Re: [S] SE's for ratio of two parameters

Douglas Bates (
25 Jun 1998 10:31:03 -0500

Pedro de Barros <> writes:

> Dear all, this is in fact more like a statistical question, but I hope
> someone from the list will know the answer.
> I have been fitting the Michaelis-Menten model (simple hyperbola) to several
> data sets. I have been able to get approximate SE's for the two parameters
> thanks to Prof. Ripley, but I am unsure of how to calculate the SE for a
> derived parameter which is A=B1/B2. I have the (approximate) var-covar
> matrix for B1, B2, so I thought I would use it to get an approximation to
> the SE of A.
> Any good hints? (I was thinking of treating A as a ratio estimator, but I
> could not get at bibliography on this specific problem...)

If you are fitting the Michaelis-Menten model by nonlinear least
squares, you can re-define the model so the ratio you see is one of
the parameters in the model, then re-fit.

The Michaelis-Menten is often defined as
velocity ~ Vm * concentration / (K + concentration)
where Vm and K are the parameters. If you would prefer to write it as
velocity ~ concentration/ (R1 + R2 * concentration)
so that R1 = K / Vm, then do so and re-fit the data. This will
provide estimates of the standard errors of the R1 and R2 parameters.
As with any nonlinear model, these are approximate standard errors.

This message was distributed by To unsubscribe
send e-mail to with the BODY of the
message: unsubscribe s-news