The short answer is that what you seem to want is the rq() default with 
tau not specified.   (Default is tau=.5). 

In general rq() minimizes a sum of weighted absolute residuals.  The 
weights depend on tau (the conditional quantile of 
interest), and turn out to be equal with tau = 0.5, i.e., median 
regression in rq is LAD. 


r-sig-ecology-bounces@r-project.org wrote on 04/26/2011 03:45:23 PM:

> From:
> 
> Jane Shevtsov <jane.eco@gmail.com>
> 
> To:
> 
> r-sig-ecology@r-project.org
> 
> Date:
> 
> 04/26/2011 03:46 PM
> 
> Subject:
> 
> [R-sig-eco] Using rq() for least absolute deviation regression
> 
> Sent by:
> 
> r-sig-ecology-bounces@r-project.org
> 
> I've seen several websites say that the function rq() from the package
> quantreg can be used to do least absolute deviation regression. How do
> you go about doing this and what's the connection between quantile
> regression and LAD? (I'm very new to the former topic.)
> 
> Thanks,
> Jane
> 
> -- 
> -------------
> Jane Shevtsov
> Ecology Ph.D. candidate, University of Georgia
> co-founder, <www.worldbeyondborders.org>
> Check out my blog, <http://perceivingwholes.blogspot.com>Perceiving 
Wholes
> 
> "In the long run, education intended to produce a molecular
> geneticist, a systems ecologist, or an immunologist is inferior, both
> for the individual and for society, than that intended to produce a
> broadly educated person who has also written a dissertation." --John
> Janovy, Jr., "On Becoming a Biologist"
> 
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