topic Re: 3rd power parameter DOE in Discussions

3rd power parameter DOE

Ella — Fri, 09 Jun 2023 00:22:45 GMT

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?

Re: 3rd power parameter DOE

statman — Thu, 15 Oct 2020 15:11:47 GMT

Assuming you have 4 factors at 4 levels, when using the Customer Design platform, in the Model, highlight the effects you want. If it says If Possible, you can change that to Necessary.

Re: 3rd power parameter DOE

Ella — Thu, 15 Oct 2020 18:33:25 GMT

I tried but got same correlation again.
Did you check your correlation picture? Do i miss something diffrent?

Re: 3rd power parameter DOE

statman — Thu, 15 Oct 2020 21:10:29 GMT

Ella,

What you are seeing is a result of the coding of values for the factors. -1^3 = -1, 1^3 = 1

So if you use "actual values" you will see the correlation matrix without those terms correlated.

Re: 3rd power parameter DOE

Ella — Fri, 16 Oct 2020 05:34:01 GMT

i got same picture with real values :(

Re: 3rd power parameter DOE

Ella — Fri, 16 Oct 2020 05:35:37 GMT

correlation between

x1, x1*x1*x1 - 0.92

x2, x2*x2*x2 - 0.93 etc.

Re: 3rd power parameter DOE

Dan_Obermiller — Fri, 16 Oct 2020 13:07:05 GMT

The X^3 vs X plot has a correlation of 0.916 and the density ellipse is elongated. Find 4 points on that curve that are not correlated. I don't think you can do it. Those terms will always be correlated.

For a contrast, I have also included a plot of X^2 vs. X. The correlation is -0.019 and the density ellipse is almost circular. You can get correlations close to zero between these terms.

Re: 3rd power parameter DOE

statman — Fri, 16 Oct 2020 14:29:56 GMT

I'm sorry, my understanding is that you will always get that correlation due to the coding that goes on "behind the scenes". What I meant to say, AFAIK, the x and x^3 will actually not be correlated if the appropriate designs selected and the actual values are used. The correlation matrix will always show the correlation due to the coding.

Re: 3rd power parameter DOE

Dan_Obermiller — Fri, 16 Oct 2020 15:07:21 GMT

Coding is actually used to REDUCE collinearity. But coding can only do so much. My graphs may not be the best way to illustrate, but consider this:

X1 X1^2 X1^3

100 10000 1000000

200 40000 8000000

150 22500 3375000

There is a correlation between X1 and X1^2 (0.997). But if you code to -1, +1, the correlation will drop to 0. This does not happen when cubing because, as you pointed out, -1^3 = +1 and +1^3 = 1, but the correlation on the original scale is large, too.

Re: 3rd power parameter DOE

statman — Fri, 16 Oct 2020 15:38:28 GMT

I spoke to a JMP DOE developer yesterday (JMP summit) and he confirmed the plots would always show the correlation, but in actuality with the correct design, there is no correlation.

Re: 3rd power parameter DOE

Ella — Fri, 16 Oct 2020 15:47:55 GMT

Re: 3rd power parameter DOE

Ella — Fri, 16 Oct 2020 15:46:31 GMT

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 ?

Re: 3rd power parameter DOE

statman — Fri, 16 Oct 2020 16:09:02 GMT

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.

Re: 3rd power parameter DOE

statman — Fri, 16 Oct 2020 16:11:20 GMT

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?

Re: 3rd power parameter DOE

Mark_Bailey — Fri, 16 Oct 2020 16:17:23 GMT

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.)

Re: 3rd power parameter DOE

Ryan_Lekivetz — Fri, 16 Oct 2020 17:36:29 GMT

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

Re: 3rd power parameter DOE

statman — Fri, 16 Oct 2020 18:40:43 GMT

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

Re: 3rd power parameter DOE

Ryan_Lekivetz — Fri, 16 Oct 2020 18:58:36 GMT

@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

Re: 3rd power parameter DOE

Ella — Sat, 17 Oct 2020 04:04:10 GMT

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?