topic Re: How can I compare two Poisson models (nested)? in Statistical Procedures

How can I compare two Poisson models (nested)?

KS99 — Fri, 02 Feb 2024 10:04:54 GMT

Hi, all, dear SAS community,

Please bear with me if I returned with too simple a stats question.

I ran two Poisson models, one simply with controls, the other with controls plus variables of interest.

/** Model (1) **/
proc genmod data = dataset;
model Y = X1  X2  X3  X4  X5  year1-year9 ind1-ind63 / dist=poisson link=log; run;  

/** Model (2) **/
proc genmod data = dataset;
model Y = X1  X2  X3  X4  X5  X6  X7  X8  X9   X10  year1-year9 ind1-ind63 / dist=poisson link=log; run;

I want to check whether one model is more significant (in terms of fit) than the other. In other words, I want to perform a model test like F-Test when comparing OLS models. According to my internet search, Poisson works differently; they suggest using CONTRAST option in PROC GENMOD but I am not really sure. And the ways they show how to use CONTRAST options look so complicated. Please help! I really appreciate you, SAS community!

Sincerely,

KS -,

Re: How can I compare two Poisson models (nested)?

StatDave — Fri, 02 Feb 2024 15:33:39 GMT

See this note and the examples it links to.

Re: How can I compare two Poisson models (nested)?

sbxkoenk — Fri, 02 Feb 2024 17:30:14 GMT

Indeed, you need a a likelihood ratio test.

Like is said on this page:

SAS® 9.4 and SAS® Viya® 3.5 Programming Documentation
SAS Visual Statistics Programming Guide
Regression Action Set
Poisson Regression
https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/casactstat/casactstat_regression_examples02.htm

See the "Fit Statistics" table. The –2 log likelihood at the converged estimates is a certain numeric value (the lower the better -- a perfect fitting model would have a value of 0). You can use this –2 log likelihood value to compare the model to nested model alternatives by means of a likelihood ratio test.
To compare models that are not nested, information criteria such as AIC (Akaike’s information criterion), AICC (Akaike’s bias-corrected information criterion), and BIC (Schwarz Bayesian information criterion) are used. These criteria penalize the –2 log likelihood for the number of parameters.

Koen

Re: How can I compare two Poisson models (nested)?

KS99 — Sat, 03 Feb 2024 20:29:03 GMT

Thank you StatDave! This is a great help! Somebody expanded what you hinted at. I can consult them all!

Re: How can I compare two Poisson models (nested)?

KS99 — Sat, 03 Feb 2024 20:30:21 GMT

Thank you, sbxkoenk! This is a great and detailed help! I can use it my entire life as long as I get troubled by Poisson!

KS -