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Shrinkage of regression coefficients in statistical modeling can be used to reduce overestimation of some effects caused by variable selection. While global shrinkage modifies all regression coefficients by the same factor, parameterwise shrinkage factors differ between regression coefficients. With highly correlated or semantically related variables, such as several columns of a design matrix describing a non-linear effect, a compromise between global, and parameterwise shrinkage, termed 'joint shrinkage', is a useful extension of the present methodology.

Shrinkage factors are often estimated using leave-one-out resampling. As an alternative a computationally simple shortcut to resampling-based shrinkage factor estimation is based on DFBETA residuals, which are readily available in most standard software packages for regression analyses.

The R package shrink implements these existing and new approaches to post-estimation shrinkage methods for models fitted by lm, glm, coxph and mfp. It also works for models incorporating restricted cubic splines computed with the rcs function from the rms library.

Author(s): Daniela Dunkler and Georg Heinze
Maintainer: Daniela Dunkler (daniela.dunkler @


Dunkler D, Sauerbrei W, Heinze G (2016): "Global, parameterwise and joint shrinkage factor estimation." Journal of Statistical Software 2016: 69:1-19

Sauerbrei W (1999): "The use of resampling methods to simplify regression models in medial statistics." Applied Statistics  48(3):313-329.

Verweij P, van Houwelingen J (1993): "Cross-validation in survival analysis." Statistics in Medicine 12(24):2305-2314.


The R package
shrink  is available under a General Public License Version 3 (GPL-3) on CRAN.