ols.shrink {apricom} R Documentation

## Estimation of a Shrinkage Factor for Linear Regression

### Description

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

### Usage

```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

```## 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)

```

[Package apricom version 1.0.0 Index]