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]

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.  

 

[#3]

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

[#4]

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.

[#5]

i got same picture with real values

[#6]

correlation between

x1, x1*x1*x1 - 0.92

x2, x2*x2*x2 - 0.93 etc.

[#7]

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. 

 

[#8]

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.

[#9]

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.

[#10]

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.