Compute the conditional expectations (i.e. predictions) at the unobserved
space-time locations. Predictions are computed for the space-time locations in
object and/or STdata, conditional on the observations (and
temporal trends) in object and parameters given in x.
# S3 method for STmodel
predict(object, x, STdata = NULL, Nmax = 1000,
only.pars = FALSE, nugget.unobs = 0, only.obs = FALSE,
pred.var = TRUE, pred.covar = FALSE, beta.covar = FALSE,
combine.data = FALSE, type = "p", LTA = FALSE, transform = c("none",
"unbiased", "mspe"), ...)STmodel object for which to compute predictions.
Model parameters for which to compute the conditional
expectation. Either as a vector/matrix or an estimateSTmodel from
estimate.STmodel.
STdata/STmodel object with locations/times for
which to predict. If not given predictions are computed for locations/times
in object
Limits the size of matrices constructed when computing expectations. Use a smaller value if memory becomes a problem.
Compute only the regression parameters (using GLS) along with the related variance.
Value of nugget at unonserved locations, either a scalar
or a vector with one element per unobserved site. NOTE: All sites in
STdata are considered unobserved!
Compute predictions at only locations specified by
observations in STdata. Used to limit computations when doing
cross-validation.
only.obs=TRUE implies pred.covar=FALSE and
combine.data=FALSE.
Further createSTmodel will be called on any STdata
input, possibly reordering the observations.
Compute point-wise prediction variances; or
compute covariance matrices for the predicted time series at each location.
pred.covar=TRUE implies pred.var=TRUE and sets
Nmax equal to the number of timepoints.
Compute the full covariance matrix for the latent beta-fields, otherwise only the diagonal elements of V(beta|obs) are computed.
Combine object and STdata and predict for
the joint set of points, see c.STmodel.
A single character indicating the type of prediction to
compute. Valid options are "f", "p", and "r", for full,
profile or restricted maximum likelihood (REML). For profile
and full the predictions are computed assuming that both covariance
parameters and regression parameters are known,
e.g. E(X|Y,cov_par,reg_par); for REML predictions are compute
assuming only covariance parameters known,
e.g. E(X|Y,cov_par). The main difference is that REML will have
larger variances due to the additional uncertainty in the
regression parameters.
Compute long-term temporal averages. Either a logical value or a
list; if TRUE then averages at each location (and variances if
pred.var=TRUE) are computed; otherwise this should be a list with
elements named after locations and each element containing a vector (or
list of vectors) with dates over which to compute averages. If
only.obs=TRUE averages are computed over only the observations.
Regard field as log-Gaussian and apply exponential transformation to predictions. For the final expectations two options exist, either a unbiased prediction or the (biased) mean-squared error predictions.
Ignored additional arguments.
The function returns a list containing (objects not computed will be missing):
Copy of options used in the function call.
A list with regression parameters and related variances.
pars contain gamma.E and alpha.E with
regression coefficients for the spatio-temporal model and
land-use covaraiates; variances are found in gamma.V
and alpha.V; cross-covariance between gamma and alpha in
gamma.alpha.C.
A list with estimates of the beta-fields, including the
regression mean mu, conditional expectations EX,
possibly variances VX, and the full covariance matrix
VX.full.
predictions based on the regression parameters, geographic covariates, and temporal trends. I.e. only the deterministic part of the spatio-temporal model.
Predictions based on the latent-beta fields, but excluding the residual nu field.
Full predictions at the space-time locations in
object and/or STdata.
Only for transform!="none", full predictions
including bias correction for prediction error.
Pointwise variances and prediction variances (i.e. incl.
contribution from nugget.unobs) for all locations in EX.
A list with (number of locations) elements, each element is a (number of timepoints) - by - (number of timepoints) temporal covariance matrix for the timeseries at each location.
Pointwise mean-square prediction errors for the log-Gaussian fields.
Pointwise predictions and variances for
the un-transformed fields when transform!="none"
A data.frame with temporal averages for locations specified by
LTA.
A vector with the locations of the observations in object or
STdata. To extract predictions at the observations locations use
EX[I].
In addition to computing the conditional expectation at a number of space-time locations the function also computes predictions based on only the regression part of the model as well as the latent beta-fields.
Prediction are computed as the conditional expectation of a latent field
given observations. This implies that E(X_i| Y_i) != Y_i, with the
difference being due to smoothing over the nugget. Further two possible
variance can be computed (see below), V(X_i|Y_i) and
V(X_i|Y_i)+nugget_i. Here the nugget for unobserved locations needs
to be specified as an additional argument nugget.nobs. The two
variances correspond, losely, to confidence and prediction intervals.
Variances are computed if pred.var=TRUE point-wise variances for the
predictions (and the latent beta-fields) are
computed. If instead pred.covar=TRUE the full covariance matrices for
each predicted time series is computed; this implies that the covariances between
temporal predictions at the same location are calculated but not, due
to memory restrictions, any covariances between locations.
beta.covar=TRUE gives the full covariance matrices for the latent
beta-fields.
If transform!="none" the field is assumed to be log-Gaussian and
expectations are transformed, and if pred.var=TRUE the mean squared
prediction errors are given.
Other STmodel methods: MCMC.STmodel,
c.STmodel, createSTmodel,
estimate.STmodel,
estimateCV.STmodel,
plot.STdata, print.STmodel,
print.summary.STmodel,
qqnorm.predCVSTmodel,
scatterPlot.predCVSTmodel,
simulate.STmodel,
summary.STmodel
Other predictSTmodel methods: plot.predCVSTmodel,
print.predictSTmodel
# NOT RUN {
##load data
data(mesa.model)
data(est.mesa.model)
##find regression parameters using GLS
x.reg <- predict(mesa.model, est.mesa.model, only.pars = TRUE)
str(x.reg$pars)
# }
# NOT RUN {
##compute predictions at all locations, including beta-fields
pred.mesa.model <- predict(mesa.model, est.mesa.model,
pred.var=TRUE)
# }
# NOT RUN {
##Let's load precomputed results instead.
data(pred.mesa.model)
##study results
print(pred.mesa.model)
# }
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