6533b81ffe1ef96bd1277ceb
RESEARCH PRODUCT
On the calculation of derived variables in the analysis of multivariate responses
Nanny WermuthDavid Coxsubject
canonical analysisStatistics and ProbabilityMultivariate statisticsPure mathematicsNumerical AnalysisMultivariate analysisBasis (linear algebra)conditional independencederived variableCanonical analysisCombinatoricsgraphical chain modelTransformation (function)multivariate linear modelConditional independenceLinear regressionStatistics Probability and UncertaintyRandom variableMathematicsdescription
AbstractThe 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-07-01 | Journal of Multivariate Analysis |