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- Re: Dispersion Parameter of Neg Binomial Dist in Genmode procedure

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Posted 10-17-2012 11:10 AM
(3284 views)

I need to know if the dispersion estimate showed in the output of the of genmode procedure for the negative binomial dist is an estimation made before making the estimation of the general linear model predictor coefficients.

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Not sure if this is the answer, but in the Details section of the documentation, in the Dispersion Parameter section, the final sentence is:

In the case of the negative binomial distribution, PROC GENMOD reports the “dispersion” parameter estimated by maximum likelihood. This is the negative binomial parameter k defined in the section Response Probability Distributions.

To me this would indicate that the dispersion estimate is not made before the estimation, but is "simultaneously" estimated.

Steve Denham

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Here's my feeling: It is included as yet another parameter in the likelihood function, with an initial value from a weighted least squares estimate, the same as any of the other parameters.

For an example, using the Poisson regression example in the Getting Started section, and changing the code slightly:

proc genmod data=insure;

class car age;

model c = car age / dist = **negbin**

link = log

offset = ln

**itprint**;

run;

Hopefully, this answer makes some sense.

Steve Denham

This will give the value of the parameters at each step in the iteration in the output.

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This one I do have some ideas about. From each run, you will get a table of information criteria, giving things like Akaike's Information Criteria, etc. Now a likelihood ratio test looking at change in -2 log likelihood is possible, BUT since the models are not nested, getting the proper degrees of freedom is difficult, and really, I don't know that the difference will even be distributed as chi-squared. However, if the fixed effects are identical in the two models, a direct comparison of the various IC results can indicate which distribution better fits your data. SAS uses the smaller is better criterion. If there is a decided advantage to one of the distributions, then I would proceed with using it for subsequent analysis.

I hope this helps.

Steve Denham

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This is close. I would include the predictors, as the dispersion parameter for the negative binomial is going to be data dependent.

Steve Denham

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