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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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ This transmission may be confidential or protected from disclosure and is only for review and use by the intended recipient. Access by anyone else is unauthorized. Any unauthorized reader is hereby notified that any review, use, dissemination, disclosure or copying of this information, or any act or omission taken in reliance on it, is prohibited and may be unlawful. If you received this transmission in error, please notify the sender immediately. Thank you.

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**References**:**st: Problem with ZINB inflation equation estimates***From:*James Shaw <shawjw@gmail.com>

**Re: st: Problem with ZINB inflation equation estimates***From:*Stas Kolenikov <skolenik@gmail.com>

**Re: st: Problem with ZINB inflation equation estimates***From:*James Shaw <shawjw@gmail.com>

**Re: st: Problem with ZINB inflation equation estimates***From:*James Shaw <shawjw@gmail.com>

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