Multivariate analysis refers to a set of statistical procedures that are distinguished by the ability to examine several response variables within a single study and to account for their potential interrelationships in the analysis of the data. These tests are distinguished from univariate analysis procedures, such as the t-test and analysis of variance, which accommodate only one measured variable.
In a brief introduction such as this, it is not possible to cover the full scope of these complex statistical procedures. The purpose of this chapter is to present concepts related to commonly used procedures including factor analysis, sequential equation modeling, cluster analysis, multivariate analysis of variance, and survival analysis.
Exploratory Factor Analysis
The technique of factor analysis is quite different from any of the statistical procedures we have examined thus far. Rather than using data for comparison or prediction, factor analysis examines the structure within a large number of variables, to reflect how they cluster to represent different dimensions of a construct.
Factor analysis is more controversial than other analytic methods because it leaves room for subjectivity and judgment. However, it makes an important contribution to multivariate methods because it can provide insights into the nature of abstract constructs and allows us to superimpose order on complex phenomena. A statistician should be consulted to make decisions about using particular methods under specific research conditions. Those interested in greater detail should refer to several useful resources.1-5
The overarching term “factor analysis” is actually used to refer to several approaches with different goals. Exploratory factor analysis (EFA) is used to examine linear combinations of underlying factors that explain a latent variable or construct. Confirmatory factor analysis (CFA) is used to confirm hypotheses about the structure of underlying constructs. These two approaches will be discussed in the following sections. A third technique called principal components analysis (PCA) attempts to reduce data to a smaller set of summary variables or components that account for most of the variance in a set of observed variables. Although many of the statistical techniques used for these analyses are similar, there are important differences in assumptions and purpose.
-See the Chapter 31 Supplement for further discussion of principal components analysis.
Exploratory Factor Analysis
The concept of EFA is illustrated in Figure 31-1. The set of “variables” at the top are part of an overarching construct of “green.” We assume that there is some relationship among circles that have similar hues of green, that light green circles are related to other light green circles, but not to darker green circles, but together all the hues explain “green.” Through factor analysis, these variables are reorganized into three relatively independent factors, each one representing a unique cluster of variables that are highly correlated among themselves but poorly correlated with items on other factors. Not ...