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On the calculation of derived variables in the analysis of multivariate responses

Author

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  • Cox, D. R.
  • Wermuth, Nanny

Abstract

The multivariate regression of a p - 1 vector Y of random variables on a q - 1 vector X of explanatory variables is considered. It is assumed that linear transformations of the components of Y can be the basis for useful interpretation whereas the components of X have strong individual identity. When p >= q a transformation is found to a new q - 1 vector of responses Y* such that in the multiple regression of, say, Y1* on X, only the coefficient of X1 is nonzero, i.e. such that Y1* is conditionally independent of X2, ..., Xq, given X1. Some associated inferential procedures are sketched. An illustrative example is described in which the resulting transformation has aided interpretation.

Suggested Citation

  • Cox, D. R. & Wermuth, Nanny, 1992. "On the calculation of derived variables in the analysis of multivariate responses," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 162-170, July.
    • Handle: RePEc:eee:jmvana:v:42:y:1992:i:1:p:162-170
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    Cited by:

    1. Wermuth, Nanny & Cox, D. R., 1995. "Derived variables calculated from similar joint responses: some characteristics and examples," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 223-234, February.

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