predictNaive: Naive Temporal Predictions
In SpatioTemporal: Spatio-Temporal Model Estimation

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

Computes naive predictions that are based on a few sites. These predictions can then be used, e.g. in summary.predCVSTmodel, to evaluate how much better the spatial-temporal model performs compared to simple (temporal) predictions.
The function requires one of location and type to be specified, if both are given location will be used over type. If type is given locations such that
as.character(STmodel$locations$type) %in% type
will be used.

1	predictNaive(STmodel, locations = NULL, type = NULL)

`STmodel`	`STmodel` object for which to compute simple predictions.
`locations`	Locations on which to base the naive predictions.
`type`	The type of sites to base the predictions on, uses the (optional) field `STmodel$locations$type`.

Given a set of locations the function computes 4 sets of naive prediction for the observations in STmodel:

smooth.fixed: The smooth trend in STmodel$trend is fit to all observations at the sites in locations using a linear regression. The resulting smooth is used as a naive prediction for all locations.
avg.fixed: The temporal average over sites in locations is used as a naive prediction.
smooth.closest.fixed: This fits the smooth trend in STmodel$trend to each site in locations; using the smooth at the closest fixed site as a naive prediction.
closest.fixed: This uses the observations at the closest site in locations to predict observations at all other sites.

A list with items:

`pred`	A (number of observations) - by - (6) data.frame containing the four naive predictions described under `details`, along with dates and IDs.
`locations`	The locations used for the naive predictions.

Johan Lindstrom

Other STmodel functions: createCV, createDataMatrix, createSTmodel, dropObservations, estimateBetaFields, loglikeSTdim, loglikeST, processLUR, processLocation, updateCovf, updateTrend.STdata

Other cross-validation functions: computeLTA, createCV, dropObservations, estimateCV.STmodel

##load data
data(mesa.model)

##naive predictions based on either AQS,
pred.aqs <- predictNaive(mesa.model, type="AQS")
##...or only one sites,
pred.1site <- predictNaive(mesa.model, locations="60372005")

##plot the predictions - The two cases that are constant in space
par(mfcol=c(2,1), mar=c(4.5,4.5,1,.5))

##observations as a function of date
plot(mesa.model, "loc.obs", type=as.factor(mesa.model$locations$ID),
     legend.loc=NULL, pch=19, cex=.25)
##Add the predictions based on the smooth fitted to all sites
with(pred.aqs$pred, lines(date, smooth.fixed, col=1, lwd=2) )
with(pred.1site$pred, lines(date, smooth.fixed, col=2, lwd=2) )

##plot the predictions - One of the cases that vary in space, i.e. the smooth
##fit to the closest site.
##first extract as a data matrix
D <- with(pred.aqs$pred, createDataMatrix(obs=smooth.closest.fixed,
                                          date=date, ID=ID) )

##observations as a function of date
##(only five sites for clarity)
mesa.model <- dropObservations(mesa.model, !(mesa.model$obs$idx %in% c(1,2,3,23,24)))
plot(mesa.model, "loc.obs", type=as.factor(mesa.model$locations$ID),
     legend.loc=NULL, pch=19, cex=.25)
##Add the predictions based on the smooth
##fitted to the closest site
for(i in 1:5){
  lines(as.Date(rownames(D)), D[,mesa.model$locations$ID[i]], col=i, lwd=2)
}