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RE: st: Problem with ZINB inflation equation estimates


From   "Craig, Benjamin M." <Benjamin.Craig@moffitt.org>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Problem with ZINB inflation equation estimates
Date   Wed, 1 Sep 2010 19:12:11 -0400

ZINB is a mixture model, similar to a spoonful of whipped cream on top of an already skewed count distribution. It is important to remember that a mixture model has additional requirements for identification, and further specification tests under the parametric framework. It is likely that the primary model suffices for some of your states, which caused your second mixture to misbehave. As stated previously, this is similar to too trying to estimate a logit with few zero, because many of the zeros have been eaten up by the NB. The logit just gets the leftovers and starts acting odd (Sorry for the food analogies, but finished dinner).
 
Your question suggests that this is an atheoretical exercise, and if so, I would recommend a 2-part model. The 2-part separates out the dependent variable into separate models; therefore, these models will not compete to explain the same zeros. Unlike ZINB, you can test the 2-part framework using a likelihood ratio test on a constraint.
 
Finishing with the food talk, I am not sure a sandwich correction is appropriate for a mixture model, but someone else can dig into that question. I'm on a non-parametric diet. Cheers, Ben 
 
 
 
Benjamin M. Craig, Ph.D. Assistant Member, Health Outcomes & Behavior Moffitt Cancer Center Associate Professor, Department of Economics University of South Florida Contact Information 12902 Magnolia Drive, MRC-CANCONT Tampa, FL 33612-9416 Phone: (813) 745-6710 Fax: (813) 745-6525 benjamin.craig@moffitt.org

________________________________

From: owner-statalist@hsphsun2.harvard.edu on behalf of James Shaw
Sent: Wed 9/1/2010 5:26 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Problem with ZINB inflation equation estimates



Thanks for the prompt response.  Yes, zero cells in the inflation
equation (corresponding to an absence of zero counts for groups
indicated by regressors with extreme negative estimates) would make
sense.  However, as shown in Table 1 below, there are zero counts for
these groups.  In the table, "0" indicates the number of zero count
observations, while "1" indicates the number of observations with a
count >=1.

This is a repeated-measures data set.  Counts for the 24 states are
observed for the same set of individuals.  The sandwich variance
estimator was used to account for person-level clustering.  Without
application of the cluster-robust variance estimator, estimates of
standard errors for the extreme parameter estimates tended toward
infinity.

Additionally, I am wondering whether the extreme estimates are an
indication of the inability of the inflation model to capture
heterogeneity due to excess zeros after taking into account
individual-level heterogeneity, as reflected by alpha.  The
zero-inflated Poisson (ZIP) model is comparatively well behaved (see
Table 2 below).  After adjusting for individual-level heterogeneity,
the probability of some states having a zero count may approach zero.
Thus, ZINB may be unable to provide reliable estimates of the
corresponding inflation model parameters.

Based on your comments, it would appear that I should exclude ZINB
from consideration and focus on ZIP and negative binomial (without
zero inflation) instead.

--
Jim


TABLE 1

state     0     1

1       6,723   5,677
2       4,077   8,323
3       6,857   5,543
4       4,186   8,214
5       6,886   5,514
6       4,034   8,366
7       6,655   5,745
8       3,882   8,518
9       6,178   6,222
10      3,853   8,547
11      6,555   5,845
12      3,801   8,599
13      6,795   5,605
14      4,136   8,264
15      6,847   5,553
16      4,041   8,359
17      6,513   5,887
18      4,139   8,261
19      6,600   5,800
20      3,972   8,428
21      6,299   6,101
22      3,408   8,992
23      6,553   5,847
24      3,989   8,411


