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Tracing ridge regression coefficients

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Ridge regression is a parameter estimation method used to address the collinearity problem frequently arising in multiple linear regressions. The methodology defines a class of estimators indexed by a non‐negative scalar parameter, k. When utilizing ridge regression, the analyst eventually chooses a particular value of k which, in turn, uniquely determines the regression parameter estimates within the ridge class. Many such methods of determination, both deterministic and stochastic, have been proposed and evaluated in the literature. A plot of the ridge regression estimates as a function of k, the so‐called ridge trace, is often used in the selection process. In this article, one such criterion, the square of the correlation coefficient of the actual dependent variable and its predicted values, is examined. It can be used, along with a ridge trace and other quantitative measures, as another important tradeoff between using ordinary least squares estimates and estimates from the ridge class. WIREs Comp Stat 2010 2 695–703 DOI: 10.1002/wics.126

Figure 1.

Ridge regression displays for the mortality versus N0x and HC pollution potential example: top is ridge trace; bottom is R2 and \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$[\widehat{\beta} (k)]^{\prime}[\widehat{\beta}(k)]/50$ \end{document}.

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