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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.

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