An objective Bayesian estimation of parameters in a log-binomial model

• We consider objective Bayesian approach to estimation with log-binomial regression models.
• Two objective priors for the regression coefficients are considered: an improper flat prior and a proper prior.
• We establish conditions for the flat prior to yield proper posterior distribution.
• We found slice sampling algorithm to simulate from the posterior to be more efficient.
• We found that the two objective priors yield similar inference, and recommend the flat prior for Bayesian estimation.

Log-binomial model is commonly recommended for modeling prevalence ratio just as logistic regression is used to model log odds-ratio. However, for the log-binomial model, the parameter space turns out to be restricted causing difficulties for the maximum likelihood estimation in terms of convergence of numerical algorithms and calculation of standard errors. Bayesian approach is a natural choice for modeling log-binomial model as it involves neither maximization nor large sample approximation. We consider two objective or non-informative priors for the parameters in a log-binomial model: an improper flat prior and a proper prior. We give sufficient conditions for the posterior from the improper flat prior to be proper, and compare the two priors in terms of the resulting posterior summaries. We use Markov Chain Monte Carlo via slice sampling to simulate from the posterior distributions.