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A Test of Multivariate Independence Based on a Single Factor Model

Author

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  • Wong, M. Y.
  • Cox, D. R.

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.

Suggested Citation

  • Wong, M. Y. & Cox, D. R., 2001. "A Test of Multivariate Independence Based on a Single Factor Model," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 219-225, November.
    • Handle: RePEc:eee:jmvana:v:79:y:2001:i:2:p:219-225
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    References listed on IDEAS

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    1. Yuan, Ke-Hai & Bentler, Peter M., 1999. "On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 107-113, April.
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