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fitting a threshold model

To: s-news@lists.biostat.wustl.edu
Subject: fitting a threshold model
From: Lauren Keim <lkeim@zen.uq.edu.au>
Date: Mon, 13 May 2002 15:52:24 +1000
I'm hoping that someone here can solve a problem that none of the S-plus
wizards in my lab can solve.  I'm investigating gecko distribution at
suburban/forest edges - the data I have consists of the presence/absence
of geckos and distance from edge. Using likelihood methods, I am trying
to fit a number of different models to the distribution of the geckos,
one of which is a threshold model that takes this form:

                            p = Z if x < (or equal to) T
                            p = 0.05 if x>T

p = probability that geckos are present.
x = distance from the edge
T= threshold distance
Z = a constant value of p for distances less than the threshold distance
(T)

The value I am trying to find is the threshold distance (T) which gives
me the smallest min neg log likelihood to be compared with the min neg
log likelihood of other models (eg. GLMs).  I've tried to find a way of
doing this with the linear model function but couldn't get anything to
work.  I know that it is possible to fit a threshold model using the
'solver' function in Excel so it seems very strange that it would not be
possible in S-plus!   If anyone has any ideas on how to do this (using
s-plus 2000) I'd be very grateful if you could let me know (however I am
very much an s-plus novice, so please keep your answers as simple as
possible).

Thanks,

Lauren Keim
Department of Zoology and Entomology
University of Queensland




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