An explanation of the use of principal-components analysis to detect and correct for multicollinearity

Abstract Multicollinearity can be a serious statistical problem in data analysis in which the contribution of each individual risk factor is being evaluated. Symptoms, effects and techniques that are useful in detecting the presence of multicollinearity in a data base are discussed. The mathematical basis of the principal-components analysis technique for detecting, quantifying, and adjusting the regression coefficients for the effects of multicollinearity in a data base was demonstrated.

[1]  Gary Smith,et al.  A Critique of Some Ridge Regression Methods , 1980 .

[2]  R. L. Mason,et al.  Selecting principal components in regression , 1985 .

[3]  J. T. Webster,et al.  Latent Root Regression Analysis , 1974 .

[4]  M. Goldstein,et al.  Multivariate Analysis: Methods and Applications , 1984 .

[5]  W. Massy.  Principal Components Regression in Exploratory Statistical Research , 1965 .

[6]  E. Pedhazur.  Multiple Regression in Behavioral Research: Explanation and Prediction , 1982 .

[7]  J. T. Webster,et al.  An Analytic Variable Selection Technique for Principal Component Regression , 1977 .

[8]  G. Judge,et al.  The Theory and Practice of Econometrics , 1981 .

[9]  B. Carnes,et al.  The Use of Regression for Detecting Competition with Multicollinear Data , 1988 .

[10]  R. C. Hill,et al.  Multicollinearity and the value of a priori information , 1979 .

[11]  Hrishikesh D. Vinod,et al.  Recent Advances in Regression Methods. , 1983 .

[12]  V. Clark,et al.  Computer-aided multivariate analysis , 1991 .

[13]  Mark J. Schervish,et al.  A Review of Multivariate Analysis , 1987 .

[14]  Robert L. Mason,et al.  Biased Estimation in Regression: An Evaluation Using Mean Squared Error , 1977 .

[15]  Douglas M. Hawkins,et al.  On the Investigation of Alternative Regressions by Principal Component Analysis , 1973 .

[16]  T. Fomby,et al.  MSE evaluation of ridge estimators based on stochastic prior information , 1977 .

[17]  D. Conniffe,et al.  A Critical View of Ridge Regression , 1973 .

[18]  S. Chatterjee,et al.  Regression Analysis by Example , 1979 .

[19]  Robert L. Mason,et al.  Regression Analysis and Its Application: A Data-Oriented Approach. , 1982 .

[20]  C T Scialfa,et al.  Problems with step-wise regression in research on aging and recommended alternatives. , 1987, Journal of gerontology.

[21]  J. T. Webster,et al.  Regression analysis and problems of multicollinearity , 1975 .

[22]  Michael H. Kutner.  Applied Linear Statistical Models , 1974 .

[23]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .