A Test of Multivariate Independence Based on a Single Factor Model

✍ Scribed by M.Y. Wong; D.R. Cox

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 95 KB
• Volume: 79
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2000.1969

✦ Synopsis

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 # 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 # is appreciably more powerful than that based on r 1 , 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 r 1 .