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Presenting coefficients from a poisson or negative binomial modal

Solution Question: What do you think is the best way to present negative binomial regression results?

Detailed answer:

You can interpret the change in expected rate for a binary variable by exponentiating the coefficient, i.e. exp(beta), directly, but for for continuous variables, we prefer tables of fitted values or a plot of the expected rate for different levels of the independent variable. Use a method such as Stata's "clarify" or R's Zelig to produce CIs. Just as with the % change idea, you have to hold all other variables constant at some value, usually a mean or median.

The reason that the IRR (incident rate ratio, or exp(beta) is hard to interpret for continuous variables is that the % change is only meaningful relative to its current baseline. So if the expected count is say .0004 (really low!) and the exp(hat{beta}) is 3.19, then this suggests that you have a 219% increase but this is still negligible since you are still predicting just 1/100th of a count (zero, in other words).

Better to not report the % change at all, and instead use a table of fitted values such as

Yes No
Rapporteur Status 3.1 2.2
(.63) (.45)
Committee Membership No 1.1 0.7
(.34) (.41)

where this shows your prediction of counts, holding other variables constant at their means, for the combinations of committee membership and rapporteur status, along with SEs (or confidence intervals if you prefer).

For continuous variables, you can predict the count for a set of specific levels of the covariate, and plot the expected count on the y-axis with confidence intervals from a method such as simulation (aka "parametric bootstrapping") available from CLARIFY or Zelig. (This method performs better than the delta method for predicted counts near zero.)

In your text if you want you can interpret the proportional change in terms of exp(hat{beta}) if you wish but I would not put it in the table.

Note that interpreting the results of other count regressions, such as the Poisson model, are done in exactly the same fashion.

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Article ID: 2
Category: Knowledgebase
Date added: 2012-01-10 22:15:26
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