(v2) [R] quadratic trends and changes in slopes (R-help digest, Vol 1 #52 - 16 msgs)

[vito muggeo]

It is well-known that change-point estimation is a non-trivial task.

You could find interesting the followings

Pastor and Guallar 1998. "use of two-segmented logistic regression to
estimate changepoint in epidemiological studies" Am J Epid, 148, 631-642

Goetghebeur and Pocock 1995 "detection and estimation og J-shaped
risk-response relationships" JRSSA,158,107-121

where a quadratic polynomial before or after the change has been used in
order to allow the score function to be continuous at the changepoint.
However the aforementioned papers do not seem to solve the problem in
practice: Goetghebeur and Pocock 1995 use a grid-search-type method to
estimate the break-point and Pastor and Guallar 1998 use a non standard
algorithm to maximize the log-lik.

If you are dealing with time-serie regression models and the changepoint is
a time-point (i.e. on the time-axis) you could see the strucchange package
by Achim Zeleis (see also his paper on R-news 2002, I don't remeber the
issue).

best,
vito


----- Original Message -----
From: "kjetil brinchmann halvorsen" <kjetil at entelnet.bo>
To: <r-help at stat.math.ethz.ch>; "Chuck White" <chuck at chuckandmaggi.com>
Cc: "'Martin Michlmayr'" <tbm at cyrius.com>
Sent: Tuesday, January 21, 2003 11:06 PM
Subject: RE: (v2) [R] quadratic trends and changes in slopes (R-help digest,
Vol 1 #52 - 16 msgs)


> On 20 Jan 2003 at 21:49, Chuck White wrote:
>
> >
> > I'd like to use linear and quadratic trend analysis in order to find
> > out a change in slope.  Basically, I need to solve a similar problem as
> > discussed in
> > http://www.gseis.ucla.edu/courses/ed230bc1/cnotes4/trend1.html
> >
>
> This response show how to do the test of non-linearity in a
> complicated way, all can be done much easier in R, start to
> look at poly() and contr.poly() (and summary.aov with the argument
> split=). But that is not the point. The original poster did'nt want
> to test for nonlinearity, he assumed there is nonlinearity and wanted
> to estimate the change point. He also said that the usual procedure
> to do that in his field is to estimate cuadratic models for data
> 1, 1:2, 1:3, ..., 1:9 (or some similar number) and take the change-
> point as the value of i above (in 1:i) where the quadratic term
> first is significant. That cannot be sound, as you obviously must go
>  somewhat past the changepoint before the quadratic term can become
> significant! So this method cannot possibly give an consistent
> estimator of the change-point. He should use some other method, like
> building a model with an explicit change-point and estimate that.
>
> Kjetil Halvorsen
>
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