From: roger koenker <roger_at_ysidro.econ.uiuc.edu>

Date: Sun 23 Jul 2006 - 21:25:41 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Sun Jul 23 21:31:22 2006

Date: Sun 23 Jul 2006 - 21:25:41 EST

On Jul 23, 2006, at 5:27 AM, roger koenker wrote:

*> When computing the median from a sample with an even number of
**> distinct
**> values there is inherently some ambiguity about its value: any
**> value between
**> the middle order statistics is "a" median. Similarly, in
**> regression settings the
**> optimization problem solved by the "br" version of the simplex
**> algorithm,
**> modified to do general quantile regression identifies cases where
**> there may
**> be non uniqueness of this type. When there are "continuous"
**> covariates this
**> is quite rare, when covariates are discrete then it is relatively
**> common, at
**> least when tau is chosen from the rationals. For univariate
**> quantiles R provides
**> several methods of resolving this sort of ambiguity by
**> interpolation, "br" doesn't
**> try to do this, instead returning the first vertex solution that it
**> comes to. Should
**> we worry about this? My answer would be no. Viewed from an
**> asymptotic
**> perspective any choice of a unique value among the multiple
**> solutions is a
**> 1/n perturbation -- with 2500 observations this is unlikely to be
**> interesting.
**> More to the point, inference about the coefficients of the model,
**> which provides
**> O(1/sqrt(n)) intervals is perfectly capable of assessing the
**> meaningful uncertainty
**> about these values. Finally, if you would prefer an estimation
**> procedure that
**> produced unique values more like the interpolation procedures in
**> the univariate
**> setting, you could try the "fn" option for the algorithm. Interior
**> point methods for
**> solving linear programming problems have the "feature" that they
**> tend to converge
**> to the centroid of solutions sets when such sets exist. This
**> approach provides a
**> means to assess the magnitude of the non-uniqueness in a particular
**> application.
**>
**> I hope that this helps,
**>
*

> url: www.econ.uiuc.edu/~roger Roger Koenker

*> email rkoenker@uiuc.edu Department of
**> Economics
**> vox: 217-333-4558 University of Illinois
**> fax: 217-244-6678 Champaign, IL 61820
**>
**>
**> On Jul 22, 2006, at 9:07 PM, Neil KM wrote:
**>
**>> I am a new to using quantile regressions in R. I have estimated a
**>> set of
**>> coefficients using the method="br" algorithm with the rq command
**>> at various
**>> quantiles along the entire distribution.
**>>
**>> My data set contains approximately 2,500 observations and I have 7
**>> predictor
**>> variables. I receive the following warning message:
**>>
**>> Solution may be nonunique in: rq.fit.br(x, y, tau = tau, ...)
**>>
**>> There are 13 warnings of this type after I run a single model. My
**>> results
**>> are similiar to the results I received in other stat programs
**>> using quantile
**>> reg procedures. I am unclear what these warning messages imply and
**>> if there
**>> are problems with model fit/convergence that I may need to consider.
**>> Any help would be appreciated. Thanks!
**>>
**>> ______________________________________________
**>> R-help@stat.math.ethz.ch mailing list
**>> https://stat.ethz.ch/mailman/listinfo/r-help
**>> PLEASE do read the posting guide http://www.R-project.org/posting-
**>> guide.html
**>> and provide commented, minimal, self-contained, reproducible code.
**>
*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Sun Jul 23 21:31:22 2006

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