If I want to draw a calibration curve comparing predicted probabilities to actual events, some (e.g., Frank Harrell) suggest lowess regression of events against predicted probabilities as the preferred method, but also mention splines as another possibility. When fitting a calibration curve using splines, my intuition due to the is that I should fit a generalized additive model from a binomial family rather than assume a Gaussian error structure. When I do this, I often get wildly different results than using Gaussian GAM or lowess. Usually, the calibration curves using a binomial GAM looks much worse.
My question is what semi-parametric or non-parametric method to use when fitting calibration curves and why.