shrink (Q35861)

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.