TABLE 2

            |               Robust
            |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
nlic2
_Istate_2       .9865309        .0514006        -0.26   0.795
.8907607        1.092598
_Istate_3       1.051092        .0850525        0.62    0.538
.8969394        1.231739
_Istate_4       1.142369        .090406 1.68    0.093   .9782348        1.334043
_Istate_5       1.037862        .0817944        0.47    0.637
.8893154        1.21122
_Istate_6       1.111375        .0884138        1.33    0.184
.9509215        1.298903
_Istate_7       1.065085        .1035223        0.65    0.517
.8803406        1.2886
_Istate_8       1.039028        .0877759        0.45    0.650
.8804785        1.226128
_Istate_9       1.319903        .1289443        2.84    0.004
1.089899        1.598445
_Istate_10      1.239489        .111583 2.38    0.017   1.038998        1.478668
_Istate_11      1.236957        .1227598        2.14    0.032
1.018307        1.502556
_Istate_12      1.227542        .1110276        2.27    0.023   1.02813 1.465633
_Istate_13      .9693349        .0508785        -0.59   0.553
.8745728        1.074365
_Istate_14      .9100219        .0516526        -1.66   0.097
.8142128        1.017105
_Istate_15      1.164887        .0990005        1.80    0.073   .986149 1.376021
_Istate_16      1.106839        .093111 1.21    0.228   .9385959        1.30524
_Istate_17      1.129445        .0927545        1.48    0.138
.9615265        1.326689
_Istate_18      1.079823        .0878866        0.94    0.345
.9206048        1.266577
_Istate_19      1.00173 .0680997        0.03    0.980   .8767674        1.144504
_Istate_20      .9557701        .0558659        -0.77   0.439
.8523141        1.071784
_Istate_21      1.224653        .1024695        2.42    0.015   1.03942 1.442896
_Istate_22      1.271586        .1071609        2.85    0.004
1.077983        1.499959
_Istate_23      1.180238        .1004533        1.95    0.052
.9988986        1.394497
_Istate_24      1.154552        .0989566        1.68    0.094
.9760166        1.365746
nlop    (exposure)

inflate
_Istate_2       -.6431842       .0884337        -7.27   0.000
-.8165111       -.4698574
_Istate_3       -.1121791       .159063 -0.71   0.481   -.4239368       .1995787
_Istate_4       -.6264557       .1642806        -3.81   0.000
-.9484399       -.3044716
_Istate_5       -.1062271       .1542732        -0.69   0.491
-.4085969       .1961428
_Istate_6       -.6813996       .1620086        -4.21   0.000
-.9989306       -.3638687
_Istate_7       -.0572668       .1481622        -0.39   0.699
-.3476594       .2331259
_Istate_8       -.714012        .1411174        -5.06   0.000
-.990597        -.4374269
_Istate_9       -.1271494       .163172 -0.78   0.436   -.4469608       .1926619
_Istate_10      -.6918837       .162056 -4.27   0.000   -1.009508
 -.3742597
_Istate_11      -.0714629       .1640151        -0.44   0.663
-.3929267       .2500009
_Istate_12      -.7078715       .1596094        -4.44   0.000
-1.0207 -.3950428
_Istate_13      .0188447        .0861727        0.22    0.827
-.1500508       .1877401
_Istate_14      -.6176321       .0898303        -6.88   0.000
-.7936964       -.4415679
_Istate_15      .04241  .1593765        0.27    0.790   -.2699622       .3547823
_Istate_16      -.6410692       .162872 -3.94   0.000   -.9602924       -.321846
_Istate_17      -.1178183       .1591056        -0.74   0.459
-.4296597       .194023
_Istate_18      -.6074913       .1553598        -3.91   0.000
-.911991        -.3029916
_Istate_19      -.0944102       .1100006        -0.86   0.391
-.3100073       .121187
_Istate_20      -.6751463       .0927802        -7.28   0.000
-.8569921       -.4933004
_Istate_21      -.1707728       .1600858        -1.07   0.286
-.4845353       .1429897
_Istate_22      -.8657041       .1643409        -5.27   0.000
-1.187806       -.543602
_Istate_23      -.0754311       .163291 -0.46   0.644   -.3954756       .2446135
_Istate_24      -.6647537       .1589559        -4.18   0.000
-.9763015       -.3532059
_cons   -.3606622       .1763068        -2.05   0.041   -.7062172
 -.0151071

--
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
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