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# Re: st: Interpretation of coefficients for predictor with linear and quadratic terms in negative binomial regression

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation of coefficients for predictor with linear and quadratic terms in negative binomial regression Date Mon, 21 Oct 2013 11:43:55 +0200

```On Mon, Oct 21, 2013 at 6:10 AM, Rachael Wills wrote:
> I am using -nbreg- in Stata MP 12.1 to run a negative binomial regression where the outcome is the number of children at a centre taking an extended departure during the year (variable is called 'exits') with an offset term containing the number of children attending the centre at all during the year (variable is called 'children').  A scatterplot of 'exits' as a percentage of 'children' against occupancy (%) suggests that a term in occupancy squared may also be necessary, and indeed both linear and quadratic terms are significant at the 95% level in the model:
>
> gen occ2 = occ^2
> nbreg exits occ occ2, exposure(children)
>
> My question then, is how I can interpret the dual coefficients for the occupancy terms. Is it best to use the coefficients, or can a simpler interpretation be made using the -irr- option? I would like to be able to provide a statement such as 'For every 1% increase in occupancy there is a X decrease in the exit rate'. However, I'm not even sure if such a simple statement is possible when there are both linear and quadratic terms involved.

The kind of statement you want to make assumes a constant effect.
Since you added a quadratic term, you do not believe that that is
accurate. You could look into linear splines, which will get you
closest to what you want: instead of one such statement, you split up
the range of occ in sections and you'll get multiple statements of the
form you like, on for each section. Alternative you could graph your
effect.

If we take the example below. I first estimate the model with linear
splines. You interpret the results as follows: if mpg is less than 30
then a mile per gallon increase is associated with (.945 - 1)*100% =
-5.5% decrease in price, while if mpg is larger than 30 a mile per
gallon increase is associated with a (1.039 - 1)*100%= 3.9% increase
in price. In the second example I use factor variable notation (see:
-help fvvarlist-) to estimate a model with a quadratic term and use
-margins- and -marginsplot- to graph the result.

*------------------ begin example ------------------
sysuse auto, clear
mkspline sp1 30 sp2=mpg
poisson price sp1 sp2, irr vce(robust)

poisson price c.mpg##c.mpg, vce(robust)
margins, at(mpg=(12/41))
marginsplot
*------------------- end example -------------------
* (For more on examples I sent to the Statalist see:
* http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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```