Re: st: Poisson and NBREG

[Roger Harbord <Roger.Harbord@bristol.ac.uk>]

I don't see why you think the betas should be the same.

You *would* get the same betas as the poisson model, but different SEs & 
p-values, if you fitted a quasi-likelihood poisson model with 
overdispersion, using -glm- with the option -scale(x2)- or -scale(dev)-.

But i don't believe the same is true for the negative binomial model. With 
such a large estimated value as 12 for the dispersion parameter delta, i'm 
not particularly surprised the betas are different to those obtained from a 
poisson model.

Roger.
----------------------------------------------------
Roger Harbord     mailto:roger.harbord@bristol.ac.uk
Department of Social Medicine, University of Bristol


--On 27 September 2002 14:08 +0800 Kieran McCaul <kieran@dph.uwa.edu.au> 
wrote:


> In the two models below I'm using the same data.  The first run is a
> Poisson analysis, the second a negative binomial (B1 in Cameron and
> Trivedi parlance).
>
> Now as far as I know my betas should bethe same in both models.  the only
> thing that should change are SEs and p-values.
>
> So why am I getting different betas.
>
> What am I doing wrong here?
>
>
> . poisson alfil1a group, expos(filter1)
>
> Poisson regression                                Number of obs   =
> 34
>                                                   LR chi2(1)      =
> 34.27
>                                                   Prob > chi2     =
> 0.0000
> Log likelihood = -341.07851                       Pseudo R2       =
> 0.0478
>
> -------------------------------------------------------------------------
> --- --
>      alfil1a |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
> Interval]
> -------------+-----------------------------------------------------------
> --- --
>     grouping |   .6831764   .1200077     5.69   0.000     .4479656
> .9183873
>        _cons |  -2.313518      .2073   -11.16
> 0.000    -2.719819   -1.907218
>      filter1 | (exposure)
> -------------------------------------------------------------------------
> --- --
>
> . nbreg alfil1a group, expos(filter1) disp(const)
>
> Negative binomial (constant dispersion)           Number of obs   =
> 34
>                                                   LR chi2(1)      =
> 0.73
>                                                   Prob > chi2     =
> 0.3932
> Log likelihood = -116.99016                       Pseudo R2       =
> 0.0031
>
> -------------------------------------------------------------------------
> --- --
>      alfil1a |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
> Interval]
> -------------+-----------------------------------------------------------
> --- --
>     grouping |   .2718017   .3178545     0.86   0.392    -.3511816
> .8947851
>        _cons |  -1.649793   .5384459    -3.06
> 0.002    -2.705127   -.5944583
>      filter1 | (exposure)
> -------------+-----------------------------------------------------------
> --- --
>     /lndelta |   2.506257   .3217237                       1.87569
> 3.136824
> -------------+-----------------------------------------------------------
> --- --
>        delta |   12.25896   3.943999                      6.525323
> 23.03061
> -------------------------------------------------------------------------
> --- --
> Likelihood ratio test of delta=0:  chibar2(01) =  448.18 Prob>=chibar2 =
> 0.000
>
>
> _______________________________________________________________________
> Kieran McCaul
> School of Population Health
> University of Western Australia

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