Flexible Modeling of Binary Data Using the Log-Burr Link

Popular link functions often fit skewed binary data poorly. We propose the log-Burr link as flexible alternative. The link nests the complementary-log-log and logit link as special cases, determined by a shape parameter which can be estimated from the data. Shrinkage priors are used for the shape parameter, furthermore the parameter is allowed to vary between subgroups for clustered data. For modeling of nonlinear effects basis function expansions are used. Inference is done in a fully Bayesian framework. Posterior simulation is done via the No-U-Turn sampler implemented in Stan, avoiding convergence problems of the Gibbs sampler and allowing for easy use of nonconjugate priors. Regression coefficients associated with basis functions are reparameterized as random effects to speed up convergence. The proposed methods and the effect of misspecification of the modeled dgp are investigated in a simulation study. The approach is applied on large scale unemployment data.