Cross-validation-derived Shrinkage After Estimation
Shrink regression coefficients using a Cross-validation-derived shrinkage factor.
kcrossval(dataset, model, k, nreps, sdm, int = TRUE, int.adj)
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". |
k |
the number of cross-validation folds. This number must be within the range 1 < k <= 0.5 * number of observations |
nreps |
the number of times to replicate the cross-validation 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 k-fold cross-validation to a dataset in order to derive a shrinkage factor and apply it to the regression coefficients. Data is randomly partitioned into k equally sized sets. One set 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 partitioned set is used as the validation set once, resulting in k folds. The mean of k shrinkage factors is then applied to the original regression coeffients, and the regression intercept may be re-estimated. This process is repeated nreps times and the mean of the regression coefficients is returned.
This process can currently be applied to linear or logistic regression models.
kcrossval 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 nreps cross-validation replicates. |
nFolds |
the number of cross-validation folds. |
nreps |
the number of cross-validation replicates. |
sdm |
the shrinkage design matrix used to apply the shrinkage factor(s) to the regression coefficients. |
## Example 1: Linear regression using the iris dataset ## 2-fold Cross-validation-derived shrinkage with 50 reps data(iris) iris.data <- as.matrix(iris[, 1:4]) iris.data <- cbind(1, iris.data) sdm1 <- matrix(c(0, 1, 1, 1), nrow = 1) kcrossval(dataset = iris.data, model = "linear", k = 2, nreps = 50, sdm = sdm1, int = TRUE, int.adj = TRUE) ## Example 2: logistic regression using a subset of the mtcars data ## 10-fold CV-derived shrinkage (uniform shrinkage and intercept re-estimation) data(mtcars) mtc.data <- cbind(1,datashape(mtcars, y = 8, x = c(1, 6, 9))) head(mtc.data) set.seed(321) kcrossval(dataset = mtc.data, model = "logistic", k = 10, nreps = 10)
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