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I am a bit of a SAS novice so please forgive my ignorance.

I have a generalized Linear mixed model in SAS based on past data but I don't know how to export it to a pure mathematical formula that could be used to generates probabilities varying different inputs.

For example, I want to be able to input a values to different parameters and get a probability for that instance. Is there an easy way to export the mathematical model from SAS?

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Yes there are various ways to export your model. The quickest and easiest method that comes to my mind is using ODS output tables

You should look specifically for ParameterEstimates output table. This table (or dataset) will contain all the estimated parameters of your model. From here you can exported to R, Excel or use it with Proc Score within SAS to score new observations.

So your code should look like this:

ods output ParameterEstimates=ParameterEstimates;

proc GLMMIX or GML;
Model ...;
<more options> ...;
run;

Here is a link to all the output tables available for GLMMIX.

Hope it helps

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it depends on exactly what's needed but sas can actually provide the predicted values for you. I assume you're using genmod, thus, see 'predicted' in the output statement: https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_genmod_sect023.htm, or "plots=predicted" on the genmod statement

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