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Michal
Level I

third order terms in linear model

Dear JMP Experts,

I would like to hear your opinions on the topics below:

1)Does it make sense to include 3rd order (cubic, interaction) terms into a model with experimental runs consisting of factors investigated on 3 levels only?

2)Under what circumstances would you include 3rd order terms that in respect to industrial process model?

Thanks very much,

Michal

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Re: third order terms in linear model

First, you cannot estimate the parameters for the third-order terms with only three levels. If you have an experiment that successfully fit the second-order model albeit with lack of fit, then use DOE > Augment Design to add the new terms and make the new runs that compliment the original runs.

 

Second, I would explore the third-order terms if either my second order model exhibited significant lack of fit or I was unable to verify the second-order model predictions. This failure indicates model bias that cannot be tested as lack of fit.

 

The second-order model successfully models most cases with a non-linear response but over an extended range, either a higher-order linear model or another model entirely (e.g., neural network) might be required for elimination of the bias. For example, if your response exhibits an asymptote, the polynomial function will not successfully model the response.

Learn it once, use it forever!

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2 REPLIES 2
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Re: third order terms in linear model

First, you cannot estimate the parameters for the third-order terms with only three levels. If you have an experiment that successfully fit the second-order model albeit with lack of fit, then use DOE > Augment Design to add the new terms and make the new runs that compliment the original runs.

 

Second, I would explore the third-order terms if either my second order model exhibited significant lack of fit or I was unable to verify the second-order model predictions. This failure indicates model bias that cannot be tested as lack of fit.

 

The second-order model successfully models most cases with a non-linear response but over an extended range, either a higher-order linear model or another model entirely (e.g., neural network) might be required for elimination of the bias. For example, if your response exhibits an asymptote, the polynomial function will not successfully model the response.

Learn it once, use it forever!

View solution in original post

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Re: third order terms in linear model

To add to my colleague @markbailey's recommendations and advise, with respect to your second question about 'when'?, I'll add the thought that, if your knowledge of physics, chemistry, biology, or socioeconomic behavior or general domain expertise is such that BEFORE conducting experimentation, you suspect there may be active 3 factor interaction effects, well that's a time when I'd set up a design that allowed for estimation of those effects. You can make this happen most efficiently within the JMP Custom Design platform by explicitly articulating the specifice 3 factor interaction effects that you'd like to estimate.

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