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

[Rachael Wills <rwills@goodstart.org.au>]

Thank-you to everyone who has given me suggestions for my problem. 

Given my audience, and the lack of any other covariates in my model, I may investigate using splines (thanks Maarten). However, I really appreciate the resources and information on -margins-. Richard, your powerpoint slides were very informative and much appreciated.

In answer to your questions Kieran:
1. Occupancy is a measure of how full a childcare centre is. It is an aggregate measure over a given time period (I am using the average over a year). Very simplistically, two centres may be licenced to care for 100 children at a time. If one centre was attended by 70 children in a day they would have an occupancy of 70%, while the other may have been attended by 96, thus having an occupancy of 96%.

2. Extended departures have to be more than 6 weeks in length, and during this time the business does not know that the child is going to return to the centre (i.e. they have ceased care, but later return). I take your point that this exit may free up space for a new child to begin attending the centre, and in high occupancy centres which have waiting lists, this happens. However, this is not the case in centres with lower occupancy as there was spare room in that centre already. From this the theory arises that extended departures may be more likely to occur in centres with lower occupancy as there is less danger of not being able to re-enrol the child if a decision is made to commence care again (this is what I am trying to test). Due to the varying sizes and occupancies of centres I believe it is necessary to model the extended departures as rates, hence the use of the children offset. 

Thanks again to all,

Rachael



>Date: Mon, 21 Oct 2013 10:24:08 -0500
>From: Richard Williams <richardwilliams.ndu@gmail.com>
>Subject: Re: st: Interpretation of coefficients for predictor with linear and quadratic terms in negative binomial regression
>
>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
>HOME:   (574)289-5227
>EMAIL:  Richard.A.Williams.5@ND.Edu
>WWW:    http://www.nd.edu/~rwilliam

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