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RE: st: Fractional Logit


From   "Maarten Buis" <M.Buis@fsw.vu.nl>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Fractional Logit
Date   Mon, 31 Oct 2005 10:40:19 +0100

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. 

>-----Original Message-----
>From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Rijo John
>Sent: zondag 30 oktober 2005 22:02
>To: Statalist
>Subject: RE: st: RE: Fractional Logit
>
>Nick, could you please explain the portion "alphavar(varlist1)
>betavar(varlist2)" in betafit command? Is there any standard way of
>deciding which are the variables to be included in the varlist1 and
>varlist2 for alphavar and betavar respectively?



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