Asymptotic Properties of Monte Carlo Strategies for a Cumulative Link Model

For a cumulative link model in the Bayesian context, the posterior distribution cannot be obtained in closed form, and we have to resort to an approximation method. A simple data-augmentation strategy is widely used for that purpose but is known to work poorly. The marginal augmentation procedure and the parameter-expanded data-augmentation procedure are considered to be remedies, but such strategies are still not free from poor convergence. In this paper, we propose a kind of the hybrid Markov chain Monte Carlo strategy. To evaluate the efficiency, a local non-degeneracy is introduced, and we also provide a numerical simulation to show the effect.