Estimation of the ridge constant: an approach based on the condition index

Conference · Sat Jan 01 04:00:00 EST 1983

OSTI ID:5807413

Carnes, B. A.; Ginevan, M. E.; Eychner, D. M.

A Monte Carlo simulation was conducted to evaluate the response of ridge regression solutions to increasing collinearity. Specifically, the magnitude of the ridge constant was sensitive to variability in the response vector while appearing insensitive to collinearity. The insensitivity to collinearity was especially apparent when the response vector was oriented toward a minor dimension in the structure of the predictor variables. Limit arguments indicated that, in the minor dimension case, the increasing magnitude of the inner product of the least squares coefficient vector in the denominator of the optimum estimate for the ridge constant was responsible for the insensitivity to collinearity. Since ridge regression was proposed to deal with collinearity, this behavior suggests a defect in the generally used estimate for the optimum ridge constant. To solve this problem, we propose a condition index estimate for the ridge constant based on the eigenvalues of the augmented X'X matrix; this approach ensures sensitivity to collinearity and insensitivity to the behavior of the response vector.

• Research Organization: Argonne National Lab., IL (USA)
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 5807413
• Report Number(s): CONF-830899-3; ON: DE83017955
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
DATA ANALYSIS
LIMITING VALUES
MATHEMATICS
MONTE CARLO METHOD
REGRESSION ANALYSIS
SIMULATION
STATISTICS