# Information matrix

### Description

Computes the information matrix of a given design.

### Usage

1 | ```
od.infmat(F, w)
``` |

### Arguments

`F` |
The |

`w` |
The non-negative vector of length |

### 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.

### 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.

### Author(s)

Radoslav Harman, Lenka Filova

### See Also

`od.crit, od.print, od.plot`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# 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)
``` |