# ols.shrink: Estimation of a Shrinkage Factor for Linear Regression In apricom: Tools for the a Priori Comparison of Regression Modelling Strategies

## Description

Estimate a shrinkage factor for shrinkage-after-estimation techniques, with application to linear regression models.

## Usage

 `1` ```ols.shrink(b, dat, sdm) ```

## Arguments

 `b` 1 x `m` matrix of regression coefficients, derived by resampling or sample splitting `dat` a `p` x `m` data matrix, where the final column is a continuous outcome variable. This dataset acts as a "test set" or "validation set". `sdm` the shrinkage design matrix. This determines the regression coefficients that will be involved in the shrinkage process.

## Details

This is an accessory function that works together with `bootval`, `splitval`, `kcrossval` and `loocval` to estimate a shrinkage factor. For further details, see References. This function should not be used directly, and instead should be called via one of the aforementioned shrinkage-after-estimation functions.

## Value

the function returns a shrinkage factor.

## Note

Currently, this function can only derive a single shrinkage factor for a given model, and is unable to estimate (weighted) predictor-specific shrinkage factors.

## References

Harrell, F. E. "Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis." Springer, (2001).

Steyerberg, E. W. "Clinical Prediction Models", Springer (2009)

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## Shrinkage design matrix examples for a model with an ## intercept and 4 predictors: ## 1. Uniform shrinkage (default design within apricomp). sdm1 <- matrix(c(0, rep(1, 4)), nrow = 1) print(sdm1) ## 2. Non-uniform shrinkage; 1 shrinkage factor applied only to the ## first two predictors sdm2 <- matrix(c(0, 1, 1, 0, 0), nrow = 1) print(sdm2) ```

apricom documentation built on May 2, 2019, 6:21 a.m.