How to get standards errors of the parameters of a non-linear model (R and Excel) I am working on the movement of fish species from the centre of a protected area to a non-protected area. Based on the article by R. Abesamis, itself inspired by the work of B. Kaunda-Arar (page 91), I applied to my dataset a logistic decay D = 1/(1+exp(S*(I-d)) where D is the proportion of biomass in the middle of the reserve, d is the distance from the centre of the protected area, S is the slope and I is the inflection point. The parameters to be estimated in this model are S and I. However, I had to use Excel to estimate these parameters because the nls function in R was giving me constant error messages (the well-known singular gradient error). I successfully estimated S and I using the Excel solver, but I need to know the standard errors of these parameters. For this, the article states that a linearization of my logistic model is necessary, but despite my research on this subject I do not understand how to do this.
My questions are therefore the following:

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*Is it possible to get the standard error of my parameters directly from Excel? If so, how?

*If this is not possible in Excel, how can I get the standard errors of my S and I parameters in R? (note: using the nls function, even when applying the values obtained by my Excel model as starting values for S and I, the gradient error message is still displayed. Same thing when using nlsLM.)


I'd be tempted to approach this with Bayesian methods, especially if observations are correlated and you also want to model this. For example, using the brms R package makes it very easy to fit models with non-linear terms in them as illustrated in the vignette on this topic. By having at least vague prior information (which you probably have based on simple physical limitations one can deduce) any problems in identifying them model parameters are often substantially reduced. The standard deviation of MCMC samples from the posterior for a parameter then play a similar role as a SE in frequentist inference (but you could also look at the posterior median and credible intervals based on distribution quantiles).
