objfnD_BD: Calculate D-optimality criterion value for a Block Design

Description

This function calculates the determinant of the Fisher information matrix for a block design with a Poisson response. This function assumes that there are b blocks, each containing k experimental units and v treatments in total. Block effects are assumed to be normal with mean 0 and standard deviation sigb. Additional residual error can be specified through sige.

Usage

objfnD_BD(des, ntmt, blksz, sigb, sige, means, probs)

Arguments

des

The design under consideration, a list of length b x k containing treatment indices (1, 2, ..., v)

ntmt

The number of distinct treatments (v)

blksz

The number of treatments in each block (k)

sigb

Standard deviation of block effect

sige

Standard deviation of excess error

means

A list of length v containing conditional means for each treatment e.g. c(1,1,2) for three treatments with means 1, 1, and 2 respectively

probs

a list of probabilities specifying the probability that each step of the simulated annealing substitutes a certain number of design points. The first entry corresponds to the probability that only one substitution is made in a simulated annealing step, the second is the probability that two substitutions are made and so on. By default this is set to c(1) which means that only one substitution is made in each simulated annealing step.

Value

Returns the negative of the determinant of the Fisher information matrix for the proveded design.

Details

This function is designed to work with findOptimalBlockDesign, and as such shares the arguments of updateDesign_BD. It can, however, be used on its own. The probs argument is not used in this function, but is in updateDesign_BD.

References

Bush, S., and Ruggiero, K. (2016) Optimal block designs for experiments with responses drawn from a Poisson distribution, Under Review, preprint available at http://arxiv.org/abs/1601.00477

Examples

Run this code

# Finding the D-optimality objective value for the design ((1,1,2,2),(1,1,2,3),(1,2,2,3))
# where there are three treatments in three blocks of size four when the treatment means
# are 1, 2, and 4, the between block standard deviation is 0.2 (sigb=0.2) and there is
# no overdispersion (sige=0)

objfnD_BD(c(1,1,2,2,1,1,2,3,1,2,2,3), ntmt=3, blksz=4, sigb=0.2, sige=0, means=c(1,2,4))

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