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st: Notation of the Negative Binomial Model


From   Francisco Rowe <frowe@ucn.cl>
To   statalist@hsphsun2.harvard.edu
Subject   st: Notation of the Negative Binomial Model
Date   Thu, 2 Jun 2011 22:19:01 +1000

I am a little confused on the notation of the Negative Binomial Model.
I want to express the equation such as the variables are used by the stata command nbreg

Let say that I want to estimate this:
nbreg y x1 x2 x3 (1)
where y: dependent variable; xs: explanatory variables.

My confusion starts when I look at the notation on books that usually write it in general terms as:
lamda = E[ yi | xi ] = exp(xi’Beta)

Where: E[ yi | xi ] : the expected mean of y conditional on xi. The latter express in matrix form.

Regarding my model (1), my question is can I write this:
y= exp(b0+ b1*x1 + b2*x2 + b2*x2+e)
where: bs: beta parameters; e: random error

Thank you in advance.

Francisco.
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