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:
$design X1 X2 X3 X4 X5 X6 4 1 1 -1 -1 -1 -1 5 -1 -1 1 -1 -1 -1 ................ 57 -1 -1 -1 1 1 1
From what I understand, doing a regression analysis on all 64 combinations should lead to the same regression parameters as those obtained if I use only the reduced set (i.e. 12 combinations from the fractional factorial design).
- Do the code and the resulting output make sense?
- Could anyone point me to a good and simple reference on how this fractional design works? I am afraid I might be doing things wrong by selecting a subset that produces different results from those obtained if a full factorial design was employed.