Fx_ItoA {OptimalDesign}

Transformation of candidate regressors for I-optimality

Description

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

Usage

Fx_ItoA(Fx, 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.

echo

Print the call of the function?

Details

It is simple to see that the problem of I-optimality is equivalent to the problem of A-optimality for a transformed matrix of candidate regressors. This function performs the transformation. 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 I-optimal design for the problem defined by Fx.

Note

It is also simple to transform the weighted I-optimality to A-optimality; just multiply the rows of Fx by the squares roots of weights of individual design points and transform the resulting matrix by Fx_ItoA.

Author(s)

Radoslav Harman, Lenka Filova

See Also

Fx_CtoA

Examples

## Not run: 
# Compute an I-efficient exact size 20 design without replications
# for the Scheffe mixture model with 4 components
# using the AQUA heuristic for A-optimality.

Fx <- Fx_simplex(~x1 + x2 + x3 + x4 + I(x1*x2) + I(x1*x3) + I(x1*x4) +
                  I(x2*x3) + I(x2*x4) + I(x3*x4) - 1, 11)

w <- od_AQUA(Fx_ItoA(Fx), b3=24, bin=TRUE, crit="I", conic=FALSE)$w.best
od_plot(Fx, w, Fx[, 2:4])

## End(Not run)