topic Re: Compare polynomial regression lines in Discussions

Compare polynomial regression lines

Ben11 — Sat, 10 Jun 2023 23:51:21 GMT

This may be basic but I'm struggling to find a way around this in JMP. Pardon me if this has been discussed previously on this forum. I essentially want to statistically compare regression lines. However, these are polynomial curves. All the options I have tried in JMP fits a linear curve by default which is not a good fit for the data.

Briefly, I want to perform a hypothesis test to assess whether there are differences among the categories within my dataset. I am able to do this using the 'Fit Model' dialog. But I am unable to the regression as 3rd order polynomials. Hence, JMP automatically applies a linear fit.

Is there a way to tell JMP to perform polynomial fitting in the "Fit Model" dialog.

Your help is appreciated.

Re: Compare polynomial regression lines

Georg — Tue, 19 Jul 2022 20:23:05 GMT

In platform fit y by x you can perform polynomial regression, and you can also show confidence region,

maybe this helps?

Re: Compare polynomial regression lines

Ben11 — Tue, 19 Jul 2022 21:05:11 GMT

Hello Georg,

Thanks but this doesn't help my situation. I have two categorial variables by which I need to compare the regressions.

So the Fit Y by X doesn't help, unless there's some way around this that I don't know.

What I need to do is fit a polynomial curve through the Fit Model dialogue.

Re: Compare polynomial regression lines

Georg — Tue, 19 Jul 2022 21:18:13 GMT

You can build this model as well in fit model platform (Macros --> Polynomial to degree ...),

using sex in By-role you can fit separate regression models, save them as formula and compare them as you need.

Re: Compare polynomial regression lines

Dan_Obermiller — Tue, 19 Jul 2022 22:04:09 GMT

If you want a formal statistical test to compare the curves, then you would add the categorical variable into the model. Using Georg's example, your model would be Height, Height^2, Height^3, Sex, Sex*Height, Sex*Height^2, Sex*Height^3.

The test of the parameter for Sex would tell you if there are differences in the intercepts.

The test of the Sex*Height parameter would tell you if there are differences in the slopes of Height.

The test of Sex*Height^2 would tell you if there are differences in the quadratic parameter estimates.

The test of Sex*Height^3 would tell you if there are differences in the cubic parameters.

Re: Compare polynomial regression lines

Mark_Bailey — Wed, 20 Jul 2022 14:22:47 GMT

I think @Georg helped but didn't go far enough. That is to say, you need to add interaction terms for all the X terms. Here is the same example, but with an interaction term for all the :height terms:

So this case concludes that there is no need for a unique intercept, first-order, or second-order term across sexes.

Note that these effect tests are appropriate for a difference in the parameter estimates across groups. They are not appropriate for equivalence.