modelFit: Fitting metamodels

Description

modelFit is used to fit a metamodel of class lm, gam, mars, polymars or km.

Usage

modelFit (X,Y, type, ...)

Value

A list with the following components:

X: a data frame representing the design of experiments
Y: a vector representing the response
type: the type of metamodel
model: a fitted model of the specified class

and the value of the parameter(s) depending on the fitted model.

Arguments

X

a data.frame containing the design of experiments

Y

a vector containing the response variable

type

represents the method used to fit the model:

`"Linear"`	linear model,
`"StepLinear"`	stepwise,
`"Additive"`	gam,
`"MARS"`	mars
`"PolyMARS"`	polymars
`"Kriging"`	kriging model.

...

corresponds to the parameter(s) of the model. The list of the needed arguments for each type of models is given below:

`"Linear"`	`formula` (see `formulaLm`),
`"StepLinear"`	`formula`
	`penalty` parameter,
`"Additive"`	`formula` (see `formulaAm`),
`"MARS"`	`degree`,
`"PolyMARS"`	`gcv` criteria.
`"Kriging"`	`formula`
	`covtype`

Author

D. Dupuy

Examples

Run this code

# A 2D example
Branin <- function(x1,x2) {
  x1 <- x1*15-5   
  x2 <- x2*15
  (x2 - 5/(4*pi^2)*(x1^2) + 5/pi*x1 - 6)^2 + 10*(1 - 1/(8*pi))*cos(x1) + 10
}
# a 2D uniform design and the value of the response at these points
X <- matrix(runif(24),ncol=2,nrow=12)
Z <- Branin(X[,1],X[,2])
Y <- (Z-mean(Z))/sd(Z)

# construction of a linear model
modLm <- modelFit(X,Y,type = "Linear",formula=Y~X1+X2+X1:X2+I(X1^2)+I(X2^2))
summary(modLm$model)

if (FALSE) {
# construction of a stepwise-selected model 
modStep <- modelFit(X,Y,type = "StepLinear",penalty=log(dim(X)[1]),
		formula=Y~X1+X2+X1:X2+I(X1^2)+I(X2^2))
summary(modStep$model)

# construction of an additive model
library(gam)
modAm <- modelFit(X,Y,type = "Additive",formula=Y~s(X1)+s(X2))
summary(modAm$model)

# construction of a MARS model of degree 2
library(mda)
modMARS <- modelFit(X,Y,type = "MARS",degree=2)
print(modMARS$model)

# construction of a PolyMARS model with a penalty parameter equal to 1
library(polspline)
modPolyMARS <- modelFit(X,Y,type = "PolyMARS",gcv=1)
summary(modPolyMARS$model)

# construction of a Kriging model
modKm <- modelFit(X,Y,type = "Kriging")
str(modKm$model)
}