Description Usage Arguments Details Value Examples

Shrink regression coefficients using a bootstrap-derived shrinkage factor.

1 |

`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. |

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.

`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 |

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)
``` |

```
$raw.coeff
[,1]
-0.2403074
Sepal.Length -0.2072661
Sepal.Width 0.2228285
Petal.Length 0.5240831
$shrunk.coeff
[,1]
[1,] -0.2403263
[2,] -0.2072688
[3,] 0.2228315
[4,] 0.5240900
$lambda
[1] 1.000013
$N
[1] 200
$sdm
[,1] [,2] [,3] [,4]
[1,] 0 1 1 1
mpg wt am vs
[1,] 1 21.0 2.620 1 0
[2,] 1 21.0 2.875 1 0
[3,] 1 22.8 2.320 1 1
[4,] 1 21.4 3.215 0 1
[5,] 1 18.7 3.440 0 0
[6,] 1 18.1 3.460 0 1
$raw.coeff
[,1]
2.396504
mpg 0.421866
wt -2.948354
am -4.868638
$shrunk.coeff
[,1]
[1,] 1.1664241
[2,] 0.2303914
[3,] -1.6101684
[4,] -2.6588825
$lambda
[1] 0.5461245
$N
[1] 500
$sdm
[,1] [,2] [,3] [,4]
[1,] 0 1 1 1
There were 50 or more warnings (use warnings() to see the first 50)
```

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