A Test of Multivariate Independence Based on a Single Factor Model

M. Y. Wong and D. R. Cox

Journal of Multivariate Analysis, 2001, vol. 79, issue 2, 219-225

Abstract: A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation [gamma] between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of [gamma] is appreciably more powerful than that based on r1, the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r1.

Keywords: maximum; canonical; correlation; characteristic; root; latent; variable; linear; structural; relation; maximum; likelihood; estimator; multiple; indicator (search for similar items in EconPapers)
Date: 2001
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