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


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, "statalist@hsphsun2.harvard.edu" <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 10:24:08 -0500

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
OFFICE: (574)631-6668, (574)631-6463
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EMAIL:  Richard.A.Williams.5@ND.Edu
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