Comparison of several non-linear-regression methods for fitting the Michaelis-Menten equation

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Abstract
The known jackknife methods (i.e. standard jackknife, weighted jackknife, linear jackknife and weighted linear jackknife) for the determination of the parameters (as well as of their confidence regions) were tested and compared with the simple Marquardt''s technique (comprising the calculation of confidence intervals from the variance-co-variance matrix). The simulated data corresponding to the Michaelis-Menten equation with defined structure and magnitude of error of the dependent variable were used for fitting. There were no essential differences between the results of both point and interval parameter estimations by the tested methods. Marquardt''s procedure yielded slightly better results than the jackknives for five scattered data points (the use of this method is advisable for routine analyses). The classical jackknife was slightly superior to the other methods for 20 data points (this method can be recommended for very precise calculations if great numbers of data are available). The weighting does not seem to be necessary in this type of equation because the parameter estimates obtained with all methods with the use of constant weights were comparable with those calculated with the weights corresponding exactly to the real error structure whereas the relative weighting led to rather worse results.