Shrinkage

Shrinkage reflects the bias found between sample statistics and inferred population parameters. Multiple regression generally overestimates population values from sample multiple correlation coefficients (R) and coefficients of multiple determination (R2). A common adjustment method for overinflation is to use the shrunken or adjusted R2. The adjusted R2 accounts for the amount of shrinkage between the sample R2 and the population squared multiple correlation (ρ2). Similarly, results from a model fitted in one sample are often an overestimate of how it would fit using a separate sample from the same population (i.e., a cross-validation sample), and such results also often need to be adjusted for shrinkage.

This entry begins by explaining why regression overestimates the population parameters. Next, the entry provides an example of shrinkage and discusses ...