LOOCV {bestglm} | R Documentation |

## 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

### 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)
```

*bestglm*version 0.37.3 Index]