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 [EMAIL PROTECTED] 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.