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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 10:36:03 -0000

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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