topic Re: How to best use discrete principal component data points in a design in Statistical Procedures

How to best use discrete principal component data points in a design

doechemist — Sat, 12 Jan 2019 23:30:38 GMT

Hi there,

I am on my way to investigate a chemical reaction, where I would like to vary different factors in the experiment:

Temperature (I probably need a split-plot design for this; I am going to run several test at the same temperature at the same time)
Reaction time
Concentration
Ratio of different reagents
and the three first principal components (PC) of the solvent

I really like the concept of PCs to describe the solvents, as this gives a better (and probably a qualitative) discrimination between different solvents.

What troubles me is that I cannot change the PCs of the solvents continuously - meaning that my range of candidate solvents rather gives me a 'cloud' of discrete points in 3D space instead. Each solvent has a particular set of PCs.

I might be able to circumvent this issue by selecting solvents 'close enough' to the targeted design points (+1/-1 in each PC dimension) and then use the true (coded) coordinates for the analysis.

However, due to a restriction in chemical stability, all I have left is two classes of solvents with PC1-3 coordinates that sort of form two distinct domains in the PC1-3 space. This makes it impossible to find solvents sufficiently close to any reasonable design point.

I have tried to use the custom design tool by putting all my solvents and their data into a table, and then use them as a covariate factor (cf. the DOE manual). Trying different number of runs, I have to use a lot of runs (>80, JMP suggests 125) to get a reasonable power (0.8) for the PCs and avoid aliasing. For some number of runs, there seems to be partial aliasing of main factors as well as interaction terms. Sometimes, JMP doesn't give my any estimate of power.

Is there any smarter way to implement the PCs in my design? Could I ignore the low power for the PCs when using much fewer runs, hoping to a) still detect an effect anyway or b) remove certain non-significant factors and keep the PCs for the next iteration?

(JMP 14.0.0)

Re: How to best use discrete principal component data points in a design

PaigeMiller — Sun, 13 Jan 2019 01:23:45 GMT

The only thing that comes to mind, if you have discrete levels of the solvent PCs rather than continuous levels that you can put exactly where the design says they should go, is to use something called an Optimal design. In layman's terms, it will choose from the available discrete levels of your solvent PCs the combinations that give you something "closest" to an orthogonal design.

In SAS, PROC OPTEX will do this for you.

https://documentation.sas.com/?docsetId=qcug&docsetTarget=qcug_optex_toc.htm&docsetVersion=14.2&locale=en

Re: How to best use discrete principal component data points in a design

doechemist — Sun, 13 Jan 2019 11:26:16 GMT

Thank you for your input! I will definitely check it out.

I just saw, however, that I somehow posted my question here in the SAS community, rather than in the JMP community.

I've reposted my question the place I originally intended: https://community.jmp.com/t5/Discussions/How-to-best-use-discrete-principal-component-data-points-in-a/m-p/105823#M38953

Re: How to best use discrete principal component data points in a design

PaigeMiller — Mon, 14 Jan 2019 13:26:10 GMT

Hello, @doechemist

Wouldn't the answer apply also to JMP? I don't know how to create an Optimal design in JMP, but I can use that Google thing and it's pretty clear that JMP does create Optimal designs.