# Full and fractional factorial designs

I have a data set consisting of six independent environmental variables (all binomial: present / absent) and one dependent variable (binomial: disease present / absent). In order to determine the combination of factors that have the highest probability of leading to disease, I first need to conduct an Expert Opinion poll where I will have several experts rank all possible combinations of variables according to their probability of leading to the occurrence of disease. Then, I will obtain regression parameters for each variable using a conjoint analysis approach where each expert conforms a level (hierarchical design), the six environmental variables are independent variables, and the rankings are the dependent variable. There being six factor variables, there exist a total of 64 possible orthogonal combinations. I reduced this overwhelming number of possible combinations (while retaining orthogonality) using the AlgDesign package of R. Here is the code followed only by relevant pieces of output:

levels.design = c(2,2,2,2,2,2)
full.design <- gen.factorial(levels.design)

X1 X2 X3 X4 X5 X6
1  -1 -1 -1 -1 -1 -1
2   1 -1 -1 -1 -1 -1
3  -1  1 -1 -1 -1 -1
.................
63 -1  1  1  1  1  1
64  1  1  1  1  1  1

set.seed(69)
fractional <- optFederov(~., data=full.design, approximate=FALSE, criterion="D")
fractional


The result is a subset of 12 combinations to be included in the conjoint analysis: