Canonical correlation analyses for three data sets: A unified framework with application to management

Researchers in management, economics and other social sciences often find that they have very large data sets (a cross section over many firms, individuals or projects), but little theoretical knowledge of how to model the data. The common solution is to resort either to partial models that use small subsets of the data or to large linear models. In the first case, the researcher runs the risk of omitting important variables from the model. In the second case, there is a risk of specifying an inappropriate functional form of the relations among the variables. In this paper we survey, classify and apply several methodologies of generalized canonical correlation analysis (CCA) and partial canonical correlation analysis (PCCA) to estimate and analyze the relationships among several data sets. We present all the methods on a uniform basis - as optimization problems with several kinds of parameter restrictions. Further, we analyze all the methods within the convenient theoretical structure of generalized nonlinear eigenvector problems. These methods are applied to data on 310 Israeli manufacturing firms.