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Re: st: Looking for Box-Cox transformation for a quantile of dependent variable


From   <skolenik@email.unc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Looking for Box-Cox transformation for a quantile of dependent variable
Date   Tue, 17 Aug 2004 13:52:22 -0400

> I am looking for a STATA command that would perform the Box-Cox 
> transformation for a quantile of dependent variable y conditional on 
> covariates x. An example of such an application is Moshe Buchinsky,
> Journal of Econometrics, 1995, "Quantile regression, Box-Cox
> transformation model, and the U.S. wage structure, 1963-1987".

That's a little bit weird way of looking at the Box-Cox transformation.
Its prime aim in the regression analysis has been to make the dependent
variable / regression residuals approximately unskewed, which is
irrelevant for quantile regression. Buchinsky (1995) claims that his
estimation procedure helps finding a linear index, but the estimation
procedure itself is not aimed at that, and it is a by-product of the
Box-Cox procedure, at best. He should have derived some measure of
remaining non-linearity, like the score test statistic for the basic
regression for the null that all interactions are zero, and minimize
that, rather than the sum of the check functions, as in the regular
quantile regression. I don't think he cares to check for the remaining
nonlinearity anywhere in the paper, even though that is supposed to be
the only selling point of Box-Cox transformation in his context.

As long as 

findit quantile regression

does not produce anything that links to the Box-Coxed quantile
regression, you would have to work on that for yourself following his
steps, and then see how you can get the correct covariance matrix.

 ---                                    Stas Kolenikov
 --       Ph.D. student in Statistics at UNC-Chapel Hill
 - http://www.komkon.org/~tacik/  -- Stas.Kolenikov@unc.edu

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