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RE: st: Fractional Logit


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Fractional Logit
Date   Mon, 31 Oct 2005 10:41:28 -0000

In the meantime you could also have it both ways
using -nlcom-, or so I imagine. 

Nick 
n.j.cox@durham.ac.uk 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Nick Cox
> Sent: 31 October 2005 10:36
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: st: Fractional Logit
> 
> 
> This seems fair comment. The history of -betafit- is 
> that it grew out of some work I did in fitting beta 
> distributions to single variables, so no covariates
> were in sight. However, adding the options for 
> dependence on covariates was very easy given the 
> facilities of -ml- and Stephen Jenkins' prior work 
> on programs for fitting other distributions given 
> covariates. I am not surprised that other parameterisations
> can make more scientific sense. As I think that -betafit- 
> can do some things that -mlbeta- can't, supporting 
> an alternative parameterisation is on the to do list, 
> but no promises. 
> 
> P.S. picky point: there's no stop after "et" in "et al.". In Latin 
> (and in French) "et" is a complete word meaning "and". 
> 
> Nick 
> n.j.cox@durham.ac.uk 
> 
> Maarten Buis
>  
> > The -betafit- command fits the beta distribution in the 
> > conventional parameterization (e.g. Evans et. al. 2000), the 
> > -mlbeta- command reparameterizes the distribution in terms of 
> > a mean and a scale factor for the variance (the variance also 
> > depends on the mean). In a regression context the 
> > parameterization of -mlbeta- makes more sense, because you 
> > usually want to model the how the mean response changes when 
> > your explanatory variable changes. If you want to use 
> > -betafit- in a regression context you have to give 
> > substantive meaning to the alpha and beta parameter. If the 
> > outcome is a proportion than the alpha and beta parameter can 
> > be seen as expected counts for the two groups. However, I 
> > have only used this as a rule of thumb (within a bayesian 
> > context when I formulate a prior). I am not sure whether this 
> > is interpretation is applicable within a regression context, 
> > since you don't observe the counts, just the proportions. The 
> > expected proportions are inferred from the combinat
> >  ion of spread and mean. However inferring counts from a 
> > proportion (without knowing the total) seems like an 
> > Ecological Inference problem to me, and I would stay away 
> > from that if you can. So I would advise you to use -mlbeta- 
> > for your problem instead of -betafit-.
> > 
> > Hope this helps,
> > Maarten
> > 
> > Merran Evans, Nicholas Hastings and Brian Peacock (2000), 
> > "Statistical Distributions", Third edition. New York: Wiley 
> > Inter-science. 
> > 
> 
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