# Regression with nonlinear function (almost logistic)

I'm doing a multiple nonlinear regression that involves $y=A+B\cdot \text{erf}(\frac{C-x}{\sqrt{2}w})$. Parameters $A$, $B$, and $C$ (the one I really care about), all need to be estimated and $x$ is a vector of around 20 elements (samples). Now, erf is pretty similar to sigmoid (the usual logistic function that people seem to use as a basis). I'm not too familiar with logistic regression, so I'll ask a really open-ended question: do any logistic regression experts see any method or advantage to framing this more as a logistic type regression? I imagine the best thing to do is to stick with least-squares cost function and an L2 (i.e. ridge, tikhonov, etc.) regularizer, my planned course, but don't want to discount the similarity to a whole other field.

• You refer to this as "multiple nonlinear regression" but you only mention one predictor-variable ($x$). Is $w$ a variable or a parameter? Sep 13 '17 at 22:57

I see no benefit in trying to connect a straightforward nonlinear least squares problem (which would still be NLS after adding a $L_2$ penalty in the coefficients) to logistic regression (or another binomial GLM, like probit regression), which it's not especially closely related to nonlinear least squares except in the superficial sense that they have a rough similarity of appearance.