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Re: st: glm and reg produce different results for loglinear model?


From   "Joao Ricardo F. Lima" <jricardofl@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: glm and reg produce different results for loglinear model?
Date   Fri, 31 Oct 2008 20:44:25 -0300

Dear Matthew,

see this Maarten's answer:

http://www.stata.com/statalist/archive/2008-10/msg01362.html

it´s other case, but I think that you can understand the difference.

HTH,

Joao Lima

2008/10/31 Matthew Mercurio (matthewmercurio) <matthewmercurio@fscgroup.com>:
> I have two variables,
>
> (1) outagecost (estimated costs to each customer of a short electrical
> power interuuption)
> (2) mwhannual (annual megawatt hours of electricity consumption fpr each
> customer)
>
> Since these variables appear approximately lognormal, I have been
> estimating the following simple model:
>
> reg lnoutagecost lnmwhannual
>
> where lnoutagecost and lnmwhannual represent the natural log of the two
> variables desribed above.  The results are:
>
> . reg lnoutagecost lnmwhannual
>
>      Source |       SS       df       MS           Number of obs =
> 32345
> -------------+------------------------------        F(  1, 32343) =
> 9370.20
>       Model |  34151.9301     1  34151.9301        Prob > F      =
> 0.0000
>    Residual |  117881.722 32343   3.6447368        R-squared     =
> 0.2246
> -------------+------------------------------        Adj R-squared =
> 0.2246
>       Total |  152033.652 32344  4.70052104        Root MSE      =
> 1.9091
> ------------------------------------------------------------------------
> ----
> lnoutagecost |      Coef.   Std. Err.      t    P>|t|   [95% Conf.
> Interval]
> -------------+----------------------------------------------------------
> ----
>  lnmwhannual |   .3824726   .0039512    96.80   0.000   .3747282
> .3902171
>       _cons |   5.370938   .0232302   231.21   0.000   5.325406
> 5.41647
> ------------------------------------------------------------------------
> ----
>
> I then tried the following model in glm which I had expected to produce
> identical results:
>
> glm outagecost lnmwhannual, link(log)
>
> Generalized linear models                        No. of obs      =
> 52418
> Optimization     : ML                            Residual df     =
> 52416
>                                                 Scale parameter =
> 7.59e+09
> Deviance         =  3.97873e+14                  (1/df) Deviance =
> 7.59e+09
> Pearson          =  3.97873e+14                  (1/df) Pearson  =
> 7.59e+09
> Variance function: V(u) = 1                        [Gaussian]
> Link function    : g(u) = ln(u)                    [Log]
>                                                  AIC            =
> 25.5881
> Log likelihood   = -670636.5416                   BIC            =
> 3.98e+14
> ------------------------------------------------------------------------
> ----
>             |                 OIM
>  outagecost |      Coef.   Std. Err.      z    P>|z|   [95% Conf.
> Interval]
> -------------+----------------------------------------------------------
> ----
>  lnmwhannual |   .5568004   .0130092    42.80   0.000   .5313029
> .5822979
>       _cons |   5.355758   .1384432    38.69   0.000   5.084414
> 5.627102
> ------------------------------------------------------------------------
> ----
>
> Obviously the results are very similar, but not identical.
>
> I read the Stata Manual section on GLM and checked a large number of
> posts on Statalist related to loglinear models, but I was not able to
> understand exactly why glm using link(log) doesn't produce the same
> results as logging both variables and using reg.   Based on my reading
> of the Stata manual it appears to have someing to do with the fact that
> the link() option relates to the expectation od the dependent variable,
> not the dependent variable itself.  Can anyone tell me why the results
> are different?
>
> Matthew G. Mercurio, Ph.D.
> Senior Consultant
> Freeman, Sullivan & Co.
>
>
>
> *
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> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>



-- 
-------------------------------
Joao Ricardo Lima
Professor
UFPB-CCA-DCFS
+553138923914
-------------------------------

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