plot: 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 km
plot(x, y, kriging.type = "UK", trend.reestim = FALSE, ...)

Arguments

an object of class "km" without noisy observations.

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.

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,

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.

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.

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.

Examples

Run this code

# NOT RUN {
# 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)
# }

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