Global, Parameterwise and Joint Shrinkage Factor Estimation
Description
The predictive value of a statistical model can often be improved
by applying shrinkage methods. This can be achieved, e.g., by regularized
regression or empirical Bayes approaches. Various types of shrinkage factors can
also be estimated after a maximum likelihood. While global shrinkage modifies
all regression coefficients by the same factor, parameterwise shrinkage factors
differ between regression coefficients. With variables which are either highly
correlated or associated with regard to contents, such as several columns of a
design matrix describing a nonlinear effect, parameterwise shrinkage factors are
not interpretable and a compromise between global and parameterwise shrinkage,
termed 'joint shrinkage', is a useful extension. A computational shortcut to
resampling-based shrinkage factor estimation based on DFBETA residuals can be
applied. Global, parameterwise and joint shrinkage for models fitted by lm(),
glm(), coxph(), or mfp() is available.