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st: fitting a gompertz curve, not in the context of survival analysis
From |
"Stephen P. Jenkins" <[email protected]> |
To |
<[email protected]> |
Subject |
st: fitting a gompertz curve, not in the context of survival analysis |
Date |
Fri, 29 May 2009 10:34:26 +0100 |
================
Date: Thu, 28 May 2009 14:56:00 -0700 (PDT)
From: Dan Waldo <[email protected]>
Subject: st: fitting a gompertz curve, not in the context of survival
analysis
Dear list members,
I am trying to test whether government revenues as a percentage of GDP
can be fit over time with a Gompertz curve -- especially to determine
(if the fit is appropriate) the limiting value.
The help I have found comes in the form of survival analysis models,
which I have trouble reconciling to the model I am trying to fit.
Is there a Stata add-on that fits Laird's tumor-growth variant of the
Gompertz? This would be specified as:
X(t)= K exp(log(X(0)/K)exp(-at))
where X is known and K and a are estimated.
Thanks in advance for any tips.
Dan Waldo
=======================================
Your model can be rewritten as
logX(t)= logK + (1/K)*logX(0) - a*t
which is of the form
logX(t)= b + c*logX(0) - a*t
which is a linear model. Assuming you have no censoring in your
context (the issue of particular importance in the survival analysis
context), then could the model not be estimated by OLS (-regress-)?
Whether the constraints on b and c hold is then something you can use
as a specification check? Alternatively, you could fit the model
incorporating constraints by non-linear least squares (-nl-).
BTW does the scale for "t" (time) matter in your problem? Is there a
natural origin? (In survival analysis, t=0 has a clear meaning:
beginning of when at risk of the event in question.) What if you
rewrite the model as
logX(s)= logK + (1/K)*logX(s-v) - a*s
where v is some arbitrary value like "1961"?
Stephen
-------------------------------------------------------------
Professor Stephen P. Jenkins <[email protected]>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374. Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/iser/teaching/module-ec968
Downloadable papers and software: http://ideas.repec.org/e/pje7.html
Learn about the UK's new household panel survey, "Understanding
Society": http://www.understandingsociety.org.uk/
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