I am using the nls procedure in R to fit a logistic growth model. In their SSlogis function, José Pinheiro and Douglas Bates chose the formulation
Asym / (1 + exp((xmid-input) / scal))
for their model. As I am fairly inexperienced with the numerical properties of such models, I wonder:
Can somebody explain why the authors chose this formulation instead of possible alternatives? In particular, ecologists seem to prefer a model with initial population, carrying capacity and growth rate. Does the formulation above have favourable numerical properties?
It seems that when the model is misspecified and the data are actually fairly linear with time, this formulation often fails to converge. Could such a problem be avoided?
Is parameter orthogonality a key concern here or are other aspects of the model more important?
Is it trivial to extend this model to allow a flexible intercept? Would the following model provide sensible numerical properties?
Intercept + (Asym - Intercept ) / (1 + exp((xmid-input) / scal))
I am, of course, open for alternatives as long as it allows for some flexibility in intercept, location where 50% of the growth has been achieved and asymptote.