Calculate the A or D optimality score based on current experimental design
Description
According to the current experimental design, the Fisher information matrix is obtained and then either the A or D optimality score is computed.
Usage
1 2 3  designScore( genotype, array.allocation, condition.allocation,
nEnvFactors, nLevels, Level, nConditions, weight=1,
optimality="A", bTwoColorArray, envFactorNames)

Arguments
genotype 
genotype data: a nMarkerbynRILs matrix with two allels being 0 and 1 (or A and B) or three allels being 0, 0.5 and 1 (or, A, H, and B), where 0.5 (or H) represents heterozygous allele. 
array.allocation 
matrix with nArray rows and nRIL columns. Elements of 1/0 indicate this RIL (or strains) is/not selected for this array. 
condition.allocation 
matrix with nCondition rows and nRIL columns. Elements of 1/0 indicate this RIL (or strains) is/not selected for this condition. 
nEnvFactors 
number of environmental factors, an integer bewteen 1 and 3.
When 
nLevels 
number of levels for each factor, a vector with each
component being an integer. The length of it should equal

Level 
a list which specifies the levels for each factor in the
experiment. There are in total 
nConditions 
number of all possible combination of all environmental factors. 
weight 
a vector with length of variableNumber which is calculated
from function 
optimality 
type of optimality, i.e. "A" (Aoptimality) or "D" (Doptimality). Aoptimality minimizes $Trace((X'X)^1)$, which corresponds to minimum average variance of the parameter estimates. Doptimality minimizes $det(X'X)^1$, which corresponds to minimum generalized variance of the parameter estimates. 
bTwoColorArray 
binary variable indicating experiment type: 
envFactorNames 
a vector with names for all environmental factor(s). For example, for the
experiment with two environmental factors of temperature and drug treatment:

Details
Example parameter settings:
Suppose to design an experiment with two environmental factors (F1, F2) and
there are two diffferent levels for each environment. The levels are 16
and 24 for F1, and 5 anf 10 for F2. Thus the following command can be used:
nEnvFactors < 2
nLevels < c ( 2, 2 )
levels < list ( c(16, 24), c(5, 10) )
The length of parameter weight
is dependent on the number of environmental
factors:
When nEnvFactor
= 0,
weight
is 1 as there is only one parameter of interest (genotype).
When nEnvFactor
= 1,
weight
= c( $w_Q$, $w_F1$, $w_QF1$ )
When nEnvFactor
= 2,
weight
= c( $w_Q$, $w_F1$, $w_F2$, $w_QF1$, $w_QF2$, $w_F1F2$, $w_QF1F2$)
When nEnvFactor
= 3,
weight
= c( $w_Q$, $w_F1$, $w_F2$, $w_F2$,
$w_QF1$, $w_QF2$, $w_QF3$, $w_F1F2$, $w_F1F3$, $w_F2F3$,
$w_QF1F2$, $w_QF1F3$, $w_QF2F3$, $w_QF1F2F3$ )
Here $w_Q$ represents the weight for genotype effect, $w_F1$ represent the
weight for F1 effect and $w_QF1$ represent the weight for interaction between
genotype and F1 effect, etc.
Value
The score is defined as the "double" sum of the variances, summed over all parameters and over all markers.
Author(s)
Yang Li <yang.li@rug.nl>, Gonzalo Vera <gonzalo.vera.rodriguez@gmail.com>
Rainer Breitling <r.breitling@rug.nl>, Ritsert Jansen <r.c.jansen@rug.nl>
References
Y. Li, M. Swertz, G. Vera, J. Fu, R. Breitling, and R.C. Jansen. designGG:
An Rpackage and Web tool for the optimal design of genetical genomics
experiments. BMC Bioinformatics 10:188(2009)
http://gbic.biol.rug.nl/designGG
Y. Li, R. Breitling and R.C. Jansen. Generalizing genetical
genomics: the added value from environmental perturbation, Trends Genet
(2008) 24:518524.
E. Wit and J. McClure. Statistics for Microarrays: Design, Analysis
and Inference. (2004) Chichester: Wiley.
See Also
designGG