Use of dummy in Plackett-Burmann screening

#1
I am trying to set up an experiment for optimizing medium composition for bacterial growth using the Plackett-Burman design. I am planning to do a 12-run Plackett-Burman design. I have 11 factors that i want to test, this however does not leave any room for a dummy. My two questions are:

1. How necessary is it to include the dummy, would it be best to do increase to a 24-run Plackett-Burman design and include 1-3 dummies?

2. I have not been able to figure out how to use the dummy in practice. Which values do you assign the dummy variable, and how is it included in the experiment?

Thanks for your help
 
#2
Hi Essen,
I'm having exactly the same problem regarding dummies now, as you have posted this question long back, have you came out with any solutions....what if I've left no room for dummies, which values to assign the dummy variable etc. The answer becomes more important when we are using Design Expert for analysis.
 

rogojel

TS Contributor
#3
hi,
I just read the relevant chapter from Box-Hunter yesterday and though I did not try this in real life yet, as far as I understand you simply ignore the dummy variables, i.e. they get no values assigned.

Having 11factors for a PB12 should be completely acceptable -at least I found no mention of having to have dummy variables in the book.
regards
rogojel
 

rogojel

TS Contributor
#5
hi Greta,
this is IMHO something different. You can have a situation where you have 9 factors you want to analyse but the closest PB design has 12 factors. So, you run the 12 factor PB but do not set the 12-9=3 factors, only the 9 you are interested in. The one that eill not be set were called dummies in the original post, Box -Hunter calls them inert factors.

regards
rogojel
 
#6
It seems like they want to save a few degrees of freedom to get some kind of estimate of the error variance.

But I don't think that I would run such a design (at least not in the beginning). First it is not possible to estimate any interactions at all. They would be aliased/confounded with all the other main effects (or with such a try to estimate error).

I would maybe suggest a 2^(8-4) design. That is, 8 factors in 16 experimental runs. Then at least some interactions can be estimated. Still power calculations need to be done. Just because 11 factors can be estimated in 12 runs, does not mean that only 12 runs are enough.

But we will see what puriadarsh really meant, if she comes back here.
 

rogojel

TS Contributor
#7
hi,
I see PB designs in a more favourable light, Because of the projectivity property if there are no more then 3 active factors then the PB12 is equivalent to a 2^3 full factorial with a half replicate. So, it is a lottery in a way, but assuming effect sparsity there is a lgood chance it will pay off. If there are more the 3 active factors then one can extend the design with a few runs to get full or a half factorial, so nothing is lost.

it is a bit difficult to analyse the PB design though, that would be the downside.

regards
rogojel
 
#8
I agree with rogojel.

I just believed that both the original posters were in an early stage of their investigation. Then often the most important factors are mentioned and tested first. That is, factors that often have both main effects and interactions.

I would say that then, when the most obvious factors have been tested, it is time to pick up a Plackett Burman design to check if there are any further possible factors.

- - -

it is a bit difficult to analyse the PB design though, that would be the downside.
Maybe I have missed something here. I thought that it was just to run linear regression on the dummys and look what is large, or simply plot the estimated parameters in a QQ-plot.
 

rogojel

TS Contributor
#9
hi Greta,
it is the Box Hunter book again. The alias structure is more complex for PB designs then for factorials, which makes main effect plots pretty much meaningless. They advise using a Bayes type of analysis, a package is available in R.

regards
rogojel