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st: Zero-inflated binomial regression


From   "Meryle Weinstein" <mgw216@nyu.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Zero-inflated binomial regression
Date   Tue, 23 Oct 2007 09:16:28 -0400

Sorry if this is a resend.  I didn't see it posted on the stata digest.

I have count data and have been doing analyses using negative binomial
regression.   I've been doing reading and think that the zero-inflated
binomial regression may be more appropriate given the number of zeros in
data (243 out of 626).  The data is the count of academic after-school
programs in an elementary school zone.  The zones could have zero because
they don't have any after-school programs (which is the majority of cases)
or zero because there are no academic programs.   What I don't understand
and haven't been able to find in the readings is how to choose the variables
for inflate.  

The model I'm running using nbreg is:

nbreg nacadz totregz   totregzsq pblack2 phisp2 pasian2 pubschracehet pfl2
plep2 pimmig2 pimmigdum math2 lntppe2 lntppedum edu160pz old0z bronx
brooklyn queens si, vce (robust) dispersion(mean)

Fitting Poisson model:

Iteration 0:   log pseudolikelihood = -1627.6197  
Iteration 1:   log pseudolikelihood = -1626.5176  
Iteration 2:   log pseudolikelihood = -1626.5165  
Iteration 3:   log pseudolikelihood = -1626.5165  

Fitting constant-only model:

Iteration 0:   log pseudolikelihood = -1363.9816  
Iteration 1:   log pseudolikelihood = -1346.5563  
Iteration 2:   log pseudolikelihood = -1346.4582  
Iteration 3:   log pseudolikelihood = -1346.4582  

Fitting full model:

Iteration 0:   log pseudolikelihood = -1302.2992  
Iteration 1:   log pseudolikelihood = -1292.2209  
Iteration 2:   log pseudolikelihood = -1290.9536  
Iteration 3:   log pseudolikelihood = -1290.9484  
Iteration 4:   log pseudolikelihood = -1290.9484  

Negative binomial regression                      Number of obs   =
626
Dispersion           = mean                       Wald chi2(19)   =
158.02
Log pseudolikelihood = -1290.9484                 Prob > chi2     =
0.0000

----------------------------------------------------------------------------
--
             |               Robust
      nacadz |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
     totregz |   .0008722   .0003337     2.61   0.009     .0002182
.0015263
   totregzsq |  -2.32e-07   1.20e-07    -1.94   0.053    -4.68e-07
2.90e-09
     pblack2 |   .7755238   .3485507     2.22   0.026     .0923769
1.458671
      phisp2 |   .8144126   .4552516     1.79   0.074    -.0778641
1.706689
     pasian2 |   .3063356   .5594969     0.55   0.584    -.7902581
1.402929
pubschrace~t |   .3563023   .3128879     1.14   0.255    -.2569468
.9695514
        pfl2 |    .743668   .3495116     2.13   0.033     .0586378
1.428698
       plep2 |  -.8755225   .6955994    -1.26   0.208    -2.238872
.4878273
     pimmig2 |   2.311658   1.230789     1.88   0.060    -.1006446
4.72396
   pimmigdum |  -.3017149   .2244602    -1.34   0.179    -.7416488
.138219
       math2 |  -.1652905    .395245    -0.42   0.676    -.9399564
.6093754
     lntppe2 |   .2537448   .3210432     0.79   0.429    -.3754884
.882978
   lntppedum |  -2.117665   2.958555    -0.72   0.474    -7.916326
3.680997
    edu160pz |   1.828772   .4098704     4.46   0.000     1.025441
2.632103
       old0z |   -.414051   1.360419    -0.30   0.761    -3.080423
2.252321
       bronx |  -.6916427   .1667281    -4.15   0.000    -1.018424
-.3648615
    brooklyn |  -.5968491   .1453163    -4.11   0.000    -.8816638
-.3120344
      queens |  -.7938416   .1628973    -4.87   0.000    -1.113114
-.4745688
          si |  -.2746133   .2809568    -0.98   0.328    -.8252785
.2760519
       _cons |  -.4891405   .5163121    -0.95   0.343    -1.501094
.5228126
-------------+--------------------------------------------------------------
--
    /lnalpha |   .1586018   .1005712                     -.0385142
.3557178
-------------+--------------------------------------------------------------
--
       alpha |   1.171871   .1178565                       .962218
1.427205
----------------------------------------------------------------------------
--
Likelihood-ratio test of alpha=0:  chibar2(01) =  671.14 Prob>=chibar2 =
0.000

Thanks for your help.
Meryle Weinstein
Research Scientist
Institute for Education & Social Policy
New York University
Pless Hall
82 Washington Square East, 7th floor
New York, NY 10003
(212) 998-5817
(212) 995-4564 (fax)
www.steinhardt.nyu.edu/iesp

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