ERIC Number: EJ878835
Record Type: Journal
Publication Date: 2010-Mar
Abstractor: As Provided
Reference Count: 0
Correlation Weights in Multiple Regression
Waller, Niels G.; Jones, Jeff A.
Psychometrika, v75 n1 p58-69 Mar 2010
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 R[superscript 2] (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, R[subscript xx], and (2) the orientation of the correlation weights to the latent vectors of R[subscript xx].
Descriptors: Least Squares Statistics, Correlation, Comparative Analysis, Prediction, Multiple Regression Analysis, Theories, Evaluation Methods
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
Authoring Institution: N/A