modelFit function

Fitting metamodels

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

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

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

Returns

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.

Author(s)

D. Dupuy

See Also

modelPredict

Examples

# 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)

## Not run:

# 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)
## End(Not run)