Approximate Bayesian logistic regression via penalized likelihood by data augmentation

Abstract

We present a command, penlogit, for approximate Bayesian logistic regression using penalized likelihood estimation via data augmentation. This command automatically adds specific prior-data records to a dataset. These records are computed so that they generate a penalty function for the log likelihood of a logistic model, which equals (up to an additive constant) a set of independent log prior distributions on the model parameters. This command overcomes the necessity of relying on specialized software and statistical tools (such as Markov chain Monte Carlo) for fitting Bayesian models, and allows one to assess the information content of a prior in terms of the data that would be required to generate the prior as a likelihood function. The command produces data equivalent to normal and generalized log-F priors for the model parameters, providing flexible translation of background information into prior data, which allows calculation of approximate posterior medians and intervals from ordinary maximum likelihood programs. We illustrate the command through an example using data from an observational study of neonatal mortality.