Alternatives to least squares in multiple linear regression to predict production traits

Summary The objectives of this study were to describe and compare the efficacy of least-squares, ridge-and principal-components-regression methodology for analysis of data for which multicollinearity existed among regressor variables. A data set composed of calfhood traits (regressor variables) and first-progeny weaning weight (the dependent variable) of 771 Angus females was used. The statistics variance-inflation factors, eigenvalues, condition numbers and variance proportions were used in diagnosing multicollinearity. Although biased, the regression-coefficient estimates produced by ridge and principal components regression had smaller variances than estimates obtained from least squares. Between the two alternatives to least squares, ridge regression produced better results than principal-components regression. Ridge and least-squares regression produced similar regression-coefficient estimates, prediction sum of squares (PRESS-like) statistics and, to a lesser extent, conceptual predictive criteria (Cp-like) statistics. For prediction, the performance of least-squares and ridge-regression models was very similar. Zusammenfassung Alternativen zu Minimum-Quadrat bei multipler linearer Regression zur Voraussage von Leistungsmerkmalen Die Untersuchung bezieht auf Beschreibung und Vergleich der Wirksamkeit von Minimum-Quadrat, Ridge und Hauptkomponentenregressionsmethodik zur Analyse von Daten mit Multicollinearitat zwischen Regressorvariablen. Das Datenmaterial aus Kalberleistungen (Regressorvariable) und Absatzgewicht der ersten Nachkommen (abhangige Variable) von 771 Anguskuhen wurde verwendet. Die statistischen Grosen Varianz inflationsfaktoren, Eigenwerte, Bedingungszahl und Varianzverhaltnisse wurden zur Diagnose der Multicollinearitat verwendet. Obwohl verzerrt, haben die Regressionskoeffizientenschatzungen aus Ridge-und Hauptkomponentenregression geringere Varianzen als Minimum-Quadratschatzungen. Von den zwei Alternativen hat Ridge-Regression bessere Resultate als Hauptkomponentenregression ergeben. Ridge und Miniumum-Quadratregression haben ahnliche Regressionskoeffizienten ergeben, Schatzungsquadratsumme (PRESS-ahnlich), Statistik und, in einem geringeren Ausmas, Schatzungskriterien (Cp-ahnliche)-statistik. Im Hinblich auf Voraussage war die Leistung der Minimum-Quadrat-und Ridge-Regressions-Modelle sehr anlich.

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