (both published and new) are used to
illustrate these methods and to highlight the problems that arise - these practical
examples are returned to throughout as the various issues are discussed. Much of the
motivation for the development of the methodology has been driven by the needs of the
archaeologists providing the data, who were consulted extensively during the study.
The first (introductory) chapter includes a detailed description of the data sets examined
and the archaeological background to their collection. Chapters Two, Three and Four
explain in detail the mathematical theory behind the three techniques. Their uses are
illustrated on the various examples of interest, raising data-driven questions which
become the focus of the later chapters. The main objectives are to investigate the
influence of various design quantities on the inferences made from such multivariate
techniques. Quantities such as the sample size (e.g. number of artefacts collected), the
number of categories of classification (e.g. of sites, wares, contexts) and the number of
variables measured compete for fixed resources in archaeological and ecological
applications. Methods of variable selection and the assessment of the stability of the
results are further issues of interest and are investigated using bootstrapping and
procrustes analysis. Jack-knife methods are used to detect influential sites, wares,
contexts, species and artefacts.
Some existing methods of investigating issues such as those raised above are applied and
extended to correspondence analysis in Chapters Five and Six. Adaptions of them are
proposed for biplots in Chapters Seven and Eight and for canonical correspondence
analysis in Chapter Nine. Chapter Ten concludes the thesis.