loocv: Leave One Out Cross Validation (LOOCV)
In MarloesEeftens/LUR: A nostalgic package for land use regression ESCAPE-style.

Description Usage Arguments Value Note Author(s) Examples

This function takes a dataframe with n sites and the predictors you specified, and adds a column called "loocv" containing the predicted value for i, had the model been fit on the other n-1 sites and applied to site i.

1	loocv(x,dependent,predictors,export_coefficients=FALSE)

`x`	An R dataframe which includes a dependent variable and predictors.
`dependent`	The name of the variable which the model aims to estimate.
`predictors`	A vector of strings, including the names of all the predictor variables which should be considered for inclusion in your LUR model.
`export_coefficients`	Defaults to FALSE: If set to TRUE, this option will add one column to the output dataframe for each fixed predictor that was included. For a given predictor "ABC", the column will be named "ABC_coeff" and will have the value of the coefficient as calculated for all observations except the one being estimated.

The function returns the dataframe x, with an additional column names "loocv" which contains the predicted value for i, fitted on the entire dataset EXCEPT observation i.

While validation of any model on an independent, held-out test set is always preferable, this is not always realistic if the number of training sites is small.

Marloes Eeftens, marloes.eeftens@swisstph.ch

#Let's assume we did a monitoring campaign with 20 sites and 80 predictors
nr_sites<-20
nr_predictors<-80

#Generate some normally distributed air pollution data:
NO2_conc<-rnorm(n=nr_sites,m=25,sd=8)
#And (independently) some normally distributed predictor data:
predictors<-as.data.frame(matrix(rnorm(n=nr_sites*nr_predictors,m=0,sd=1),nrow=nr_sites))
names(predictors)<-paste0("var_",seq(1:nr_predictors))
my_LUR_data<-cbind(NO2_conc,predictors)
#Find the best predictors for your model:
LUR_fit<-good_old_stepwise(x=my_LUR_data,dependent="NO2_conc",predictors=paste0("var_",seq(1:nr_predictors)))
#Sometimes LUR_fit will give you a model, sometimes not...
LUR_fit
#Did you get one? Great!
#Not so lucky? Not to worry! This is random data, not real life. Simply go up to the blank line, generate some more air pollution data, some new predictors, and re-run.

#The following only works if a model was actually possible...
#Extract the selected predictors from the model:
selected_preds<-c(names(LUR_fit$coefficients)[-1])
#Cross-validate:
LUR_data_loocv<-loocv(x=my_LUR_data,dependent="NO2_conc",predictors=selected_preds)
#Calculate the cross-validated R squared:
cor(LUR_data_loocv$NO2_conc,LUR_data_loocv$loocv)^2
#Plot measured concentrations against loocv predictions:
plot(x=LUR_data_loocv$NO2_conc,y=LUR_data_loocv$loocv)