I want to use Ridge Regression to find out whether my estimated coefficients in a linear regression are stable (as the variance inflation factors tell me that there is multicollinearity). But I'm not sure which lambda values, i. e. multiplication factors for the variances compared to the covariances of the predictors, I should specify using the MASS::lm.ridge function. Is lambda=seq(0,100,by=1) and looking at the first ten rows of the ridge estimates a good criterion?
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Perhaps ridge regression has been misrepresented to you. It isn't a diagnostic tool for OLS, but a model unto itself that's often used in place of OLS when predictive accuracy is of interest. Generally, ridge models yield more accurate predictions than the corresponding OLS models.
answered Oct 31, 2016 at 20:08
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$\begingroup$ I know that ridge regression can be used to get (not BLUE) coefficient estimates. But, in my opinion, if the coefficients estimated by the ridge regression don't change with increasing lambda values compared with the OLS estimates, then this should indicate that the OLS estimates are stable. I.e. the multicollinearity didn't lead to "wrong" OLS coefficients. $\endgroup$ Sep 21, 2017 at 20:32
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3$\begingroup$ @statmerkur Happy almost-birthday to your question. If you're concerned with the stability or sensitivity of the coefficient estimates, there are more direct ways to examine such issues, such as constructing confidence intervals, perturbing the data, bootstrapping, etc. $\endgroup$ Sep 21, 2017 at 21:15
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$\begingroup$ I thought the
MASS::lm.ridgefunction would be a good tool for diagnosing my estimates as it sequentially increases the variances compared to the covariances of the predictors. But I agree that constructing confidence intervals via bootstrapping would be another option. $\endgroup$ Sep 21, 2017 at 21:42