In generating logistic regressions for treatment-survival data, perfect separation is a problem in a few of my data sets. I've decided to use a Bayesian approach to account for the perfect separation Sources: (Gelman 2008) and this question. This approach also allows me to easily make predictions from the regression using a developed function in R.
My understanding of this Bayesian approach is limited. I can set the prior df to an arbitrary value, increasing it until I don't have a problem fitting the model due to perfect separation, but I don't understand what this regularization is effectively doing.
From my understanding, using informative priors assumes I know something about the data and I'm including it as a starting point for model fitting. A weakly informative prior doesn't supply any controversial information but can pull data away from incorrect estimations. I think the latter is more aligned with my proposed method (Source). I've read this but I do not have any prior information on which to base prior distributions or df.
I know this is an oversimplified understanding which leads to my question:
What information am I providing to the model when I arbitrarily set the prior df (in R
prior.df)at a level that allows for the model to converge?