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Question of "Quantile Regression for Longitudinal Data"

3 messages · Helen Chen, Tirthankar Chakravarty, Roger Koenker

Helen Chen
# 
Hi, 

I am trying to estimate a quantile regression using panel data. I am trying
to use the model that is described in Dr. Koenker's article. So I use the
code the that is posted in the following link: 

http://www.econ.uiuc.edu/~roger/research/panel/rq.fit.panel.R

How to estimate the panel data quantile regression if the regression
contains no constant term? I tried to change the code of rq.fit.panel by
delect "X=cbind(1,x)" and would like to know is that correct ?


Thanks 
I really would appreciate some suggestions. 
Best 
Helen Chen
Tirthankar Chakravarty
# 
This is a nontrivial problem. This comes up often on the Statalist
(-qreg- is for  cross-section quantile regression):
"
You want to fit a plane through the origin using the L-1 norm.
This is not as easy as with L-2 norm (LS), as it is more
than a matter of dropping a constant predictor yet otherwise using the
same criterion of fit. You are placing another constraint on a
problem that already does not have a closed-form solution,
and it does not surprise me that -qreg- does not support this.
" (N.J. Cox)
http://www.stata.com/statalist/archive/2007-10/msg00809.html

You will probably have to program this by hand. Note also the
degeneracy conditions in Koenker (2003, pg. 36--). I am not sure how
this extends to panel data though.

References:
@book{koenker2005qre,
  title={{Quantile Regression; Econometric Society Monographs}},
  author={Koenker, R.},
  year={2005},
  publisher={Cambridge University Press}
}

T
On Sun, Apr 26, 2009 at 8:24 AM, Helen Chen <96258011 at nccu.edu.tw> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Roger Koenker
    

    

      
      #
    

  


  

      
I was trying to resist responding to this question since the original  
questioner
had already been admonished twice  last october about asking questions
on R-help about posted code that was not only not a part of R-base,
but not even a part of an R package.  But the quoted comment about
Stata is too enticing a provocation to resist.

First, it should be said that omitting intercepts in any regression  
setting
should be undertaken "at one's peril"  it is generally a very dangerous
activity, somewhat akin to fitting interactions without main effects,  
but if
there is a good rational for it, it is no different in principle for  
median
regression than for mean regression.  It may well be that Stata  
prohibits
this sort of thing out of some sort of paternalistic motive, but in R  
the
usual formula convention  y ~ x1 + x2 -1 suffices.  Of course it  
situations
in which such a formula is used for several quantiles it should be  
understood
that it is forcing each conditional quantile function through the origin
effectively implies that the conditional distribution degenerates to a  
point
mass  at the origin.

Second,  I would like to remark that "closed-form solutions" are in  
the eye
of the beholder, and many people who can recall the infamous formula:

	betahat = (X'X)^{-1} X'y

would be hard pressed to  dredge up enough linear algebra to use the
formula for anything more than the bivariate case on  the proverbial
desert island  without the aid of their trusty  laptop "Friday".

Finally,  cbind(1,x) does introduce an intercept in the code  
originally asked
about, so if you don't want an intercept don't do that, but be sure  
that that is
really want you want to do.


url:    www.econ.uiuc.edu/~roger                Roger Koenker
email   rkoenker at uiuc.edu                       Department of Economics
vox:    217-333-4558                            University of Illinois
fax:    217-244-6678                            Champaign, IL 61820

        
On Apr 26, 2009, at 6:35 AM, Tirthankar Chakravarty wrote: