ERIC Number: EJ863077
Record Type: Journal
Publication Date: 2009-Dec
Abstractor: As Provided
Reference Count: 0
Locating the Extrema of Fungible Regression Weights
Waller, Niels G.; Jones, Jeff A.
Psychometrika, v74 n4 p589-602 Dec 2009
In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of "fungible weights" (Waller, Psychometrica, "in press") that yields identical "SSE" (sum of squared errors) and R[superscript 2] values. When the R[superscript 2] using the alternate weights is a fixed value, fungible weights ("a[subscript i]") that yield the maximum or minimum cosine with an OLS weight vector ("b") are called "fungible extrema." We describe two methods for locating fungible extrema and we report "R" code (R Development Core Team, "2007") for one of the methods. We then describe a new approach for populating a class of fungible weights that is derived from the geometry of alternate regression weights. Finally, we illustrate how fungible weights can be profitably used to gauge parameter sensitivity in linear models by locating the fungible extrema of a regression model of executive compensation (Horton & Guerard, "Commun. Stat. Simul. Comput." 14:441-448, 1985).
Descriptors: Multiple Regression Analysis, Predictor Variables, Algebra, Geometric Concepts, Weighted Scores, Models
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Authoring Institution: N/A