bootval: Bootstrap-derived Shrinkage After Estimation

In apricom: Tools for the a Priori Comparison of Regression Modelling Strategies

Description

Shrink regression coefficients using a bootstrap-derived shrinkage factor.

Usage

bootval(dataset, model, N, sdm, int = TRUE, int.adj)

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 datashape function beforehand is recommended, especially if categorical predictors are present. For regression with an intercept included a column vector of 1s should be included before the dataset (see examples).
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 ols.shrink
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

## 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)

Example output

$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

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