A Bayesian multivariate partially linear single-index probit model for ordinal responses

ABSTRACT

Combining the multivariate probit models with the multivariate partially linear single-index models, we propose new semiparametric latent variable models for multivariate ordinal response data. Based on the reversible jump Markov chain Monte Carlo technique, we develop a fully Bayesian method with free-knot splines to analyse the proposed models. To address the problem that the ordinary Gibbs sampler usually converges slowly, we make use of the partial-collapse and parameter-expansion techniques in our algorithm. The proposed methodology are demonstrated by simulated and real data examples.

Keywords:

• Free-knot splines
• Gibbs sampler
• Ordinal data
• Probit models
• Single-index models

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Hai-Bin Wang http://orcid.org/0000-0001-5950-0032

Additional information

Funding

The project was supported by the National Natural Science Foundation of China [Nos. 11471272 and 11661074].