[R] Warning Messages using rq -quantile regressions

[roger koenker]

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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>