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Dec 23, 2015

## Main and cubic effects confounding

I'm trying (unsuccessfully) to generate a custom design without confounding of main and cubic effects. I always obtain a correlation of nearly 1 between these effects.

Any suggestions?

thanks
Matteo Patelmo

3 REPLIES 3

Joined:

Apr 3, 2013

## Re: Main and cubic effects confounding

What you are trying to do is not really possible. The easiest way for me to explain this is to consider the X range from -1 to 1. When X is -1, X^3 is -1. When X is 0, X^3 is 0. When X is 1, X^3 is 1. That is a pretty strong relationship! Expanding or contracting the range of X will make the relationship non linear, but  is not going to break that fundamental relationship. That's not exactly how the math works, but I hope it conveys the thought on why you have high correlations.

The best approach to minimizing the correlations is to tell Custom Designer to create an Alias Optimal design. Before clicking "Make Design", go to the red popup menu and choose "Optimality Criterion" and then choose "Alias Optimal." That will give you the lowest correlations possible for your given number of runs.

Dan Obermiller

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Joined:

Dec 23, 2015

## Re: Main and cubic effects confounding

Thanks DanO! the idea is clear.  So: if I need to run a DOE with some cubic effects, would I just neglect the high correlation and execute/analyze whatever is suggested (even with Alias optimal) or should I do something different during the analysis?

For example the following:

Joined:

Apr 3, 2013

## Re: Main and cubic effects confounding

If you must have a cubic term in the model, there is not much you can do about the correlation. You can "ignore" it, but realize how it is impacting your modeling efforts. You could switch to another type of analysis that would not be affected by the correlation (PLS for example). It all depends on what you are trying to do with your design and analysis.

Which brings up the point of why a cubic term is in the model. They are rare, so hopefully there is some fundamental reason for including it.

As an additional note, for the design you created you are not following the model hierarchy. If including a cubic term you should also include the quadratic terms in the model. I would recommend doing that. In fact, when conducting the analysis JMP will warn you that you are missing effects from the model.

Dan Obermiller