Correlation Weights in Multiple Regression

Autor/inn/en	Waller, Niels G.; Jones, Jeff A.
Titel	Correlation Weights in Multiple Regression
Quelle	In: Psychometrika, 75 (2010) 1, S.58-69 (12 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0033-3123
DOI	10.1007/s11336-009-9127-y
Schlagwörter	Least Squares Statistics; Correlation; Comparative Analysis; Prediction; Multiple Regression Analysis; Theories; Evaluation Methods + Suchen Sie Ihr Suchwort? Korrelation; Vorhersage; Theory; Theorie
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 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]. (As Provided).
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Update	2017/4/10