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.

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

Publication Title

Communications in Statistics - Theory and Methods

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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Publisher's PDF

Included in

Mathematics Commons

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