I am new to ridge regression. When I applied linear ridge regression, I got the following results:
>myridge = lm.ridge(y ~ ma + sa + lka + cb + ltb , temp, lamda = seq(0,0.1,0.001))
> select(myridge)
modified HKB estimator is 0.5010689
modified L-W estimator is 0.3718668
smallest value of GCV at 0
Questions:
GCV? myridge?You might be better off with the penalized package or the glmnet package; both implement lasso or elastic net so combines properties of the lasso (feature selection) and ridge regression (handling collinear variables). penalized also does ridge. These two packages are far more fully featured than lm.ridge() in the MASS package for such things.
Anyway, $\lambda = 0$ implies zero penalty, hence the least squares estimates are optimal in the sense that they had the lowest GCV (generalised cross validation) score. However, you may not have allowed sufficiently large a penalty; in other words, the least squares estimates were optimal of the small set of of $\lambda$ values you looked at. Plot the ridge path (values of the coefficients as a function of $\lambda$ and see if the traces have stabilised or not. If not, increase the range of $\lambda$ values evaluated.
The reason you are getting a 0 GCV is because you used:
myridge = lm.ridge(y ~ ma + sa + lka + cb + ltb , temp, lamda = seq(0,0.1,0.001))
instead of
myridge = lm.ridge(y ~ ma + sa + lka + cb + ltb , temp, lambda = seq(0,0.1,0.001))
