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st: zinb


From   "Theodoropoulos, N." <nt18@leicester.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: zinb
Date   Sat, 22 Nov 2003 17:49:00 -0000

Dear Statalisters,

I am using a zero inflated negative binomial model (zinb) and I get the following results: 

Fitting zip comparison model:
Iteration 0:   log likelihood = -37967.757  
Iteration 4:   log likelihood = -37030.893  

Fitting constant-only model:
Iteration 0:   log likelihood =  -46827.44  
Iteration 9:   log likelihood = -37967.757  (not concave)

Fitting full model:
Iteration 0:   log likelihood = -37967.757  (not concave)
Iteration 4:   log likelihood = -37030.894  

Zero-inflated negative binomial regression        Number of obs   =      21826
                                                  Nonzero obs     =      14687
                                                  Zero obs        =       7139

Inflation model = logit                           LR chi2(92)     =    1873.73
Log likelihood  = -37030.89                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
          b2 |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
.
.
-------------+----------------------------------------------------------------
    /lnalpha |  -70.67075   28.69921    -2.46   0.014    -126.9202   -14.42133
-------------+----------------------------------------------------------------
       alpha |   2.03e-31   5.83e-30                      7.57e-56    5.46e-07
------------------------------------------------------------------------------
Likelihood ratio test of alpha=0: chibar2(01) =  1.4e-03 Pr>=chibar2 =  0.4849

I know the zip command specifies that a zero-inflated Poisson comparison model should be fit and the LR test of the zero-inflated negative binomial model versus the nested zero-inflated Poisson model be included. 
In this case the LR test is positive and very small (reject Ho). Does this test suggest that once we allow for excess zeros (inflated Poisson), unobserved heterogeneity coming through a negative binomial model does not matter? Is my interpretation correct? 
In other words, is the null hypothesis for the LR test: Ho=overdispersion, versus Ha=Not Ho?

We can also see that the estimated parameter alpha is positive but not significantly different from zero. This implies that the conditional mean is equal to the conditional variance and the zero inflated negative binomial model reduces to the zero-inflated Poisson model.

Is the above testing adequate so that I can proceed with the zero-inflated Poisson model?
I know there exists a Vuong test for discriminating between a Poisson and a zip and an nbreg and a zinb. In my case the Vuong test is in favour of the zero-inflated models.   
However, is there a test in Stata for discriminating between a zero-inflated Poisson model and a negative binomial model (Vuong, 1989)?

Any comments will be highly appreciated,
Regards
Nick 
  


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