# Multivariate Analysis

Multivariate analysis is useful when you have several different measurements on a set of n objects. In Genstat the measurements would usually be stored in separate variates, and these would have a unit for each object. The objects are often regarded as being a set of n points in p dimensions (p being the number of variates). Many techniques, for example principal components analysis (Chapter 2) and canonical variates analysis (Chapter 3) are aimed at reducing the dimensionality. That is, they aim to find a smaller number of dimensions (usually 2 or 3) that exhibit most of the variation present in the data. This can help you determine patterns or structure in the data, as well as identify the relative importance of individual variables.

Genstat has several menus for producing graphical representations, for example principal coordinates analysis (Chapter 4) and multidimensional scaling (Chapter 5). It also has facilities for modelling multivariate data, including multivariate analysis of variance (Chapter 8) and partial least squares. Another important requirement is to take a set of units and classify them into groups based on their observed characteristics. Hierarchical cluster analysis (Chapter 6) starts with a set of groups each of which contains one of the units. These initial groups are successively merged into larger groups, according to their similarity, until there is just one group containing all the observations.

Genstat also provide menus for nonhierarchical classification (Chapter 7), where the aim is to form a single grouping of the observations that optimizes some criterion such as the within-class dispersion, or the Mahalanobis squared distance between the groups, or the between-group sum of squares. Chapter 9 describes the facilities for constructing classification trees, which allow you to predict the classification of unknown objects using multivariate observations. Regression trees, which predict the value of a response variate from multivariate observations are described in Chapter 10.

Finally, Chapter 11 describes how generalized Procrustes analysis can be used to obtain a consensus from assessors in activities such as wine tasting. The book works through a series of straightforward examples, with frequent practicals to allow you to try the methods for yourself. The examples work mainly through the menus of Genstat for Windows, so there is no need for prior knowledge of the Genstat command language.