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Level I

## 3rd power parameter DOE

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?

18 REPLIES 18
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Level VII

## Re: 3rd power parameter DOE

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.

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Level I

## Re: 3rd power parameter DOE

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

## Re: 3rd power parameter DOE

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.

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Level I

## Re: 3rd power parameter DOE

i got same picture with real values

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Level I

## Re: 3rd power parameter DOE

correlation between

x1, x1*x1*x1 - 0.92

x2, x2*x2*x2 - 0.93 etc.

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Staff

## Re: 3rd power parameter DOE

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.

Dan Obermiller
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Level VII

## Re: 3rd power parameter DOE

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.

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Staff

## Re: 3rd power parameter DOE

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

100    10000   1000000

200    40000   8000000

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.

Dan Obermiller
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Level VII

## Re: 3rd power parameter DOE

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.
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