Introduction to multivariate analyses

Abstract

Multivariate data A multivariate data set includes more than one variable recorded from a number of replicate sampling or experimental units, sometimes referred to as objects. If these objects are organisms, the variables might be morphological or physiological measurements; if the objects are ecological sampling units, the variables might be physicochemical measurements or species abundances. We have already considered multivariate data in linear models with two or more predictor variables, e.g. multiple regression (Chapter 6) and multifactor analysis of variance (Chapters 9–11). For these analyses, we have multiple predictor (independent) variables. The multivariate analyses we will discuss in the remaining chapters either deal with multiple response variables (e.g. MANOVA – Chapter 16) or multiple variables that could be response variables, predictor variables or a combination of both. This chapter will introduce some aspects of multivariate data and analysis that apply generally to many of the methods we will describe in the subsequent three chapters. We will illustrate these aspects with four data sets from the recent biological literature. For each data set, there are i = 1 to n objects with j = 1 to p variables measured for each object. Chemistry of forested watersheds In Chapter 2, we first described the study of Lovett et al . (2000) who examined the chemistry of forested watersheds in the Catskill Mountains in New York.