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# Re: st: model for fractional data with panel data

 From "Arne Risa Hole" To statalist@hsphsun2.harvard.edu Subject Re: st: model for fractional data with panel data Date Wed, 7 Nov 2007 18:40:36 +0000

Thanks Austin, I agree that transforming y and running -xtreg- (or
-xtivreg2-) is a good alternative to -glm- when the dependent variable
does not contain any zeroes or ones. I think that the incidental
parameters problem _is_ an issue for the -glm- model though, as this
can be run as a binary logit where each observation corresponds to a
week and y=1 if the person worked that week and zero otherwise. But
that is probably not very relevant from a practical point of view
since you can just as well run a linear model with y transformed as
you demonstrated...

Arne

On 07/11/2007, Austin Nichols <austinnichols@gmail.com> wrote:
> Arne--
> I'm not sure the concern about incidental parameters applies here.  To
> my mind, the question is, is there anything to be gained by using
> -glm- with indicator variables to capture fixed effects to estimate
> instead of transforming y by generating a new variable lny=ln(y) or
> logity=logit(y) or invlogity=invlogit(y) and I'm not sure there is, in
> this case.  The poster specified that y measured proportions strictly
> between 0 and 1, i.e. on the open interval.  That is the crucial
> point--there are no obs with y=0 or y=1.  In this case, you may be
> better off with -xtreg- (or -xtivreg2- with more SE adjustments) than
> -glm- if only because estimation is so much faster!  But you will get
> numerically different answers, of course...
> since y=f(Xb+e) is not the same as y=f(Xb)+e
>
> webuse psidextract, clear
> tsset id t
> gen w=wks/53
> g ilw=invlogit(w)
> qui su ilw
> replace ilw=ilw/r(sd)
> qui reg ilw lw uni south smsa, cluster(id)
> est sto reg
> qui glm w lw uni south smsa, link(logit) fam(gauss) cl(id)
> est sto glm
> qui xtreg ilw lw uni south smsa, cluster(id) fe
> est sto xtreg
> qui xi: glm w lw uni sou sms i.id, link(logit) fam(gauss) cl(id)
> est sto xtglm
> esttab *, keep(lwage union south smsa) mti
>
> ----------------------------------------------------------------------------
>                      (1)             (2)             (3)             (4)
>                      reg             glm           xtreg           xtglm
> ----------------------------------------------------------------------------
> main
> lwage               0.139*          0.127*         0.0598           0.162
>                   (2.41)          (2.03)          (0.83)          (1.55)
>
> union              -0.309***       -0.286***        0.158           0.171
>                  (-6.09)         (-6.22)          (1.33)          (1.38)
>
> south              0.0361          0.0404          -0.122          -0.275
>                   (0.67)          (0.76)         (-0.66)         (-1.16)
>
> smsa               0.0242          0.0176          0.0304          0.0468
>                   (0.45)          (0.35)          (0.35)          (0.38)
> ----------------------------------------------------------------------------
> N                    4165            4165            4165            4165
> ----------------------------------------------------------------------------
> t statistics in parentheses
> * p<0.05, ** p<0.01, *** p<0.001
>
>
> Having accepted you might transform y, the question then is which
> transformation is appropriate, and for that you need some theory.
> Neglecting theory, you might explore whether regressions using
> lny=ln(y) or logity=logit(y) or invlogity=invlogit(y) as the depvar
> produce predictions that make more sense and residuals that look less
> correlated with your transformed depvar.
>
> tw function y=50*invlogit(x)-31||function y=logit(x)||function y=ln(x)
>
>
> On 11/7/07, Arne Risa Hole <arnehole@gmail.com> wrote:
> > There was an extremely useful discussion on the list recently about
> > this issue in the context of fixed effects binary logit models. In
> > short, adding the fixed effects 'by hand' results in biased estimates
> > unless the number of time periods is large. See the thread starting
> > with:
> >
> > http://www.stata.com/statalist/archive/2007-10/msg00935.html
> >
> > Arne
> >
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