We will use the gala dataset in the faraway package to demonstrate leave-one-out cross-validation. In this type of validation, one case of the data set is left out and used as the testing set and the remaining data are used as the training set for the regression. This process is repeated until each case in the data set has served as the testing set.
The key concept in creating the iterative leave-one-out process in R is creating a column vector c1 and attaching it to gala as shown below, This allows us to uniquely identify the row that is to be left out in each iteration.
> library(faraway)
> gala[1:3,]
Species Endemics Area Elevation Nearest Scruz Adjacent
Baltra 58 23 25.09 346 0.6 0.6 1.84
Bartolome 31 21 1.24 109 0.6 26.3 572.33
Caldwell 3 3 0.21 114 2.8 58.7 0.78
>c1<-c(1:30)
> gala2<-cbind(gala,c1)
> gala2[1:3,]
Species Endemics Area Elevation Nearest Scruz Adjacent c1
Baltra 58 23 25.09 346 0.6 0.6 1.84 1
Bartolome 31 21 1.24 109 0.6 26.3 572.33 2
> diff1<-numeric(30)
> for(i in 1:30){model1<-lm(Species~Endemics+Area+Elevation,subset=(c1!=i),data=gala2)
+ specpr<-predict(model1,list(Endemics=gala2[i,2],Area=gala2[i,3],Elevation=gala2[i,4]),data=gala2)
+ diff1[i]<-gala2[i,1]-specpr }
>summ1<-numeric(1)
>summ1=0
> for(i in 1:30){summ1<-summ1+diff1[i]^2}
> summ1
[1] 259520.5
The variable summ1 holds the value of the PRESS statistic.
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