How to add a random effect in the multiple linear regression model of Plackett-Burman DOE?

[#1]

Hi community,

I have conducted a Plackett-Burman DOE for 9 continuous factors measuring 3 different responses (viability, proliferation, gene expression). For one of the responses (gene expression), I actually measure the response three times for each treatment - so these are not independent replicates. I would like to add a random effect in the model that JMP fits for this response. How can I do this practically? Or is this not possible on the JMP platform?

Thank you very much

Sara

[#2]

Hi @statman 

Thank you for these suggestions. I do have an additional question: once you have computed the mean and standard deviation or (log)standard deviation, how do you use these data together (as 1 unit) in the Fit Model platform? If I input them both as 'Y' in the Fit Model, JMP makes two regression models for mean and standard deviation separately. 

Thank you,

Sara

[#3]

As you indicated, the repeated data points are not independent from the treatments, so they are not DF's.  Essentially you have one experimental unit measured 3 times. Those 3 data points must be summarized to analyze the experimental treatments.  You put each in as a separate Y and will get 2 models.  BTW, you can also see if those Y's correlate (Multivariate Methods>Multivariate).  Factors can have no effect, can effect the mean and not variation, can effect variation and not the mean or can effect both mean and variation.  If you have a variation problem, finding factors that affect variation is more important than finding factors that affect the mean.

[#4]

To add to the previous comments, if it is repetition, you could compute a mean and a log standard deviation for modeling. The mean would serve your original purpose, and the log standard deviation would help you discover if any of the factors affect the variation of this response.