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# Re: st: Regression Equation for Zero inflated negative binomial

 From Partho Sarkar To statalist@hsphsun2.harvard.edu Subject Re: st: Regression Equation for Zero inflated negative binomial Date Tue, 20 Sep 2011 16:15:26 +0530

```Rachel

I notice you are not getting the points, so even though I have no
special experience with the ZINB model, let me try to explain a basic
simplistic.

Here your y- variable is the "count" or number of times something of
interest happens in a unit of time.

You assume that the "probability" of this (i.e., y=y0 for any y0) is
given by the "negative binomial" probability distribution, which is
defined by a parameter lambda, which in turn is determined by some
characteristics of  the observations.  This is the left hand variable

lambda=a0+a1X1+etc.

This is why  you do not have any regression in the form y=b0+b1X1 etc,
and no one would expect you to produce such a regression!

For further clarification, I would suggest you look at these sources:

http://www.ic.arizona.edu/~ce411/lectures/CountModels.ppt
http://pages.stern.nyu.edu/~wgreene/Econometrics/PanelDataNotes-19.ppt
http://www.ats.ucla.edu/stat/stata/output/Stata_zinb.htm
http://www.ats.ucla.edu/stat/stata/dae/zinb.htm

Hope this helps

Partho

2011/9/20 rachel grant <rachelannegrant@gmail.com>:
> Thanks to everyone but I am still very confused. I should explain, I
> am not a mathematician, I dont understand mathmatical formulae, I am a
> biologist. I am looking for a regression formula for ZINB but I cannot
> find anything that resembles:  ln (Y) + B0+B1X1 + B2X2.
> Yes there are formulae in the resources you are all pointing me to but
> none of them look like a regression equation, and they dont have X on
> the right hand side. I can't buy expensive books... I have been
> searching help file and internet resources for several months.
>
> thanks
> Rachel Grant
>
>
> 2011/9/19 rachel grant <rachelannegrant@gmail.com>:
>> Thank you for your help. Maybe I need to explain the problem more clearly
>> I have used Zero Inflated negative binomial regression in Stata to
>> model some overdispersed, zero inflated count data. I got very nice
>> results and also used the postestimation tools to predict Y values.
>> This is included in my PhD thesis which I am about to submit. My PhD
>> supervisor said as well as presenting the results (i.e cofficients, p
>> values etc.) I also have to show "the model". I think by this he means
>> the regression equation in the form:
>>
>> natural log (Y) = B0+B1X1 + B2X2..............
>>
>> I cannot find out what the equation is for ZINB models and also I
>> cannot find out how to make Stata display this model.
>> I could just add in the coefficients myself BUT I am not sure of the
>> exact formula of the model for ZINB (especially the ZI part) as I
>> think it may be more complicated than the simple Poisson
>>
>> log e  (Y) = β0 + β1Χ1 + β2Χ2 ...
>>
>> I have searched everywhere to find a general equation for ZINB with no
>> luck and also read all the Stata help files.
>> I am very confused about why this seemingly simple thing should prove
>> so impossible! I am a beginner with stata, and previously only used
>> simple linear regression so thank you for your patience.
>>
>> --
>> regards, Rachel Grant
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
>
>
> --
> regards, Rachel
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
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```