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st: Problem with ZINB inflation equation estimates


From   James Shaw <shawjw@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Problem with ZINB inflation equation estimates
Date   Wed, 1 Sep 2010 15:12:50 -0500

I am modeling count data that exhibit overdispersion and excess zeros
and have some concerns about the appropriateness of a zero-inflated
negative binomial (ZINB) model for the data.  As can be seen from the
results below, a Wald test of alpha = 0 is significant, which suggests
that ZINB is more correctly specified than zero-inflated Poisson
(ZIP).  However, the estimates for several of the regressors included
in the inflation equation take on extreme negative values, and tests
of the exponentiated estimates against zero cannot be performed.  Is
this an indication of a problem with the ZINB model specification or
simply an issue with using Wald tests to evaluate nonlinear
transformations of the estimates?  I am accustomed to seeing such
extreme estimates when modeling categorical outcomes with zero cells
or near-zero cells.  However, I am not certain how to interpret
extreme estimates for the parameters of the inflation model.

--
Jim


James W. Shaw, Ph.D., Pharm.D., M.P.H.
Assistant Professor
Department of Pharmacy Administration
College of Pharmacy
University of Illinois at Chicago
833 South Wood Street, M/C 871, Room 252
Chicago, IL 60612
Tel.: 312-355-5666
Fax: 312-996-0868
Mobile Tel.: 215-852-3045



            |               Robust
            |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
nlic2     |
 _Istate_2  |   1.092649    .073559     1.32   0.188     .9575832    1.246767
  _Istate_3 |   1.027985   .0974826     0.29   0.771      .853627    1.237956
  _Istate_4 |   1.260222   .1113024     2.62   0.009     1.059911    1.498391
  _Istate_5 |   1.015475   .0940208     0.17   0.868     .8469512    1.217532
  _Istate_6 |   1.244825   .1100706     2.48   0.013      1.04675    1.480382
  _Istate_7 |   1.059836   .1208843     0.51   0.610     .8475224    1.325337
  _Istate_8 |   1.171791   .1071122     1.73   0.083     .9795862    1.401708
  _Istate_9 |   1.345821   .1539067     2.60   0.009     1.075585    1.683953
 _Istate_10 |   1.390382   .1343393     3.41   0.001     1.150511    1.680264
 _Istate_11 |   1.237516    .144065     1.83   0.067     .9850502    1.554687
 _Istate_12 |   1.384367   .1349304     3.34   0.001     1.143634    1.675774
 _Istate_13 |   .9682022   .0595369    -0.53   0.599     .8582697    1.092215
 _Istate_14 |   1.002396   .0646459     0.04   0.970     .8833731    1.137456
 _Istate_15 |   1.163044   .1160887     1.51   0.130     .9563875    1.414355
 _Istate_16 |   1.229361    .119212     2.13   0.033     1.016572    1.486693
 _Istate_17 |   1.127602   .1087036     1.25   0.213     .9334643    1.362115
 _Istate_18 |    1.19585   .1122559     1.91   0.057      .994886    1.437408
 _Istate_19 |   .9935881   .0791236    -0.08   0.936     .8500053    1.161425
 _Istate_20 |   1.067782   .0769608     0.91   0.363     .9271117    1.229797
 _Istate_21 |   1.229869   .1205396     2.11   0.035     1.014922     1.49034
 _Istate_22 |   1.488745   .1343797     4.41   0.000     1.247348    1.776859
 _Istate_23 |   1.183237   .1180536     1.69   0.092     .9730741     1.43879
 _Istate_24 |   1.287411   .1179763     2.76   0.006     1.075758    1.540707
       nlop | (exposure)
-------------+----------------------------------------------------------------
inflate      |
  _Istate_2 |  -15.18086    3.86403    -3.93   0.000    -22.75422   -7.607505
  _Istate_3 |  -.9113138   .8377267    -1.09   0.277    -2.553228    .7306003
  _Istate_4 |  -37.93109   3.212119   -11.81   0.000    -44.22673   -31.63545
  _Istate_5 |  -.8688422   .7869904    -1.10   0.270    -2.411315    .6736307
  _Istate_6 |   -34.5509   1.418593   -24.36   0.000    -37.33129   -31.77051
  _Istate_7 |  -.2903815   .7019179    -0.41   0.679    -1.666115    1.085352
  _Istate_8 |  -19.12953   1.197556   -15.97   0.000     -21.4767   -16.78236
  _Istate_9 |  -.3339708   .7646007    -0.44   0.662    -1.832561    1.164619
 _Istate_10 |  -16.91487   8.778676    -1.93   0.054    -34.12076    .2910193
 _Istate_11 |  -.2927704   .7666662    -0.38   0.703    -1.795408    1.209868
 _Istate_12 |  -40.69688   4.617249    -8.81   0.000    -49.74652   -31.64723
 _Istate_13 |   .0576077   .3917056     0.15   0.883    -.7101211    .8253366
 _Istate_14 |  -4.621435    20.1191    -0.23   0.818    -44.05415    34.81128
 _Istate_15 |   .1455226   .6589907     0.22   0.825    -1.146076    1.437121
 _Istate_16 |  -4.234189   12.39485    -0.34   0.733    -28.52765    20.05928
 _Istate_17 |  -.5810501   .7541463    -0.77   0.441     -2.05915    .8970495
 _Istate_18 |  -2.642428   2.516604    -1.05   0.294    -7.574882    2.290025
 _Istate_19 |  -.5181308   .4920146    -1.05   0.292    -1.482462    .4462001
 _Istate_20 |  -15.64851   2.008452    -7.79   0.000      -19.585   -11.71201
 _Istate_21 |  -.8170193   .8394646    -0.97   0.330     -2.46234    .8283011
 _Istate_22 |  -36.16489   .9060823   -39.91   0.000    -37.94078     -34.389
 _Istate_23 |  -.2927124   .7272732    -0.40   0.687    -1.718142    1.132717
 _Istate_24 |  -15.53286   7.341087    -2.12   0.034    -29.92112   -1.144592
      _cons |  -2.111847   .5767957    -3.66   0.000    -3.242346   -.9813481
-------------+----------------------------------------------------------------
   /lnalpha |  -.1629929   .1439461    -1.13   0.258    -.4451221    .1191363
-------------+----------------------------------------------------------------
      alpha |   .8495972   .1222962                      .6407461    1.126523

. testnl exp([lnalpha]_cons)=0

  (1)  exp([lnalpha]_cons) = 0

               chi2(1) =       48.26
           Prob > chi2 =        0.0000

. testnl exp([inflate]_Istate_2)=1

  (1)  exp([inflate]_Istate_2) = 1
       warning: derivative with respect to inflate:_Istate_2
coefficient is near zero,
                derivative treated as zero
       Constraint (1) dropped

               chi2(0) =        0.00
           Prob > chi2 =             .

.	testnl exp([inflate]_Istate_4)=0

	(1)  exp([inflate]_Istate_4) = 0
	warning: derivative with respect to	inflate:_Istate_4	coefficient	is	near	zero,
	derivative treated as zero
	Constraint (1) dropped

	chi2(0) =        0.00
	Prob > chi2 =             .

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