I’m currently comparing predictive projection, Lasso (and some other variable selection methods) on a logistic regression. For this comparison, I use simulated data (including collinear data) and for most simulated data the predictive performance of predictive projection and Lasso is similar.
I also use a misspecified model, where the logistic model and the data generating process have different relations. The logistic model has linear relations while the data generating process uses a step function and an exponential relation. In this case predictive projection performs better than Lasso.
I once heard that Bayesian models are relatively better than frequentist models under misspecification, however I could never find any evidence to support this claim. Does anyone know whether this is true? If yes, why is this the case?