# Bootstrap-derived Shrinkage After Estimation

### Description

Shrink regression coefficients using a bootstrap-derived shrinkage factor.

### Usage

1 |

### Arguments

`dataset` |
a dataset for regression analysis. Data should be in the form
of a matrix, with the outcome variable as the final column.
Application of the |

`model` |
type of regression model. Either "linear" or "logistic". |

`N` |
the number of times to replicate the bootstrapping process |

`sdm` |
a shrinkage design matrix. For examples, see |

`int` |
logical. If TRUE the model will include a regression intercept. |

`int.adj` |
logical. If TRUE the regression intercept will be re-estimated after shrinkage of the regression coefficients. |

### Details

This function applies bootstrapping to a dataset in order to derive a shrinkage factor and apply it to the regression coefficients. Regression coefficients are estimated in a bootstrap sample, and then a shrinkage factor is estimated using the input data. The mean of N shrinkage factors is then applied to the original regression coeffients, and the regression intercept may be re-estimated.

This process can currently be applied to linear or logistic regression models.

### Value

`bootval`

returns a list containing the following:

`raw.coeff` |
the raw regression model coefficients, pre-shrinkage. |

`shrunk.coeff` |
the shrunken regression model coefficients |

`lambda` |
the mean shrinkage factor over N bootstrap replicates |

`N` |
the number of bootstrap replicates |

`sdm` |
the shrinkage design matrix used to apply the shrinkage factor(s) to the regression coefficients |

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## Example 1: Linear regression using the iris dataset
data(iris)
iris.data <- as.matrix(iris[, 1:4])
iris.data <- cbind(1, iris.data)
sdm1 <- matrix(c(0, 1, 1, 1), nrow = 1)
set.seed(777)
bootval(dataset = iris.data, model = "linear", N = 200, sdm = sdm1,
int = TRUE, int.adj = TRUE)
## Example 2: logistic regression using a subset of the mtcars data
data(mtcars)
mtc.data <- cbind(1,datashape(mtcars, y = 8, x = c(1, 6, 9)))
head(mtc.data)
set.seed(777)
bootval(dataset = mtc.data, model = "logistic", N = 500)
``` |

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