Fx_CtoA: Transformation of candidate regressors for regularized...
In OptimalDesign: A Toolbox for Computing Efficient Designs of Experiments

Description Usage Arguments Details Value Author(s) See Also Examples

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

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

`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?

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.

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.

Radoslav Harman and Lenka Filova

Fx_ItoA

# 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