topic Re: Fitting Different Slopes Common Intercepts in Discussions

Fitting Different Slopes Common Intercepts

vincem — Sat, 29 Feb 2020 11:03:20 GMT

Hi - i am unsure how to fit a regression model with different slopes BUT a common Interecpt.

Assume Y=response, GROUP (2-levels), TIme (Covariate)

Kind regards, Vince

Re: Fitting Different Slopes Common Intercepts

dale_lehman — Sat, 29 Feb 2020 13:40:25 GMT

You can do this in Fit Y by X: Y=response, X=time. After the plot, Group by GROUP. Then use Fit Special and constrain the intercept to 0.

Re: Fitting Different Slopes Common Intercepts

Craige_Hales — Sat, 29 Feb 2020 14:03:46 GMT

@dale_lehman Cool!

Male and Female groups have same intercept

Re: Fitting Different Slopes Common Intercepts

Mark_Bailey — Sat, 29 Feb 2020 17:57:06 GMT

If you also want to estimate the common intercept, try this approach.

Select Analyze > Fit Model.
Click the red triangle at the top left and de-select Center Polynomials.
Select the response column and click Y.
Select the time and group columns and click Macros, then select Factorial to Degree.
Select the group effect and click Remove.
JMP will ask you to if it should remove all terms with this column. Click No.
Click Run.
JMP will warn you about a missing effect. Click Continue.

In general, we would keep the group effect in the model to maintain the model hierarchy. But that leads to a unique or different intercept for each group. This way you will get estimates and tests for the common intercept and unique group slopes.

Re: Fitting Different Slopes Common Intercepts

Craige_Hales — Sat, 29 Feb 2020 20:45:00 GMT

Thanks! I made up 40 because it looked good (better than zero, anyway).

edit: adding an image. Left is fit y by x, center is fit model. Right is illustrating how to get the slopes from fit model.

@Mark_Bailey

Getting the slopes from Fit Model

Re: Fitting Different Slopes Common Intercepts

vincem — Sat, 29 Feb 2020 22:39:52 GMT

Thansk...however when i adopt the below approach the graph of Y verus TIME by group - doesnt appear to haev a common intercept. Howevre if i change Time to an ordinal variable..seems to work OK.

Re: Fitting Different Slopes Common Intercepts

vincem — Sat, 29 Feb 2020 22:42:57 GMT

Thanks...curious to knnow if there is an alternative way without this to stage process..

Re: Fitting Different Slopes Common Intercepts

Craige_Hales — Sat, 29 Feb 2020 22:53:46 GMT

Fit model does give the intercept and the two slopes in a single step. The picture is comparing the easy-to-read output in fit y by x with the parameters returned by fit model. I puzzled it out by comparing them; I hope @Mark_Bailey is watching in case I've misinterpreted something.

Re: Fitting Different Slopes Common Intercepts

vincem — Sat, 29 Feb 2020 23:50:13 GMT

Thanks - how did you estimate the common intercept using fit y by x of 49?.

Re: Fitting Different Slopes Common Intercepts

Craige_Hales — Sun, 01 Mar 2020 00:08:52 GMT

I copied it from fit model to @dale_lehman answer, instead of the zero he suggested or the 40 I initially guessed. If you start with fit model rather than fit y by x, you get parameters for both lines without copying the numbers.

Re: Fitting Different Slopes Common Intercepts

vincem — Sun, 01 Mar 2020 02:17:00 GMT

Thanks - so I assume fit model implementation is required to get the common intercept and slopes first then fit by x to get the figure. Thanks for your help . Appreciate it

Re: Fitting Different Slopes Common Intercepts

dale_lehman — Sun, 01 Mar 2020 14:31:55 GMT

Here is another approach, using the Nonlinear platform. Attached is an example: you need to set parameters to be solved for, with a single intercept but varying slope parameters for the two groups. The script is saved for the solution.

Re: Fitting Different Slopes Common Intercepts

vincem — Sun, 01 Mar 2020 19:32:22 GMT

thanks much appreciated.

Re: Fitting Different Slopes Common Intercepts

hardner — Tue, 16 Apr 2024 14:38:50 GMT

on here appreciating this older tip about using Fit Model by not centering polynomials and just thought I'd note that in Fit Model the Expanded Estimates are a little less cryptic, especially if there were more groups. I'll be using those where I want to get the slopes out of there with JSL but can see that the plot from Fit Y by X is nicer.