LOOCV {bestglm}

Leave-one-out cross-validation

Description

An observation is removed and the model is fit the the remaining data and this fit used to predict the value of the deleted observation. This is repeated, n times, for each of the n observations and the mean square error is computed.

Usage

LOOCV(X, y)

Arguments

X

training inputs

y

training output

Details

LOOCV for linear regression is exactly equivalent to the PRESS method suggested by Allen (1971) who also provided an efficient algorithm.

Value

Vector of two components comprising the cross-validation MSE and its sd based on the MSE in each validation sample.

Author(s)

A.I. McLeod and C. Xu

References

Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning. 2nd Ed.

Allen, D.M. (1971). Mean Square Error of Prediction as a Criterion for Selecting Variables. Technometrics, 13, 469 -475.

See Also

bestglm, CVd, CVDH, CVHTF

Examples

#Example. Compare LOO CV with K-fold CV.
#Find CV MSE's for LOOCV and compare with K=5, 10, 20, 40, 50, 60
#Takes about 30 sec
## Not run: 
 data(zprostate)
 train<-(zprostate[zprostate[,10],])[,-10]
 X<-train[,1:2]
 y<-train[,9]
 CVLOO<-LOOCV(X,y)
 KS<-c(5,10,20,40,50,60)
 nKS<-length(KS)
 cvs<-numeric(nKS)
 set.seed(1233211231)
 for (iK in 1:nKS)
    cvs[iK]<-CVDH(X,y,K=KS[iK],REP=10)[1]
 boxplot(cvs)
 abline(h=CVLOO, lwd=3, col="red")
 title(sub="Boxplot of CV's with K=5,10,20,40,50,60 and LOO CV in red")
 
## End(Not run)