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Fit Model: Square Transformation vs 2nd Order Polynomial

I am using the Fit Model platform in JMP to create a simple standard least squares fit with one model effect.  I noticed that using the square transformation on the effect gives a different fit than using the 2nd order polynomial of that effect (after removing the first order term to leave only the 2nd order term).  JMP gives a warning about leaving the 1st order term out of the model, but I continued with the analysis which gives a significantly different result.  What is the difference in the two approaches?

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Re: Fit Model: Square Transformation vs 2nd Order Polynomial

In the model dialog for the 2nd degree polynomial with the linear term removed, click the red triangle next to Model Specification and uncheck "Center Polynomials". Then your results will agree with the other model you made. The model predictions will be the same whether centered or not.

Michael

3 REPLIES 3

Re: Fit Model: Square Transformation vs 2nd Order Polynomial

In the model dialog for the 2nd degree polynomial with the linear term removed, click the red triangle next to Model Specification and uncheck "Center Polynomials". Then your results will agree with the other model you made. The model predictions will be the same whether centered or not.

Michael  Steven_Moore
Super User

Re: Fit Model: Square Transformation vs 2nd Order Polynomial

I like your answer, but I have wondered:  WHY center the polynomials?

Steve

Re: Fit Model: Square Transformation vs 2nd Order Polynomial

If you search the help index for "Center Polynomials" you will find this:

Causes any continuous term involved in an effect with degree greater than one to be centered by its mean. This option is checked by default, except when a term involved in the effect is assigned the Mixture Effect attribute or has the Mixture column property. Terms with the Coding column property are centered midway between their specified High and Low values.

Centering is useful is making regression coefficients more interpretable and in reducing collinearity between model effects. (my emphasis)

If you search Google for "Center Variables" you can find additional discussion on this topic.

Michael