mlegp (version 2.2.6)

plotInteractionEffect: Sensitivity Analysis for Gaussian Processes and Gaussian Process Lists

Description

Displays a contour plot that shows the 2-way interaction effect of two parameters from a Gaussian process

Usage

plotInteractionEffect(gp, effects, length1.out = 21, length2.out = 21, 
	lower = apply(gp$X, 2, min), upper = apply(gp$X, 2, max), no.plot = FALSE)

Arguments

gp

an object of class gp

effects

a vector containing 2 elements corresponding to the parameter numbers or names to plot

length1.out

the number of values to consider for the first parameter

length2.out

the number of values to consider for the second parameter

lower

a vector of minimum values for ALL parameters of the gp design matrix

upper

a vector of maximum values for ALL parameters of the gp design matrix

no.plot

set no.plot to TRUE to turn plotting off and to return the interaction effects

Value

• If no.plot is TRUE, a list with components:
• index1
  vector of parameter values for the first parameter
• index2
  vector of parameter values for the second parameter
• preds
  a matrix containing the predicted values to be plotted by contour

Details

An interaction effect of two parameters, x and y, is the predicted output when x and y are fixed, and the remaining parameters are integrated out according to a prior distribution that is independent U(a,b) for all parameters, where for each parameter, (a,b) corresponds to the (min,max) of that parameter in the design. These values can also be overwritten by the arguments lower and upper.

This function produces a contour plot of predictions for all combinations of the parameters in effects, where the values of the first parameter are seq(lower[effects[1]], upper[effects[1]], length.out = length1.out) and values for the second parameter are seq(lower[effects[2]], upper[effects[2]], length.out = length2.out).

For elements not in effects, lower and upper will determine the limits of integration.

References

Schonlau, M. and Welch, W. 2006. Screening the Input Variables to a Computer Model Via Analysis of Variance and Visualization, in Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics. A Dean and S. Lewis, eds. (New York: Springer).

http://users.nsula.edu/dancikg/mlegp/

See Also

FANOVADecomposition for quantifying the importance of an interaction effect

Examples

## fit the Gaussian process ##
x1 = kronecker(seq(0,1,by=.25), rep(1,5))
x2 = rep(seq(0,1,by=.25),5)
z = 4 * x1 - 2*x2 + x1 * x2 + rnorm(length(x1), sd = 0.001)
fit = mlegp(cbind(x1,x2), z, param.names = c("x1", "x2"))

## plot the interaction effect ##
plotInteractionEffect(fit, effects = c(1,2))

## plot the interaction effect 'manually' ##
int = plotInteractionEffect(fit, effects = c(1,2), no.plot = TRUE)
contour(int$index1, int$index2, int$preds, xlab = "x1", ylab = "x2")