Rich:  When you use tau=-1 in rq() then under the $sol you are getting
estimates for all possible quantiles for the given regression model, which
includes the objective function value minimized, the quantile value,
estimates for all the parameters, and I think the output still includes the
estimated value for the quantile at the mean of all the predictors (Qbar).
 Also available under $dsol are the dual solution values that are used for
various forms of the rankscore hypothesis tests.  Under $rho the quantile
values and objective function values are repeated.  Note that with the all
quantile solutions using tau=-1 you can plot the step function for the
empirical cdf of the parameter estimates by quantiles.  For most useful
sets of data with reasonable sample sizes, it is impractical to compute all
possible quantiles so most people would estimate say a reasonably large
subset of them,e.g. tau = 1:99/100 provides estimates by increments of 0.01
from 0.01 to 0.99.  But it is worth remembering that this subset of
estimates is just trying to approximate the step function you would obtain
if you could estimate all possible quantiles (see Cade and Noon 2003.  A
gentle introduction to quantile regression for ecologists.).

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  cadeb@usgs.gov <brian_cade@usgs.gov>
tel:  970 226-9326



On Wed, May 14, 2014 at 12:32 PM, Rich Shepard <rshepard@appl-ecosys.com>wrote:

>   I've read the quantreg vignette and ?rq and applied rq() to Brownlee's
> stack loss data set. The results when I specify the desired output quantile
> (tau) are easily understood. When I specify tau = -1 (as in the 4th example
> in ?rq) I do not know what I'm seeing as the results. The code is:
>
> data(stackloss)
> rq(stack.loss ~ stack.x, tau=-1) # which the help page tells me returns the
>                                  # full rq process
>
>   Please point me to some documentation that explains the extensive results
> of the full rq process.
>
> Rich
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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