Fx_CtoA {OptimalDesign}

Transformation of candidate regressors for regularized c-optimality

Description

Pre-transforms the matrix of all candidate regressors to the form suitable for computing regularized c-optimal designs via A-optimum algorithms.

Usage

Fx_CtoA(Fx, h=NULL, echo=TRUE)

Arguments

Fx

the n times m matrix of candidate regressors (as rows), where n is the number of candidate design points and m (where m>=2, m<=n) is the number of parameters.

h

a non-zero vector of length m corresponding to the coefficients of the linear parameter combination of interest. If crit is not "C" nor "c" then h is ignored. If crit is "C" or "c" and h=NULL then h is assumed to be c(0,...,0,1).

echo

Print the call of the function?

Details

The standard c-optimal designs are often singular, which may render them unsuitable for practical use. The regularized c-optimality, which we call C-optimality, is an approach to computing designs that are non-singular, but still efficient with respect to the criterion of c-optimality. See http://www.iam.fmph.uniba.sk/design/ for more details.

Value

The n times m matrix Fx.trans of all candidate regressors with the following property: The A-optimal design for the problem defined by Fx.trans is the same as the regularized c-optimal (i.e., C-optimal) design for the problem defined by Fx.

Author(s)

Radoslav Harman and Lenka Filova

See Also

Fx_ItoA

Examples

# We will compute a C-efficient (regularized c-optimal) design
# for estimating the mean response in x=1 for a quadratic regression
# using and algorithm for A-optimality.

Fx <- Fx_cube(~x1 + I(x1^2), n.levels=101)
Fx.trans <- Fx_CtoA(Fx, h=c(1, 1, 1))
w <- od_REX(Fx.trans, crit="A")$w.best
od_print(Fx, w, h=c(1, 1, 1))

# Compare the design to the (non-regularized) c-optimal design
w.crisp <- od_REX(Fx, crit="c", h=c(1, 1, 1))$w.best
od_print(Fx, w.crisp, h=c(1, 1, 1))

# The c-efficiency of the C-optimal design is about 0.68
# The D-efficiency of the c-optimal design is 0
# The D-efficiency of the C-optimal design is a very decent
optcrit(Fx, w) / od_REX(Fx)$Phi.best