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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Omit Constant from Count Models |

Date |
Fri, 14 Sep 2012 15:31:52 +0200 |

On Fri, Sep 14, 2012 at 2:58 PM, Habiger, Matt wrote: > 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'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 The statement that "the constant is causing the predicted visits distribution to start at ~4 days (exp(1.46))" is not quite true. Your results say that for a (hypothetical) observation with the value 0 on the variables claims2009, previnpunits, age09, inplow_ind, inphigh_ind you would predict that such an person would stay about 4 days in hospital. Depending on these variables, this can be a gross extrapolation. In general you do not want to leave the constant out. The idea that leaving the constant out will lead to better predictions is certainly wrong. But don't take my word for it, try it out: estimate the model with and without the constant, use -predict- to predict the expected days in hospital for each of these models and plot both against the observed days in hospital. As always there are exceptions. I think the most common valid reason for leaving out the constant is when you put it back in through the backdoor by the way you enter categorical variables, e.g.: M.L. Buis (2012) "Stata tip 106: With or without reference", The Stata Journal, 12(1), pp. 162-164. You may also be modeling a physical process, where there is very strong a priori evidence that there can be no constant. But any process involving humans is just too random to fall in that class of models. Hope this helps, Maarten --------------------------------- Maarten L. Buis WZB Reichpietschufer 50 10785 Berlin Germany http://www.maartenbuis.nl --------------------------------- * * 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/

**Follow-Ups**:**RE: st: Omit Constant from Count Models***From:*"Habiger, Matt" <MHabiger@ndbh.com>

**References**:**st: Omit Constant from Count Models***From:*"Habiger, Matt" <MHabiger@ndbh.com>

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