One of the most likely things to go wrong in non-linear least squares is that the model fails because your initial guesses for the starting parameter values were too far off. The simplest solution is to use one of R's ‘self-starting’ models, which work out the starting values for you automatically. These are the most frequently used self-starting functions:
SSasymp asymptotic regression model SSasympOff asymptotic regression model with an offset SSasympOrig asymptotic regression model through the origin SSbiexp biexponential model SSfol first-order compartment model SSfpl four-parameter logistic model SSgompertz Gompertz growth model SSlogis logistic model SSmicmen Michaelis–Menten model SSweibull Weibull growth curve model
In our next example, reaction rate is a function of enzyme concentration; reaction rate increases quickly with concentration at first but asymptotes once the reaction rate is no longer enzyme-limited. R has a self-starting version called SSmicmen parameterized as
where the two parameters are a (the asymptotic value of y) and b (which is the x value at which half of the maximum response, a/2, is attained). In the field of enzyme kinetics a is called the Michaelis parameter (see p. 202; in R help the two parameters are called Vm and K respectively).
Here is SSmicmen in action: