There are more ways to define ‘modelfun’ in fitnlm than the other nonlinear fitting functions. However I would use an anonymous function or function file for it, because you can use them with all the other nonlinear fitting functions as well. (You cannot use the string form with the others.) I would not use a spline, since the idea is to estimate the parameters and not get a precise fit.
If for instance you have a decaying exponential of the form:
f(t) = a * exp(b*t) * sin(c*t + d)
your ‘modelfun’ (objective function) would be:
f = @(b,t) b(1).*exp(b(2).*t).*sin(b(3).*t+b(4));
Note that the order of the arguments must be the order of the parameter vector (here ‘b’) first and the independent variable vector second.
The reason to choose the anonymous function or function file is that while fitnlm makes nonlinear curve fitting relatively easy and produces a number of relevant statistics on the fit, it does not provide confidence intervals on the parameters or data. You would need to repeat your regression using nlinfit, and use nlparci and nlpredci to get those statistics, and you can use the anonymous function or function file form for all functions, including those of the Optimization Toolbox and Global Optimization Toolbox.
