Document Type
Article
Publication Date
11-9-2024
Department
Department of Mathematical Sciences
Abstract
Multivariate probit models have been popularly utilized to analysis multivariate ordinal data. However, the identifiable multivariate probit models entail the covariance matrix for the underlying multivariate normal variables to be a correlation matrix, which brings a rigorous task to conduct efficient statistical analysis. Parameter expansion to make the identifiable model to be non-identifiable has been inevitably explored. However, the effect of the expanded parameters on the convergence of Markov chain Monte Carlo (MCMC) is seldomly investigated; in addition, the comparison of MCMC developed based on the identifiable model and that based on the non-identifiable model is hardly ever explored, especially for data with large sample sizes. In this paper, we conduct a thorough investigation to illustrate the effect of the expanded parameters on the convergence of MCMC and compare the behavior of MCMC between the identifiable and non-identifiable models. Our investigation provides a practical guide regarding the construction of non-identifiable models and development of corresponding MCMC sampling methods. We conduct our investigation using simulation studies and present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE) study.
Publication Title
Communications in Statistics - Theory and Methods
Recommended Citation
Zhang, X.
(2024).
Identifiability and convergence behavior for Markov chain Monte Carlo using multivariate probit models.
Communications in Statistics - Theory and Methods.
http://doi.org/10.1080/03610926.2024.2425738
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1232
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Version
Publisher's PDF
Publisher's Statement
© 2024 The Author(s). Published with license by Taylor & Francis Group, LLC. Publisher’s version of record: https://doi.org/10.1080/03610926.2024.2425738