Interpretation of Predicted Mean for Negative Binomial GEE with Offset

[D.G.G.]

Hello,

I have run a negative binomial GEE with population (ln) as an offset. I am
confused as to how to interpret the “predicted mean” option under the “save”
tab in SPSS. If I’ve included an offset, is the predicted mean then the
predicted rate or is it a predicted count? The output for predicted mean is
very close to my original count data, so it seems to be a predicted count,
but then I’m not sure what role the offset is playing in that outcome.

The data is an over-dispersed count for the dependent variable, one
categorical predictor, year as a covariate, with the ln of population as an
offset.

I am running SPSS 20.

Thank you,
West




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[Andy W]

An offset is just a coefficient set to the value of 1. So yes SPSS is just
giving the predicted mean. If you wanted to go back to the rate scale you
would simply divide by the predicted mean by your denominator (note you
would divide by the actual denominator, not the logged version).

See
https://utdallas.edu/~Andrew.Wheeler/PoissonReg.html#using-offsets-to-interpret-poisson-regression-as-rates
for my class notes on interpreting offsets for Poisson models (which work
the same way for negative binomial since the mean equation is the same).



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Andy W
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http://andrewpwheeler.wordpress.com/
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[D.G.G.]

Thank you, Andy! That was very helpful.



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