# od.infmat: Information matrix In OptimalDesign: Algorithms for D-, A-, and IV-Optimal Designs

## Description

Computes the information matrix of a given design.

## Usage

 `1` ``` 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.

## 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)

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