OptimalDesign (version 0.1)

od.infmat: Information matrix

Description

Computes the information matrix of a given design.

Usage

od.infmat(F, w)

Arguments

F

The n times m matrix of real numbers. Rows of F represent the m-dimensional regressors corresponding to the n design points.

w

The non-negative vector of length n representing the design.

Value

The m times m information matrix of the design w for the linear regression model with regressors F[1,],...,F[n,] and uncorrelated real-valued unit-variance observations.

Details

The information matrix of the design w is equal to w[1]*M[1,,]+...+w[n]*M[n,,], where M[i,,] is the elementary information matrix corresponding to the single trial in the i-th design point, that is, M[i,,] is the product of F[i,] and the transpose of F[i,], i=1,...,n.

Note: The actual computation of the information matrix uses an equivalent, but numerically more efficient formula.

See Also

od.crit, od.print, od.plot

Examples

# The information matrix of an approximate design with weights 1/4 
# in -1, -0.4, 0.4, 1 for the cubic model on a discretization of 
# the interval [-1,1]
F.1D <- F.cube(~x1 + I(x1 ^ 2) + I(x1 ^ 3), -1, 1, 11)
round(od.infmat(F.1D, c(0.25,0,0,0.25,0,0,0,0.25,0,0,0.25)), 6)

# The information matrix of a random exact design for the full quadratic 
# model with 2 factors; the first with levels -1,0,1, and the second with 
# levels -1,0.5,0,0.5,1.
F.2D <- F.cube(~x1*x2 + I(x1^2) + I(x2^2), c(-1, -1), c(1, 1), c(3, 5))
od.infmat(F.2D, sample(0:1, dim(F.2D)[1], replace=TRUE))

# The matrix of the lattice design at levels 0, 0.5, 1 for the Scheffe 
# quadratic mixture model with 3 mixture components, each with levels 
# {0, 0.25, 0.5, 0.75, 1}.
F.scheffe <- F.simplex(~x1 + x2 + x3 + I(x1*x2) + I(x1*x3) + 
                       I(x2*x3) - 1, 3, 5)
w.lattice <- rep(0, 15); w.lattice[c(1,3,5,10,12,15)] <- 1
od.infmat(F.scheffe, w.lattice)