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Using Principal Components as factors in a DOE

ehchandlerjr

Hello - So I have an experiment where one of the factors is categorical, solvent, but we would prefer to have as few categorical factors as possible. Toward that, we are using the results from a published journal article that takes 750+ solvents across 125+ solvent models and dimentionally reduces the solvent scales using PCA.

We would like to use a few of these principal components as continuous factors in our design, but I am not sure how best to do this. The problems are two fold. 1) do we just make the principal components discrete numeric and then add them all manually? I can't seem to find a way to make a factor table from scratch. 2) even if we do that, there are required combinations of levels across the principal components just by the definition of PCA, rather than disallowed combinations. How would you tell JMP this? Do I need to bite the bullet and learn to code?

Thanks.

Accepted answers

Mark_Bailey

I do not understand why you would go to the trouble of a double replacement. It seems that your covariates table is quite large, as you are using PC from solvent characteristics from a large published library. You could replicate the covariate any number of times (e.g., twice, thrice, ten times) and use that table when you design your experiment. JMP custom design will select the best rows, whether that be a new solvent or a replicate of a previously chosen solvent. (I assume that the covariate data table will have a data column with solvent identification in addition to the PC.)

The covariate factor represents a constraint on the factor levels but otherwise custom design works as usual.

All comments

Mark_Bailey

Perhaps you could include the solvent PC as covariate factor. See Help > Books > Design of Experiments and look up this topic.

ehchandlerjr

Hello - Thanks for the reply! So I have tried that but we don't have most of the solvents on hand, which is a problem with the covariate platform as it always seems to only pick one of each row and no more. Is there a way around that or is that a requirement by the theory of covariates?

Mark_Bailey

JMP assumes that the covariate levels in the separate data table represent all the values that you might want to include in the experiment. If the number of runs chosen for the design is less than the number of rows in the data table with the covariate values, then JMP selects the best covariate values and selects the rows.

ehchandlerjr

Ok - So is there something wrong if, for example, I told it to do, say, 10 runs, then took the 10 solvents it picks, and then just redo a design with those ten as categorical, and then, because we will replace the categorical with the principal components in the analysis, tell it to do as many runs as necessary to account for the degrees of freedom change of switching variables?

That may not make sense.