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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/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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