Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function estimates the Dissimilarity Index (DI) and the derived Area of Applicability (AOA) of spatial prediction models by considering the distance of new data (i.e. a Raster Stack of spatial predictors used in the models) in the predictor variable space to the data used for model training. Predictors can be weighted based on the internal variable importance of the machine learning algorithm used for model training. The AOA is derived by applying a threshold on the DI which is the (outlier-removed) maximum DI of the cross-validated training data.

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`newdata` |
A RasterStack, RasterBrick or data.frame containing the data the model was meant to make predictions for. |

`model` |
A train object created with caret used to extract weights from (based on variable importance) as well as cross-validation folds |

`cl` |
A cluster object e.g. created with doParallel. Should only be used if newdata is large. |

`train` |
A data.frame containing the data used for model training. Only required when no model is given |

`weight` |
A data.frame containing weights for each variable. Only required if no model is given. |

`variables` |
character vector of predictor variables. if "all" then all variables of the model are used or if no model is given then of the train dataset. |

`folds` |
Numeric or character. Folds for cross validation. E.g. Spatial cluster affiliation for each data point. Should be used if replicates are present. Only required if no model is given. |

`returnTrainDI` |
A logical: should the DI value of the cross-validated training data be returned as a attribute? |

The Dissimilarity Index (DI) and the corresponding Area of Applicability (AOA) are calculated. If variables are factors, dummy variables are created prior to weighting and distance calculation.

Interpretation of results: If a location is very similar to the properties of the training data it will have a low distance in the predictor variable space (DI towards 0) while locations that are very different in their properties will have a high DI. See Meyer and Pebesma (2020) for the full documentation of the methodology.

A RasterStack or data.frame with the DI and AOA AOA has values 0 (outside AOA) and 1 (inside AOA).

If classification models are used, currently the variable importance can only be automatically retrieved if models were traiend via train(predictors,response) and not via the formula-interface. Will be fixed.

Hanna Meyer

Meyer, H., Pebesma, E. (2020): Predicting into unknown space? Estimating the area of applicability of spatial prediction models. https://arxiv.org/abs/2005.07939

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## Not run:
library(sf)
library(raster)
library(caret)
library(viridis)
library(latticeExtra)
# prepare sample data:
dat <- get(load(system.file("extdata","Cookfarm.RData",package="CAST")))
dat <- aggregate(dat[,c("VW","Easting","Northing")],by=list(as.character(dat$SOURCEID)),mean)
pts <- st_as_sf(dat,coords=c("Easting","Northing"))
pts$ID <- 1:nrow(pts)
set.seed(100)
pts <- pts[1:30,]
studyArea <- stack(system.file("extdata","predictors_2012-03-25.grd",package="CAST"))[[1:8]]
trainDat <- extract(studyArea,pts,df=TRUE)
trainDat <- merge(trainDat,pts,by.x="ID",by.y="ID")
# visualize data spatially:
spplot(scale(studyArea))
plot(studyArea$DEM)
plot(pts[,1],add=TRUE,col="black")
# train a model:
set.seed(100)
variables <- c("DEM","NDRE.Sd","TWI")
model <- train(trainDat[,which(names(trainDat)%in%variables)],
trainDat$VW, method="rf", importance=TRUE, tuneLength=1,
trControl=trainControl(method="cv",number=5,savePredictions=T))
print(model) #note that this is a quite poor prediction model
prediction <- predict(studyArea,model)
plot(varImp(model,scale=FALSE))
#...then calculate the AOA of the trained model for the study area:
AOA <- aoa(studyArea,model)
spplot(AOA$DI, col.regions=viridis(100),main="Dissimilarity Index")
#plot predictions for the AOA only:
spplot(prediction, col.regions=viridis(100),main="prediction for the AOA")+
spplot(AOA$AOA,col.regions=c("grey","transparent"))
####
# Calculating the AOA might be time consuming. Consider running it in parallel:
####
library(doParallel)
library(parallel)
cl <- makeCluster(4)
registerDoParallel(cl)
AOA <- aoa(studyArea,model,cl=cl)
####
#The AOA can also be calculated without a trained model.
#All variables are weighted equally in this case:
####
AOA <- aoa(studyArea,train=trainDat,variables=variables)
spplot(AOA$DI, col.regions=viridis(100),main="Dissimilarity Index")
spplot(AOA$AOA,main="Area of Applicability")
## End(Not run)
``` |

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