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RE: st: RE: model for fractional data with panel data


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   RE: st: RE: model for fractional data with panel data
Date   Tue, 6 Nov 2007 20:48:49 +0000 (GMT)

--- Nick Cox <n.j.cox@durham.ac.uk> wrote:
> Thanks for reminding me of -betafit-. Note that this does not entail 
> a transformation or link function. It is certainly capable of coping 
> with unimodal skewed distributions on (0,1). 

It can actually be bimodal. In the conventional parameterization if
both alpha and beta are less than 1. In the alternative (regression
like) parameterization this occurs if phi is less than 2. Maybe we
should add a warning in cases where this occurs, as I think that this
is often unexpected and maybe undesirable. I doubt however that occurs
often in real data. 

You can see graphs of such bimodel beta distribution in the example
below. You can play with various values by changing the locals alpha
beta mu and/or phi. 

*----------------- begin example ----------------------
/*conventional parameterization*/
local alpha = .5
local beta = .5
twoway function y = betaden(`alpha', `beta', x)

/*alternative parameterization*/
local phi = 1.5
local mu = .5
local constant = exp(lngamma(`mu'))/  ///
exp(lngamma(`mu'*`phi'))*exp(lngamma((1-`mu')*`phi'))

twoway function y = `constant'* ///
                     x^(`mu'*`phi'-1)* ///
                    (1-x)^((1-`mu')*`phi'-1)
*-------------- end example --------------------------
(For more on how to use examples I sent to the Statalist, see
http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )

-- Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


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