Correlation weights in multiple regression

Niels G. Waller, Jeff A. Jones

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights. We then derive the least squares weights (for any set of predictors) that yield the largest drop in R2 (the coefficient of determination) when switching to correlation weights. Our findings suggest that two characteristics of a model/data combination are especially important in determining the effectiveness of correlation weights: (1) the condition number of the predictor correlation matrix, Rxx, and (2) the orientation of the correlation weights to the latent vectors of Rxx.

Original languageEnglish (US)
Pages (from-to)58-69
Number of pages12
JournalPsychometrika
Volume75
Issue number1
DOIs
StatePublished - Mar 1 2010

Keywords

  • Alternate weights
  • Correlation weights
  • Multiple regression
  • Parameter sensitivity

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