A Course in Statistics with R

Chapter 15Multivariate Statistical Analysis - II

Package(s): DAAG, HSAUR2, qcc

Dataset(s): iris, socsupport, chemicaldata, USairpollution, hearing, cork, adjectives, life

15.1 Introduction

In the previous chapter we built on some of the essential multivariate techniques. The results there helped set up a platform to stage more practical applications. The classification and discriminant analysis techniques work well for classifying observations into distinct groups. This topic forms the content of Section 15.2. Canonical correlations help to identify if there are groups of variables present in a multivariate vector, which will be dealt with in Section 15.3. Principal Component Analysis (PCA) helps in obtaining a new set of fewer variables, which have the overall variation of the original set of variables. This multivariate technique will be developed in Section 15.4, whereas specific areas of application of the technique will be dealt in Section 15.5. Multivariate data may also be used to find a new set of variables using Factor Analysis, check Section 15.6.

15.2 Classification and Discriminant Analysis

The application of MSA is to classify the data into distinct groups. This task is achieved through two steps: (i) Discriminant Analysis, and (ii) Classification. In the first step we identify linear functions, which describe the similarities and differences among the groups. This is achieved through the relative contribution of variables towards the separation of groups and ...