Cross-validation for Generalized Linear Models
This function calculates the estimated K-fold cross-validation prediction error for generalized linear models.
cv.glm(data, glmfit, cost, K)
data |
A matrix or data frame containing the data. The rows should be cases and the columns correspond to variables, one of which is the response. |
glmfit |
An object of class |
cost |
A function of two vector arguments specifying the cost function for the
cross-validation. The first argument to |
K |
The number of groups into which the data should be split to estimate the
cross-validation prediction error. The value of |
The data is divided randomly into K groups. For each group the generalized
linear model is fit to data omitting that group, then the function cost
is applied to the observed responses in the group that was omitted from the fit
and the prediction made by the fitted models for those observations.
When K is the number of observations leave-one-out cross-validation is used
and all the possible splits of the data are used. When K is less than
the number of observations the K splits to be used are found by randomly
partitioning the data into K groups of approximately equal size. In this
latter case a certain amount of bias is introduced. This can be reduced by
using a simple adjustment (see equation 6.48 in Davison and Hinkley, 1997).
The second value returned in delta is the estimate adjusted by this method.
The returned value is a list with the following components.
call |
The original call to |
K |
The value of |
delta |
A vector of length two. The first component is the raw cross-validation estimate of prediction error. The second component is the adjusted cross-validation estimate. The adjustment is designed to compensate for the bias introduced by not using leave-one-out cross-validation. |
seed |
The value of |
The value of .Random.seed is updated.
Breiman, L., Friedman, J.H., Olshen, R.A. and Stone, C.J. (1984) Classification and Regression Trees. Wadsworth.
Burman, P. (1989) A comparative study of ordinary cross-validation, v-fold cross-validation and repeated learning-testing methods. Biometrika, 76, 503–514
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Efron, B. (1986) How biased is the apparent error rate of a prediction rule? Journal of the American Statistical Association, 81, 461–470.
Stone, M. (1974) Cross-validation choice and assessment of statistical predictions (with Discussion). Journal of the Royal Statistical Society, B, 36, 111–147.
# leave-one-out and 6-fold cross-validation prediction error for # the mammals data set. data(mammals, package="MASS") mammals.glm <- glm(log(brain) ~ log(body), data = mammals) (cv.err <- cv.glm(mammals, mammals.glm)$delta) (cv.err.6 <- cv.glm(mammals, mammals.glm, K = 6)$delta) # As this is a linear model we could calculate the leave-one-out # cross-validation estimate without any extra model-fitting. muhat <- fitted(mammals.glm) mammals.diag <- glm.diag(mammals.glm) (cv.err <- mean((mammals.glm$y - muhat)^2/(1 - mammals.diag$h)^2)) # leave-one-out and 11-fold cross-validation prediction error for # the nodal data set. Since the response is a binary variable an # appropriate cost function is cost <- function(r, pi = 0) mean(abs(r-pi) > 0.5) nodal.glm <- glm(r ~ stage+xray+acid, binomial, data = nodal) (cv.err <- cv.glm(nodal, nodal.glm, cost, K = nrow(nodal))$delta) (cv.11.err <- cv.glm(nodal, nodal.glm, cost, K = 11)$delta)
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