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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Bayesian Analysis of Longitudinal Ordinal Data with Missing Values Using Multivariate Probit Models.

Xiao Zhang1

  • 1Department of Mathematical Sciences, Michigan Technological University 1400 Townsend Drive, Houghton, Michigan 49931-1295, USA.

Journal of Statistics Applications & Probability
|August 29, 2025
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Summary
This summary is machine-generated.

This study introduces Bayesian methods for analyzing longitudinal ordinal data with missing values. The proposed Markov chain Monte Carlo (MCMC) sampling method effectively handles missing data and improves model convergence.

Keywords:
Longitudinal ordinal datadropoutmissing datamultivariate probit modelnon-identifiable multivariate probit model

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Longitudinal ordinal data with missing values are common in scientific research.
  • Analyzing such data requires robust statistical methods to ensure accurate results.
  • Existing methods may struggle with substantial missingness, necessitating new approaches.

Purpose of the Study:

  • To propose efficient Bayesian methods for analyzing longitudinal ordinal data with missing values.
  • To develop and evaluate Markov chain Monte Carlo (MCMC) sampling techniques for multivariate probit models.
  • To compare the performance of methods based on non-identifiable versus identifiable probit models.

Main Methods:

  • Development of MCMC sampling methods for non-identifiable multivariate probit models.
  • Comparison of MCMC performance between non-identifiable and identifiable probit models.
  • Simulation studies to assess the methods' ability to handle missing data.

Main Results:

  • The proposed Bayesian methods effectively handle substantial missing values in longitudinal ordinal data.
  • MCMC sampling based on non-identifiable models, with parameter marginalization, shows superior mixing and convergence.
  • The method utilizing non-identifiable models outperforms those based on identifiable models.

Conclusions:

  • Efficient Bayesian methods using MCMC sampling can successfully analyze longitudinal ordinal data with missing values.
  • Marginalizing redundant parameters in non-identifiable models enhances MCMC performance.
  • The developed methods are applicable to real-world data, as demonstrated by the RLMS-HSE survey analysis.