Exploring Relationships Among Multiple Data Sets.

Abstract

This paper has two related aims. First, some conceptual and mathematical relationships are discussed among alternative procedures for analyzing multiple data sets, including: inter-battery factor analysis (Tucker, 1958; Kristof, 1967), multiple regression, canonical correlation, generalized canonical correlation (Horst, 1965; Kettenring, 1971), longitudinal factor analysis (Corballis and Traub, 1970), and multiple set factor analysis (Golding and Seidman, 1974; Jackson, 1975). To motivate the comparison, each technique is related to a principal components model. The second aim is to describe an exploratory data analysis strategy for integrating the relative advantages of canonical correlation and multiple set factor analysis. When considering two data sets, the testing of statistical significance of appropriate linear combinations is emphasized, together with a further transformation to enhance substantive interpretation of the data.