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Mananahi
Community Trekker

Interpretting Generalized model results on the original scale

Maybe this is a silly question but I'm new to generalized models. I have performed a beta generalized model on some proportion data that is naturally between 0 and 1. The model outputs parameter estimates that are significantly different between treatment groups as expected. The problem that I am having is that the parameter estimates are on a new scale that is not between 0 and 1. I am assuming this is due to some kind of transformation the program uses to run the model. I want to be able to interpret these results on the original scale. ie: The test mice consumed 95% of the feed treated with product A(Confidence interval [97%, 93%]) While the feed treated with product B only saw 20% consumption (Confidence interval [24%,16%]) Does anyone know an easy way of back transforming the estimates?

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julian
Staff

Re: Interpretting Generalized model results on the original scale

Hi @Mananahi,

By 'Generalized Model' do you mean the Generalized Regression personality in Fit Model? I'll assume so for this answer, but if you're doing something else let me know. 

 

Models such as this employ a link function, so your parameter estimates, as you noticed, are not in the original units of your variable. Here's a link to the statistical details for those response distributions, and here are the specific details for the beta:beta.png

There is a lot to unpack there, and my suggestion is to not work through the formulas yourself because there's an easier way in jmp. My go-to method to profile the response in the original units as a function of the input variables is the Prediction Profiler. You can access this under the Red Triangle for your model (next to Maximum Likelihood) then select Profilers > Profiler. This will append the Prediction Profiler to the report, which lets you interactively profile (click through) the response Y as a function of your inputs. What is reported along the left is the mean response given the inputs you select and the 95% confidence interval around that point estimate.

 

I hope this helps!

@julian 

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julian
Staff

Re: Interpretting Generalized model results on the original scale

Hi @Mananahi,

By 'Generalized Model' do you mean the Generalized Regression personality in Fit Model? I'll assume so for this answer, but if you're doing something else let me know. 

 

Models such as this employ a link function, so your parameter estimates, as you noticed, are not in the original units of your variable. Here's a link to the statistical details for those response distributions, and here are the specific details for the beta:beta.png

There is a lot to unpack there, and my suggestion is to not work through the formulas yourself because there's an easier way in jmp. My go-to method to profile the response in the original units as a function of the input variables is the Prediction Profiler. You can access this under the Red Triangle for your model (next to Maximum Likelihood) then select Profilers > Profiler. This will append the Prediction Profiler to the report, which lets you interactively profile (click through) the response Y as a function of your inputs. What is reported along the left is the mean response given the inputs you select and the 95% confidence interval around that point estimate.

 

I hope this helps!

@julian