Factor and Correlation Analysis of Multivariate Environmental Data

Abstract

In studies of the environment, many variables are measured to characterize the system. However, not all of the variables are independent of one another. Thus, it is essential to have mathematical techniques that permit the study of the simultaneous variation of multiple variables. One such analysis is based on examining the relationships between pairs of variables. This correlation analysis, however, does not provide a clear view of the multiple interactions in the data. Thus, various forms of eigenvector analysis are used to convert the correlation data into multivariate information. Factor analysis is the name given to one of the variety of forms of eigenvector analysis. It was originally developed and used in psychology to provide mathematical models of psychological theories of human ability and behavior.1 However, eigenvector analysis has found wide application throughout the physical and life sciences. Unfortunately, a great deal of confusion exists in the literature in regard to the terminology of eigenvector analysis. Various changes in the way the method is applied have resulted in it being called factor analysis, principal components analysis, principal components factor analysis, empirical orthogonal function analysis, Karhunen-Loeve transform, etc., depending on the way the data are scaled before analysis or how the resulting vectors are treated after the eigenvector analysis is completed.