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# st: Omit Constant from Count Models

 From "Habiger, Matt" To "statalist@hsphsun2.harvard.edu" Subject st: Omit Constant from Count Models Date Fri, 14 Sep 2012 12:58:54 +0000

```I'm hoping somebody can inform me of what impact(s) omitting a constant term from count models, such as poisson or negative binomial, have? Does it impact t-statistics or the validity of coefficient estimates? I've scoured the internet and textbooks but haven't found any conclusive answers. Is it similar to OLS? Any references would be much appreciated.

I'm modeling the number of days a patient spends in a hospital for a given year and the constant is causing the predicted visits distribution to start at ~4 days (exp(1.46)). In the actual data, roughly 25% of days are below 4 (only those with visits are being modeled). When I drop the constant my estimates are much closer to resembling the actual distribution. Below are the outputs from two models for reference.

Truncated negative binomial regression            Number of obs   =       1334
Truncation point: 0                               LR chi2(5)      =      99.50
Dispersion     = mean                             Prob > chi2     =     0.0000
Log likelihood = -3639.7431                       Pseudo R2       =     0.0135

------------------------------------------------------------------------------
inpunits |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
claims2009 |   .0047266   .0020829     2.27   0.023     .0006442    .0088091
previnpunits |   .0290032    .007004     4.14   0.000     .0152755    .0427308
age09 |   .0041179   .0016468     2.50   0.012     .0008903    .0073455
inplow_ind |   .1627803    .080974     2.01   0.044     .0040741    .3214865
inphigh_ind |   .2904038    .078893     3.68   0.000     .1357764    .4450312
_cons |   1.469507   .0654664    22.45   0.000     1.341195    1.597818
-------------+----------------------------------------------------------------
/lnalpha |   -.418825   .0693098                     -.5546696   -.2829804
-------------+----------------------------------------------------------------
alpha |   .6578193   .0455933                       .574262    .7535346
------------------------------------------------------------------------------
Likelihood-ratio test of alpha=0:  chibar2(01) = 2745.11 Prob>=chibar2 = 0.000

Truncated negative binomial regression
Truncation point: 0                               Number of obs   =       1334
Dispersion     = mean                             Wald chi2(9)    =    1040.04
Log likelihood = -3781.6517                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
inpunits |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
claims2009 |   .0102505   .0031548     3.25   0.001     .0040672    .0164338
previnpunits |   .0196405   .0113036     1.74   0.082    -.0025141    .0417951
age09 |   .0290971   .0015435    18.85   0.000      .026072    .0321222
inpdep_ind |  -1.145573   .7489945    -1.53   0.126    -2.613575    .3224292
inpschi_ind |   .4475055   .1869523     2.39   0.017     .0810857    .8139254
inplow_ind |   .5862683   .1092474     5.37   0.000     .3721473    .8003893
inphigh_ind |   .4966423   .1118703     4.44   0.000     .2773807     .715904
bluecareind |   .1664171   .0713599     2.33   0.020     .0265542      .30628
sex_ind |   .3234388   .0651693     4.96   0.000     .1957093    .4511683
-------------+----------------------------------------------------------------
/lnalpha |   .4669258   .0887536                      .2929719    .6408797
-------------+----------------------------------------------------------------
alpha |   1.595083   .1415694                      1.340405     1.89815
------------------------------------------------------------------------------
Likelihood-ratio test of alpha=0:  chibar2(01) = 4621.10 Prob>=chibar2 = 0.000

Thanks,

Matt Habiger

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