Ridge regression and MSE
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Hi I am comparing MSE of OLS and ridge regression in order to determine which estimate is best. Is there some command or procedure in MATLAB how to get MSE of the ridge estimate??
Thanks
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John D'Errico
le 21 Mar 2011
Well, since MSE is simply the mean of the squares of the errors...
MSE = mean((y-yhat).^2);
Won't that suffice?
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Richard Willey
le 21 Mar 2011
Use the "scaled" option to restore the coefficient estimates to the scale of the original data.
You can then use b to estimate yhat.
b = ridge(y,X,k,scaled) uses the {0,1}-valued flag scaled to determine if the coefficient estimates in b are restored to the scale of the original data
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pemfir
le 11 Déc 2011
there are 2 version of MSE MSE = SSE/(n-q) unlike what John D'Errico said this is not simply the mean of errors. notice the denominator. it is n-q where q is the number of parameters in the model.
the second MSE which you should use (sometimes people use "mse" lower case to differentiate it with the first MSE) is MSE = bias^2 + var Since ridge regression tries to reduce Var by introducing bias, the second version is what you need to use.
the expression for it is a bit long, but you can find it easily in regression books such as "introduction to linear regression analysis" by Montgomery in the chapter on "multicollinearity"
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