3rd power parameter DOE

[#1]

Hi JMP ers,

I have 4 factors and try to make a model with main effects, interactions, 2nd order and 3rd order power.

I make design with recomended optimality criteria. When i checked color map correlations i can always see x1 and x1*x1*x1 correlation near to 1. How can make a DOE that does not have this problem?     

[#2]

First I made custom Design with d optimality for 2nd order model and augmented Design with I Optimality for 3rd order model. Is it right ?

[#3]

AFAIK, in the custom design platform, as long as you select Necessary (vs. If Possible), JMP will create a design that will allow for estimation of those effects.

[#4]

I do have wonder what it is you are working on where you suspect cubic effects? Even if they exist, they will be difficult to "manage". Seems you might want to investigate alternative repossess variables that may be robust to those type of effects?

[#5]

I do not mean to contradict one of my colleagues, but how does one specify the factors, model, and number of runs in order to get 'correct design' without correlated estimates?

I added four continuous factors representing concentration, temperature, time, and pressure. I added terms for the second and third power of each factor to the linear model. I used the default number of runs. This example is clearly not one of the correct results:

I simulated the response so that I could launch Fit Least Squares platform. The response is not involved in the correlation of the estimates, which is also indicated by VIF > 1 in the parameter estimates report. Here is the design:

Here is the report using the default coded levels. VIF around 10 indicates a correlation around 0.9.

Here is the same analysis but without coded levels. The coding clearly helps:

What is the use of the map of correlations if it does not represent the actual correlations? (I think that it does.)

[#6]

Just to clarify, the coding used in the Custom Designer will show the correlations, which you can't get around due to the natural correlation built in by taking -1 and +1 to the third power. From the design perspective, you're still finding the D-optimal design, but the diagnostics make it look "bad".

In the future, I can see us using an orthogonal polynomial coding approach to make to make the higher order terms not look as bad as this. Note that you'll see the same issue between x^2 and x^4 if you were to include up to the fourth power.

To summarize, it's not that there's anything wrong with the design, or the correlations, but it's something that we're certainly aware of causing confusion and hope to better address this in a future version.

Hope this helps,
Ryan

[#7]

@Ryan_Lekivetz, sorry I apparently did a poor job of explain what we discussed yesterday. Thanks for your clarification.

[#8]

@statman , just making sure we're all on the same page. 

It was great talking to you yesterday, and it was great to put a face with the name. Very much appreciate your help on the community forums.

Cheers,

Ryan

[#9]

I see, thank you very much for you explanations. but i still do not clear about which tipe of Design i have to use to be abla to construct a good model ( a model without correlations) with main effects + 2 nd and 3rd order interractions + 2 nd and 3rd order powers.

Is custom Design with I optimality correct? Or do you suggest me something else?