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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Michaelis-Menten and regression |

Date |
Wed, 22 Sep 2004 15:23:43 +0100 |

Michaelis-Menten function fitting is a can of worms. The main thing is to be aware of that and to have looked at the literature on it. There is a lot, going back decades; do not try to reinvent wheels without reading first. _Biometrics_ is a good journal here. You may be able to exploit stuff on http://www.jstor.org However, in Stata one attractive route is to reformulate the problem as a generalised linear model with reciprocal link. See the exchange in Generalized Linear Models for Enzyme-Kinetic Data J. A. Nelder; D. Ruppert; N. Cressie; R. J. Carroll Biometrics 47(4) (Dec., 1991), pp. 1605-1615 which I haven't read for some years, so the memories are hazy. As I recall, the main idea is this. You have y = ax / (1 + bx) so 1/y = 1 / ax + b / a Let us define X = 1/x and reparameterise A = 1 / a B = b / a We then have 1/y = AX + B and the right-hand side is then a piece of cake. The left-hand side we take care of by using a reciprocal link, another piece of cake with -glm-. In Stata terms . gen rec_x = 1 / x . glm y rec_x, link(power -1) Of course, all this is just algebra with the deterministic curve and says nothing about error structure. Nelder I guess recommends using a gamma family. Nick n.j.cox@durham.ac.uk Simon Moore > I have a reasonably simple hypothesis that the form of relationship > between the independent variable (x) and the dependent variable (y) > follows the Michaelis-Menten rational function, f(x) = ax/(1+bx). I > want to have this in a regression model with the cluster() option: reg > y f(x) V, cluster(). But I can't see a way of achieving this and > having reg solve for a and b. I thought maybe a power expansion of > f(x) might work, but this does not seem appropriate. > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: Michaelis-Menten and regression***From:*Roger Newson <roger.newson@kcl.ac.uk>

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