predict.Krig: Evaluation of Krig spatial process estimate.

Description

Provides predictions from the Krig spatial process estimate at arbitrary points, new data (Y) or other values of the smoothing parameter (lambda) including a GCV estimate.

Usage

# S3 method for Krig
predict(
object, x = NULL, Z = NULL, drop.Z = FALSE, just.fixed
                 = FALSE, lambda = NA, df = NA, model = NA,
                 eval.correlation.model = TRUE, y = NULL, yM = NULL,
                 verbose = FALSE, ...)
predictDerivative.Krig(object, x = NULL,  verbose = FALSE,...)
# S3 method for Tps
predict(object, ... )
# S3 method for fastTps
predict(object, xnew = NULL, grid.list = NULL, ynew = NULL,
                 derivative = 0, Z = NULL, drop.Z = FALSE, just.fixed =
                 FALSE, xy = c(1, 2), ...)

Value

Vector of predicted responses or a matrix of the partial derivatives.

Arguments

derivative: The degree of the derivative to be evauated. Default is 0 (evaluate the function itself), 1 is supported by some covariance functions, Higher derivatives are not supported in this version and for mKrig.
df: Effective degrees of freedom for the predicted surface. This can be used in place of lambda ( see the function Krig.df.to.lambda)
eval.correlation.model: If true ( the default) will multiply the predicted function by marginal sd's and add the mean function. This usually what one wants. If false will return predicted surface in the standardized scale. The main use of this option is a call from Krig to find MLE's of sigma and tau2
grid.list: A grid.list specfiying a grid of locations to evaluate the fitted surface.
just.fixed: Only fixed part of model is evaluated
lambda: Smoothing parameter. If omitted, the value in the lambda of the object will be used. (See also df and gcv arguments)
model: Generic argument that may be used to pass a different lambda.
object: Fit object from the Krig, Tps, mKrig, or fastTps functions.
verbose: Print out all kinds of intermediate stuff for debugging
xy: The column positions that locate the x and y variables for evaluating on a grid. This is mainly useful if the surface has more than 2 dimensions.
y: Evaluate the estimate using the new data vector y (in the same order as the old data). This is equivalent to recomputing the Krig object with this new data but is more efficient because many pieces can be reused. Note that the x values are assumed to be the same.
x: Matrix of x values on which to evaluate the kriging surface. If omitted, the data x values will be used.
xnew: Same as x above.
ynew: Same as y above.
yM: If not NULL evaluate the estimate using this vector as the replicate mean data. That is, assume the full data has been collapsed into replicate means in the same order as xM. The replicate weights are assumed to be the same as the original data. (weightsM)
Z: Vector/Matrix of additional covariates to be included in fixed part of spatial model
drop.Z: If TRUE only spatial fixed part of model is evaluated. i.e. Z covariates are not used.
...: Other arguments passed to covariance function. In the case of fastTps these are the same arguments as predict.mKrig. This argument is usually not needed.

Details

The main goal in this function is to reuse the Krig object to rapidly evaluate different estimates. Thus there is flexibility in changing the value of lambda and also the independent data without having to recompute the matrices associated with the Krig object. The reason this is possible is that most on the calculations depend on the observed locations not on lambda or the observed data. Note the version for evaluating partial derivatives does not provide the same flexibility as predict.Krig and makes some assumptions about the null model (as a low order polynomial) and can not handle the correlation model form.

Examples

Run this code

  Krig(ChicagoO3$x,ChicagoO3$y, aRange=50) ->fit
  predict( fit) # gives predicted values at data points should agree with fitted.values
                #  in fit object 

# predict at the coordinate (-5,10)
  x0<- cbind( -5,10) # has to be a  1X2 matrix
  predict( fit,x= x0)

# redoing predictions at data locations:
   predict( fit, x=ChicagoO3$x)

# only the fixed part of the model
  predict( fit, just.fixed=TRUE) 

# evaluating estimate at a grid of points 
  grid<- make.surface.grid( list( seq( -40,40,,15), seq( -40,40,,15)))
  look<- predict(fit,grid) # evaluate on a grid of points

# some useful graphing functions for these gridded predicted values
  out.p<- as.surface( grid, look) # reformat into $x $y $z image-type object
  contour( out.p) 

# see also the functions predictSurface and surface 
# for functions that combine these steps 
   

# refit with 10 degrees of freedom in surface
  look<- predict(fit,grid, df=15)
# refit with random data 
  look<- predict( fit, grid, y= rnorm( 20))


# finding partial derivatives of the estimate
#
# find the partial derivatives at observation locations
# returned object is a two column matrix. 
# this does not make sense for the exponential covariance
# but can illustrate this with a thin plate spline with
# a high enough order ( i.e. need m=3 or greater)
# 
  data(ozone2)
# the 16th day of this ozone spatial dataset
  fit0<- Tps( ozone2$lon.lat, ozone2$y[16,], m=3)
  look1<- predictDerivative.Krig( fit0)
# for extra credit compare this to
  look2<- predictDerivative.Krig( fit0, x=ozone2$lon.lat)  
# (why are there more values in look2)