SpatioTemporal (version 1.1.9.1)

estimateCV.STmodel: Cross-Validated Estimation and Prediction

Description

Functions that perform cross-validated parameter estimation and prediction for the spatio-temporal model.

Usage

# S3 method for STmodel
estimateCV(object, x, Ind.cv, control = list(trace = 3),
  verbose.res = FALSE, ...)
estimateCV(object, x, Ind.cv, ...)
# S3 method for STmodel
predictCV(object, x, Ind.cv = NULL, ..., silent = TRUE,
  LTA = FALSE)
predictCV(object, x, Ind.cv, ...)

Arguments

object

STmodel object for which to perform cross-validation.

x

Either a vector or matrix of starting point(s) for the optimisation, see estimate.STmodel; or a matrix with parameters, the i:th row being used for prediction of the i:th cross-validation set. For prediction either a estCVSTmodel or estimateSTmodel object, results from estimateCV.STmodel or estimate.STmodel, can be used.

Ind.cv

Ind.cv defines the cross-validation scheme. Either a (number or observations) - by - (groups) logical matrix or an integer valued vector with length equal to (number or observations). For predictCV.STmodel Ind.cv can be infered from x if x is a estCVSTmodel object See further createCV.

control

A list of control parameters for the optimisation. See optim for details; setting trace=0 eliminates all ouput.

verbose.res

A TRUE/FALSE variable indicating if full results from estimate.STmodel for each CV group should be returned; defaults to FALSE

...

All additional parameters for estimate.STmodel or predict.STmodel. For predict.STmodel a number of parameters are set in predictCV.STmodel and can NOT be overriden, these are nugget.unobs, only.pars=FALSE, and combine.data=FALSE.

silent

Show status after each iteration?

LTA

TRUE/FALSE, compute long-term temporal averages, similar to computeLTA, but with the option of including the uncertainty; see predict.STmodel.

Value

Either a estCVSTmodel object with elements:

status

Data.frame with convergence information and best function value for each cross-validation group.

Ind.cv

The cross-validation grouping.

x.fixed

Fixed parameters in the estimation, see estimate.STmodel.

x.init

Matrix of inital values used, i.e. x from the input.

par.all, par.cov

Matrices with estimated parameters for each cross-validation group.

par.all.sd, par.cov.sd

Standard deviations computed from the Hessian/information matrix for set of estimated parameters.

res.all

Estimation results for each cross-validation group, contains the output from the estimate.STmodel calls, only included if verbose.res=TRUE.

Or a predCVSTmodel object with elements:

opts

Copy of the opts field in the output from predict.STmodel.

Ind.cv

The cross-validation grouping.

pred.obs

A data.frame with a copy of observations from object$obs, predictions (for different model components), variances, and residuals. Variance field will be missing if pred.var=FALSE.

pred.all

A list with time-by-location data.frames containing predictions and variances for all space-time locations as well as predictions and variances for the beta-fields. Unobserved points are NA for the option only.obs=TRUE.

Details

For predictCV.STmodel the parameters used to compute predictions for the left out observations can be either a single vector or a matrix. For a single vector the same parameter values will be used for all cross-validation predictions; for a matrix the parameters in x[,i] will be used for the predictions of the i:th cross-validation set (i.e. for Ind.cv[,i]). Suitable matrices are provided in the output from estimateCV.STmodel.

The cross-validation groups are given by Ind.cv. Ind.cv should be either a (number of observations) - by - (groups) logical matrix or an integer valued vector with length equal to (number of observations). If a matrix then each column defines a cross-validation set with the TRUE values marking the observations to be left out. If a vector then 1:s denote observations to be dropped in the first cross-validation set, 2:s observations to be dropped in the second set, etc. Observations marked by values <=0 are never dropped. See createCV for details.

See Also

Other STmodel methods: MCMC.STmodel, c.STmodel, createSTmodel, estimate.STmodel, plot.STdata, predict.STmodel, print.STmodel, print.summary.STmodel, qqnorm.predCVSTmodel, scatterPlot.predCVSTmodel, simulate.STmodel, summary.STmodel

Other cross-validation functions: computeLTA, createCV, dropObservations, predictNaive

Other estCVSTmodel methods: boxplot.estCVSTmodel, coef.estCVSTmodel, print.estCVSTmodel, print.summary.estCVSTmodel, summary.estCVSTmodel

Other predCVSTmodel functions: computeLTA

Other predCVSTmodel methods: plot.predCVSTmodel, print.predCVSTmodel, print.summary.predCVSTmodel, qqnorm.predCVSTmodel, scatterPlot.predCVSTmodel, summary.predCVSTmodel

Examples

# NOT RUN {
##load data
data(mesa.model)
data(est.mesa.model)

################
## estimateCV ##
################
##create the CV structure defining 10 different CV-groups
Ind.cv <- createCV(mesa.model, groups=10, min.dist=.1)

##use the best parameters and there starting values as
x.init <- coef(est.mesa.model, pars="cov")[,c("par","init")]

# }
# NOT RUN {
  ##estimate different parameters for each CV-group
  est.cv.mesa <- estimateCV(mesa.model, x.init, Ind.cv)
# }
# NOT RUN {
##lets load precomputed results instead
data(est.cv.mesa)

##examine the estimation results
print( est.cv.mesa )
##estimated parameters for each CV-group
coef(est.cv.mesa, pars="cov")

###############
## predictCV ##
###############
# }
# NOT RUN {
  ##Do cross-validated predictions using the just estimated parameters
  ##Ind.cv is infered from est.cv.mesa as est.cv.mesa$Ind.cv
  pred.cv.mesa <- predictCV(mesa.model, est.cv.mesa, LTA=TRUE)
# }
# NOT RUN {
##lets load precomputed results instead
data(pred.cv.mesa)

##prediction results
print( pred.cv.mesa )

##and CV-statistics
print( summary( pred.cv.mesa, LTA=TRUE) )


# }
# NOT RUN {
  ##A faster option is to only consider the observations and not to compute
  ##variances
  pred.cv.fast <- predictCV(mesa.model, est.cv.mesa, only.obs=TRUE,
                            pred.var=FALSE)
  print( pred.cv.fast )
  summary( pred.cv.fast )
# }