Hello Sas Community,
I am currently working on a project where I need to utilize PROC COUNTREG in SAS, particularly focusing on utilizing ZICMP distribution with spatialeffects.
I'm trying to manually score based on the parameters, and from the documentation, I've reconstructed the following steps.
Let:
, or
But the values of lambda vector obtained in the output of the countreg differs from the ones computed as exp(xbeta), that is instead the value mu in the countreg output.
(in documentation there is a typo in the ZICMP, but it's correct in CMP and the results are the same of countreg output)
Now there isn't a finite form for this Normalization Factor, following the paper:
Approximating the Conway–Maxwell–Poisson distribution normalization constant
Steven B. Gillispie ∗ and Christopher G. Green
University of Washington, Seattle, USA — Department of Statistics
Technical Report no. 615
June 6, 2013
I found this approximation formula
And then
Now, the predicted results obtained do not match those obtained from the output of the countreg. The differing values are: Lambda (as mentioned above), P(y=0), P(y!=0) and Predicted (those three latter are probably due to the Lambda error)
Any examples, tips, or resources you could share would be greatly appreciated. Thank you in advance for your assistance!
Best regards,
Piero
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