Just as a follow-up on T. Lumley's post, 2 citations that may be useful in 
reference to application of quantile regression with survey samples are:

Bassett and Saleh.  1994.  L_1 estimation of the median of a survey 
population.  Nonparametric Statistics 3: 277-283.  (L_1 estimation of 
median is 0.50 quantile regression).

Bassett et al.  2002.  Quantile models and estimators for data analysis. 
Metrika 55: 17-26.  (describes weighted QR for survey of school 
characteristics and student achievement scores).

Brian

Brian S. Cade, PhD

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

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



"Stas Kolenikov" <skolenik@gmail.com> 
Sent by: r-help-bounces@r-project.org
08/20/2008 01:14 PM

To
"Cheng, Yiling (CDC/CCHP/NCCDPHP)" <ycc1@cdc.gov>
cc
r-help@r-project.org
Subject
Re: [R] Quantile regression with complex survey data






On Wed, Aug 20, 2008 at 8:12 AM, Cheng, Yiling (CDC/CCHP/NCCDPHP)
<ycc1@cdc.gov> wrote:
> I am working on the NHANES survey data, and want to apply quantile
> regression on these complex survey data. Does anyone know how to do
> this?

There are no references in technical literature (thinking, Annals,
JASA, JRSS B, Survey Methodology). Absolutely none. Zero. You might be
able to apply the procedure mechanically and then adjust the standard
errors, but God only knows what the population equivalent is of
whatever that model estimates. If there is a population analogue at
all.

In general, a quantile regression is a heavily model based concept:
for each value of the explanatory variables, there is a well defined
distribution of the response, and quantile regression puts additional
structure on it -- linearity of quantiles wrt to some explanatory
variables. That does not mesh well with the design paradigm according
to which the survey estimation is usually conducted. With the latter,
the finite population and characteristics of every unit are assumed
fixed, and randomness comes only from the sampling procedure. Within
that paradigm, you can define the marginal distribution of the
response (or any other) variable, but the conditional distributions
may simply be unavailable because there are no units in the population
satisfying the conditions.

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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