I have created a simulation in R to fit asymptotic curves (similar to Michaelis-Menten plots) to some univariate data. Essentially, I would like to find the value on the x-axis where curves first reach the asymptote. Sometimes this value is in the range of the X data, other times, it is not, and extrapolation is needed to find the value. For both the interpolation and extrapolation, I am using the package 'investr'.
I want to compare various GAM smooths in mgcv such as bs = "cr" (cubic spline) with bs = "tp" (thin-plate spline). Cubic regression splines seem to be quite popular for univariate smoothing, while thin-plate splines are the default in mgcv due to MSE optimality properties.
Eventually, I want to extend this to shape-constrained additive models (SCAMs) via the R package 'scam'.
On playing around with the different smooths, I am finding that "cr" and "tp" give very similar values. I select the best model with AIC (lowest AIC = best model).
Plots of the GAMs are also very similar, but the AICs are different, which is fully expected. I am starting off with a basis dimension value of k = 20 and increasing k to achieve curve monotonicity.
I have read that choice of k is not overly important as long as it is large enough to avoid over-smoothing but small enough to avoid excessive computation time (time is not an issue in my case).
My question: does it seem reasonable to compare GAMs/SCAMs if they give similar values anyway? For example if "cr" gives a value of x = 30.2 and "tp" gives a value of x = 30.4, it seems rather pointless to choose a "best" model with AIC.
Is my thinking flawed? I am a first-time user of mgcv.
Any advice is greatly appreciated. Thank you.