linear against nonlinear alternatives - quantile regression

Dear David,

Indeed rq() accepts a vector fo tau. I used the example given by  
Frank to run

fitspl4 <- summary(rq(b1 ~ rcs(x,4), tau=c(a1,a2,a3,a4)))

and it works.

I even can use anova() to test equality of slopes jointly across  
quantiles. however, it would be interesting to test among different  
specifications, e.g. rcs(x,4) against rcs(x,3). but it does not work.

Thanks for all suggestions!

Julia

From: dwinsemius at comcast.net
Date: Sat, 5 Nov 2011 13:42:34 -0400
To: f.harrell at vanderbilt.edu
CC: r-help at r-project.org
Subject: Re: [R] linear against nonlinear alternatives - quantile  
regression

I suppose this constitutes thread drift, but your simple example,  
Frank, made wonder if Rq() accepts a vector argument for tau. I  
seem to remember that Koencker's rq() does.. Normally I would  
consult the help page, but the power is still out here in Central  
Connecticut and I am corresponding with a less capable device. I am  
guessing that if Rq() does accept such a vector that the form of  
the nonlinearity would be imposed at all levels of tau.

-- 
David

On Nov 5, 2011, at 10:43 AM, Frank Harrell  
<f.harrell at vanderbilt.edu> wrote:

Just to address a piece of this - in the case in which you are  
currently
focusing on only one quantile, the rms package can help by fitting
restricted cubic splines for covariate effects, and then run anova  
to test
for nonlinearity (sometimes a dubious practice because if you then  
remove
nonlinear terms you are mildly cheating).

require(rms)
f <- Rq(y ~ x1 + rcs(x2,4), tau=.25)
anova(f)  # tests associations and nonlinearity of x2

Frank

Julia Lira wrote:

Dear all,

I would like to know whether any specification test for linear  
against
nonlinear model hypothesis has been implemented in R using the  
quantreg
package.

I could read papers concerning this issue, but they haven't been
implemented at R. As far as I know, we only have two  
specification tests
in this line: anova.rq and Khmaladze.test. The first one test  
equality and
significance of the slopes across quantiles and the latter one  
test if the
linear specification is model of location or location and scale  
shift.

Do you have any suggestion?

Thanks a lot!

Best regards,

Julia

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-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
--
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