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st: fitting a gompertz curve, not in the context of survival analysis


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
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 <dan_waldo@yahoo.com>
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 <stephenj@essex.ac.uk>
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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