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 at 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!
>>
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>