R: Diagnostic plot for the validation of a km object

plot {DiceKriging} | R Documentation

## Diagnostic plot for the validation of a km object

### Description

Three plots are currently available, based on the `leaveOneOut.km` results: one plot of fitted values against response values, one plot of standardized residuals, and one qqplot of standardized residuals.

### Usage

    ## S4 method for signature 'km'
    plot(x, y, kriging.type = "UK", trend.reestim = FALSE, ...)

### Arguments

`x` | an object of class "km" without noisy observations.
`y` | not used.
`kriging.type` | an optional character string corresponding to the kriging family, to be chosen between simple kriging ("SK") or universal kriging ("UK").
`trend.reestim` | should the trend be reestimated when removing an observation? Default to FALSE.
`...` | no other argument for this method.

### Details

The diagnostic plot has not been implemented yet for noisy observations. The standardized residuals are defined by `( y(xi) - yhat_{-i}(xi) ) / sigmahat_{-i}(xi)`, where `y(xi)` is the response at the point `xi`, `yhat_{-i}(xi)` is the fitted value when removing the observation `xi` (see `leaveOneOut.km`), and `sigmahat_{-i}(xi)` is the corresponding kriging standard deviation.

### Value

A list composed of:

`mean` | a vector of length n. The ith coordinate is equal to the kriging mean (including the trend) at the ith observation number when removing it from the learning set,
`sd` | a vector of length n. The ith coordinate is equal to the kriging standard deviation at the ith observation number when removing it from the learning set,

where n is the total number of observations.

### Warning

Kriging parameters are not re-estimated when removing one observation. With few points, the re-estimated values can be far from those obtained with the entire learning set. One option is to reestimate the trend coefficients, by setting `trend.reestim=TRUE`.

### Author(s)

O. Roustant, D. Ginsbourger, Ecole des Mines de St-Etienne.

### References

N.A.C. Cressie (1993), Statistics for spatial data, Wiley series in probability and mathematical statistics.

J.D. Martin and T.W. Simpson (2005), Use of kriging models to approximate deterministic computer models, AIAA Journal, 43 no. 4, 853-863.

M. Schonlau (1997), Computer experiments and global optimization, Ph.D. thesis, University of Waterloo.

### See Also

`predict,km-method`, `leaveOneOut.km`

### Examples

    # A 2D example - Branin-Hoo function

    # a 16-points factorial design, and the corresponding response
    d <- 2; n <- 16
    fact.design <- expand.grid(seq(0,1,length=4), seq(0,1,length=4))
    fact.design <- data.frame(fact.design); names(fact.design)<-c("x1", "x2")
    branin.resp <- data.frame(branin(fact.design)); names(branin.resp) <- "y"

    # kriging model 1 : gaussian covariance structure, no trend,
    #                   no nugget effect
    m1 <- km(~.^2, design=fact.design, response=branin.resp, covtype="gauss")
    plot(m1)  # LOO without parameter reestimation
    plot(m1, trend.reestim=TRUE)  # LOO with trend parameters reestimation
                                  # (gives nearly the same result here)

[Package DiceKriging version 1.5.5 Index]