some colleagues and I were discussing how to decide whether a linear or a sigmoidal curve fits the data best. E.g., does the probability of catching fish increase in a linear or sigmoidal fashion depending on the number of worms used?
We thought about comparing a model with a gaussian link to a model with a logit link, but as far as I understand it, you cannot compare the fit of models with a different link function in a meaningful way? Plus, a sigmoidal function might look linear depending on the parameters of the function.
The other option would be polynomials/spline regression, but that seems pretty “heavy” considering that we know we want to compare linear vs. sigmoidal?
This sounds like a straightforward problem, but I couldn’t find an answer so far. Sorry if I overlooked something.
I’m grateful for any resources you can point me towards!
Thank you in advance