topic Re: Creating I-optimal designs for a full cubic model in Discussions

Creating I-optimal designs for a full cubic model

candcook5 — Thu, 08 Jun 2023 16:30:00 GMT

I am trying to generate an I-optimal design for a 3-factor experiment where the underlying model is assumed to be a full cubic response surface design (not a mixture experiment). Is there a way to create this design with Custom Design (or any other tool in the DOE suite)?

Re: Creating I-optimal designs for a full cubic model

Dan_Obermiller — Fri, 10 Mar 2023 19:57:39 GMT

Yes, this is possible.

Specify your factors.

Specify your model (I clicked on the interactions button and chose 3rd to get all of them. I also clicked Powers > 2nd and Powers > 3rd to get all terms including cubic.)

Go to the red pop-up menu at the top by the Custom Design heading. Choose Optimality Criterion > Make I-Optimal Design.

Complete your design process.

Re: Creating I-optimal designs for a full cubic model

candcook5 — Fri, 10 Mar 2023 22:49:57 GMT

Thanks for the reply, Dan.

I think that there are some terms missing - and those are the ones that I am having problems generating. Here are the terms that I was aiming for, with the missing ones that I cannot seem to create in blue:

x1, x2, x3,

x1^2, x2^2, x3^2, x1x2, x1x3, x2x3

x1^3,x2^3, x3^3, x1x2x3, x1x2^2, x1x3^2, x2x1^2, x2x3^2, x3x1^2, x3x2^2

Thanks for your help.

Re: Creating I-optimal designs for a full cubic model

Victor_G — Sat, 11 Mar 2023 08:51:42 GMT

Hi @candcook5,

Sorry for breaking into the conversation between you and @Dan_Obermiller.

Some remarks and comments :

For your RSM custom design, since you would like to have in your model a full cubic response surface, you can click on "RSM" button to directly introduce in the model all 2-factors interactions and quadratic powers from your factors (before adding manually your cubic powers and 3-factors interactions). This button will also automatically change the optimality criterion to "I-optimal" (minimizing the average variance of prediction, adapted for RSM designs), which is quite convenient.
In order to add the effects you mention (Partial cubic effects, in blue), it is easy to do it with the button "Cross" : for X1.X2.X2, just select the effect X2.X2 from the "Model" panel, X1 from the "Factors" panel, and click on "Cross", this will add the effect you want :

In the "Fit Model" platform, if you want to add these partial cubic effects (because for any reasons they were not introduced in the design or you have to manually enter them), there is already a macro to enter this effect (select your 3 factors, then click on "Macros" and select "Partial Cubic effects") :

I hope these answers will help you,

Re: Creating I-optimal designs for a full cubic model

Dan_Obermiller — Sun, 12 Mar 2023 02:11:30 GMT

I think the reply from @Victor_G will tell you how to add those terms that you put in blue. I apologize that I did not include those terms. If you need more guidance, let us know.