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

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 11:10 PM 10/20/2013, Rachael Wills wrote:
> Dear all,
>
> I am trying to quantify the effect of the occupancy (%) of child 
> care centres on the tendency of children to take extended departures 
> from the centre.
>
> 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.

Personally I would do

nbreg exits occ c.occ#c.occ, exposure(children)

Then I would use commands like margins or the user written mcp. See

http://www3.nd.edu/~rwilliam/xsoc73994/Margins01.pptx

http://www3.nd.edu/~rwilliam/xsoc73994/Margins03.pdf

You may also wish to see Vince Wiggins' post at

http://www.stata.com/statalist/archive/2013-01/msg00293.html

Among many other things, he says "When we regress mileage on weight 
and weight squared, we are simply admitting that a linear 
relationship doesn't match the data, and we need some flexibility in 
the relationship between mileage and weight.  We do not think that 
weight squared has its own interpretation."

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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