Zero-Inflated Negative Binomial with huge standard errors

[gprwallace]

I am performing an analysis on the number of legislative actions for each member of the U.S. House of Representatives for a particular period of time. Given there are a large number of observations with 0 actions, I estimated a zero-inflated negative binomial model. The results are reported below. My main concern is that the standard errors and p-values for every single coefficient in the bottom “Inflate” model are enormous.

From what I’ve been able to find out, this usually is due to one of two problems: multicollinearity or perfect prediction. However, neither of these seem to be an issue here. For multicollinearity, running a standard OLS model shows no vif is greater than 3. Regarding the second issue I ran a standard logit model on a binary version of the legislative outcome measure, and none of the independent variables were dropped because of perfect prediction.

The Vuong test also seems to indicate that the zinb is the appropriate type of count model to be used for this data.

Any help in understanding what is going on with the standard errors in the “Inflate” model, and what might be done, would be much appreciated.

Thanks! Geoff Wallace
Assistant Professor
Department of Political Science
Rutgers University

zinb Imm_cosponsor_afterfeb14 party latino black asian latino_perc black_perc
asian_perc urban_perc yrsinoffice age male income_med tot_Protest_MSA A2005__
_of_non_citizens, ///
inf(party latino black asian latino_perc black_perc asian_perc urban_p
erc yrsinoffice age male income_med tot_Protest_MSA A2005___of_non_citizens)
probit nolog vuong

Zero-inflated negative binomial regression Number of obs = 435
Nonzero obs = 194
Zero obs = 241

Inflation model = probit LR chi2(14) = 90.41
Log likelihood = -458.4522 Prob > chi2 = 0.0000

-------------------------------------------------------------------------------
Imm_cospon~14 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
Imm_cospon~14 |
party | -1.033834 .1766514 -5.85 0.000 -1.380064 -.6876036
latino | -.7187701 .5995016 -1.20 0.231 -1.893772 .4562314
black | -.0428508 .4696402 -0.09 0.927 -.9633287 .8776271
asian | .2408905 1.247674 0.19 0.847 -2.204505 2.686286
latino_perc | .017926 .0107126 1.67 0.094 -.0030703 .0389223
black_perc | .0038458 .0086941 0.44 0.658 -.0131943 .0208859
asian_perc | .0046104 .018943 0.24 0.808 -.0325171 .041738
urban_perc | .0014251 .0057696 0.25 0.805 -.009883 .0127333
yrsinoffice | -.0208406 .0114083 -1.83 0.068 -.0432004 .0015192
age | .0045062 .0088608 0.51 0.611 -.0128606 .0218731
male | -.1234629 .1927655 -0.64 0.522 -.5012763 .2543506
income_med | .0000191 9.16e-06 2.09 0.037 1.19e-06 .0000371
tot_Protest~A | .0557359 .0291927 1.91 0.056 -.0014807 .1129526
A2005___of_~s | -.0279595 .027407 -1.02 0.308 -.0816761 .0257572
_cons | -.9001286 .62903 -1.43 0.152 -2.133005 .3327475
--------------+----------------------------------------------------------------
inflate |
party | -204.2378 18229.4 -0.01 0.991 -35933.2 35524.72
latino | 94.03199 7344.266 0.01 0.990 -14300.46 14488.53
black | -183.6639 16546.94 -0.01 0.991 -32615.07 32247.75
asian | 532.7154 1.85e+09 0.00 1.000 -3.63e+09 3.63e+09
latino_perc | .7516061 113.0797 0.01 0.995 -220.8805 222.3837
black_perc | -1.871476 260.8058 -0.01 0.994 -513.0414 509.2985
asian_perc | -14.12696 1205.539 -0.01 0.991 -2376.939 2348.685
urban_perc | .0560466 68.08666 0.00 0.999 -133.3913 133.5034
yrsinoffice | 3.529964 246.521 0.01 0.989 -479.6423 486.7022
age | 12.51738 1048.579 0.01 0.990 -2042.659 2067.694
male | -119.0208 9863.633 -0.01 0.990 -19451.39 19213.35
income_med | -.0056572 .4733657 -0.01 0.990 -.9334369 .9221226
tot_Protest~A | 34.51761 2940.346 0.01 0.991 -5728.455 5797.49
A2005___of_~s | 4.198079 311.8879 0.01 0.989 -607.0909 615.4871
_cons | -622.0768 53483.68 -0.01 0.991 -105448.2 104204
--------------+----------------------------------------------------------------
/lnalpha | -.9816196 .305417 -3.21 0.001 -1.580226 -.3830133
--------------+----------------------------------------------------------------
alpha | .3747037 .1144409 .2059286 .6818039
-------------------------------------------------------------------------------
Vuong test of zinb vs. standard negative binomial: z = 5.46 Pr>z = 0.0000

[Joe Canner]

Given there are a large number of observations with 0 actions,...

This made me chuckle (as applied to the US Congress), so I couldn't resist a response, even though I don't have much to offer. I have only tried to use zinb once before and had a similar problem. Because of my lack of familiarity with this method and my lack of patience for finding just the right combination of covariates, I ended up doing two separate models: one logistic for the odds of an "action" and one truncated negative binomial (tnbreg) for the number of actions amongst those with an action (truncated at zero since you have removed those with zero actions).

I'll be interested to see if anyone else has a more useful solution.