Leaveoneout Crossvalidationderived Shrinkage
Description
Shrink regression coefficients using a shrinkage factor derived using leaveoneout crossvalidation.
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". 
nreps 
the number of times to replicate the crossvalidation process. 
sdm 
a shrinkage design matrix. 
int 
logical. If TRUE the model will include a regression intercept. 
int.adj 
logical. If TRUE the regression intercept will be reestimated after shrinkage of the regression coefficients. 
Details
This function applies leaveoneout crossvalidation to a dataset in order to derive a shrinkage factor and apply it to the regression coefficients. One row of the data is used as a validation set, while the remaining data is used as a training set. Regression coefficients are estimated in the training set, and then a shrinkage factor is estimated using the validation set. This process is repeated so that each data row is used as the validation set once. The mean of the shrinkage factors is then applied to the original regression coeffients, and the regression intercept may be reestimated. This process may be repeated nreps times but each rep should yield the same shrunken coefficients.
This process can currently be applied to linear or logistic regression models.
Value
loocval
returns a list containing the following:
raw.coeff 
the raw regression model coefficients, preshrinkage. 
shrunk.coeff 
the shrunken regression model coefficients. 
lambda 
the mean shrinkage factor over nreps crossvalidation replicates. 
nreps 
the number of crossvalidation replicates. 
sdm 
the shrinkage design matrix used to apply the shrinkage factor(s) to the regression coefficients. 
Note
Warning: this method is not recommended for use in practice. Due to the high variance and inherent instability of leaveoneout methods the value of the shrinkage factor may be extreme.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## Example 1: Linear regression using the iris dataset
## Leaveoneout crossvalidationderived shrinkage
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(123)
loocval(dataset = iris.data, model = "linear", sdm = sdm1,
int = TRUE, int.adj = TRUE)
## Example 2: logistic regression using a subset of the mtcars data
## Leaveoneout crossvalidationderived shrinkage
data(mtcars)
mtc.data < cbind(1,datashape(mtcars, y = 8, x = c(1, 6, 9)))
head(mtc.data)
set.seed(123)
loocval(dataset = mtc.data, model = "logistic")
