[R] fractional balanced design conjoint analysis

[S Ellison]

>> package BHH2 includes routines for 2-level fractional 
>> factorials with specified generators.
>> package FrF2 provides a different 2-level fractional 
>> factorial design toolkit.
> 
> Something tells me you won't get a balanced 2x2x2x2x3 
> fractional in 16 or fewer runs though. I think 18 is possible.

Apologies; should have noted that an 18 observation design without aliasing is possible _with additional levels_ in factors B-D.

But after re-engaging brain you can also manage a 16-run 2x2x2x2x3 that allows separation of main effects using Montgomery's trick: generate a 16-run 6-factor fractional factorial coded +-1, then add the first two columns to get a 7th, three-level, factor coded +1, 0, -1 and remove the first two columns to give a 2x2x2x2x3.

Coding for that using BHH2 would be

B<-ffDesMatrix(6, gen=list(c(5,1,2), c(6, 1,3)))
B <- cbind(B, rowSums(B[,1:2])/2)[,3:7]  #Generates a 3-level column and then cuts off the first two

#Alias check:
y <- rnorm(16)
alias(y~., data=as.data.frame(B))

This is free from main effect aliasing for a linear model, though whether the design (which is not ' balanced' in as much as the 3-level factor does not have all levels equally represented) will behave adequately for a conjoint analysis I'm afraid I can't say.

S Ellison

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