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Efficient and accurate variational inference for multilevel threshold autoregressive models in intensive longitudinal data.

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Title: Efficient and accurate variational inference for multilevel threshold autoregressive models in intensive longitudinal data.
Authors: Rahman, Azizur (AUTHOR), Jiang, Depeng (AUTHOR), Lix, Lisa M. (AUTHOR)
Source: British Journal of Mathematical & Statistical Psychology. Nov2025, Vol. 78 Issue 3, p785-803. 19p.
Subjects: Bayesian analysis, Markov chain Monte Carlo, Statistical models, Inferential statistics, Panel analysis, Optimization algorithms, Parameter estimation
Abstract: Recent technological advancements have enabled the collection of intensive longitudinal data (ILD), consisting of repeated measurements from the same individual. The threshold autoregressive (TAR) model is often used to capture the dynamic outcome process in ILD, with autoregressive parameters varying based on outcome variable levels. For ILD from multiple individuals, multilevel TAR (ML‐TAR) models have been proposed, with Bayesian approaches typically used for parameter estimation. However, fitting ML‐TAR models can be computationally challenging. This study introduces a mean‐field variational Bayes (MFVB) algorithm as an alternative to traditional Bayesian inference. By optimizing to approximate posterior densities, variational Bayes aims to find the best approximation within a defined set of distributions. Simulation results demonstrate that our MFVB algorithm is significantly faster than the standard Markov chain Monte Carlo (MCMC) approach. Moreover, increasing the number of individuals or time points enhances the accuracy of the parameter estimates using MFVB, suggesting that sufficient data are crucial for accurate estimation in complex models like ML‐TAR models. When applied to real‐world data, the MFVB algorithm was significantly more efficient than MCMC and maintained similar accuracy. Thus, the MFVB algorithm is a faster and more consistent alternative to MCMC for large‐scale inference in ILD models. [ABSTRACT FROM AUTHOR]
Copyright of British Journal of Mathematical & Statistical Psychology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Psychology and Behavioral Sciences Collection
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  Data: Efficient and accurate variational inference for multilevel threshold autoregressive models in intensive longitudinal data.
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  Data: <searchLink fieldCode="AR" term="%22Rahman%2C+Azizur%22">Rahman, Azizur</searchLink> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Jiang%2C+Depeng%22">Jiang, Depeng</searchLink> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lix%2C+Lisa+M%2E%22">Lix, Lisa M.</searchLink> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22British+Journal+of+Mathematical+%26+Statistical+Psychology%22">British Journal of Mathematical & Statistical Psychology</searchLink>. Nov2025, Vol. 78 Issue 3, p785-803. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+chain+Monte+Carlo%22">Markov chain Monte Carlo</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Inferential+statistics%22">Inferential statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Panel+analysis%22">Panel analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink>
– Name: Abstract
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  Group: Ab
  Data: Recent technological advancements have enabled the collection of intensive longitudinal data (ILD), consisting of repeated measurements from the same individual. The threshold autoregressive (TAR) model is often used to capture the dynamic outcome process in ILD, with autoregressive parameters varying based on outcome variable levels. For ILD from multiple individuals, multilevel TAR (ML‐TAR) models have been proposed, with Bayesian approaches typically used for parameter estimation. However, fitting ML‐TAR models can be computationally challenging. This study introduces a mean‐field variational Bayes (MFVB) algorithm as an alternative to traditional Bayesian inference. By optimizing to approximate posterior densities, variational Bayes aims to find the best approximation within a defined set of distributions. Simulation results demonstrate that our MFVB algorithm is significantly faster than the standard Markov chain Monte Carlo (MCMC) approach. Moreover, increasing the number of individuals or time points enhances the accuracy of the parameter estimates using MFVB, suggesting that sufficient data are crucial for accurate estimation in complex models like ML‐TAR models. When applied to real‐world data, the MFVB algorithm was significantly more efficient than MCMC and maintained similar accuracy. Thus, the MFVB algorithm is a faster and more consistent alternative to MCMC for large‐scale inference in ILD models. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of British Journal of Mathematical & Statistical Psychology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1111/bmsp.12381
    Languages:
      – Code: eng
        Text: English
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        PageCount: 19
        StartPage: 785
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      – SubjectFull: Bayesian analysis
        Type: general
      – SubjectFull: Markov chain Monte Carlo
        Type: general
      – SubjectFull: Statistical models
        Type: general
      – SubjectFull: Inferential statistics
        Type: general
      – SubjectFull: Panel analysis
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Parameter estimation
        Type: general
    Titles:
      – TitleFull: Efficient and accurate variational inference for multilevel threshold autoregressive models in intensive longitudinal data.
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            NameFull: Rahman, Azizur
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            NameFull: Jiang, Depeng
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            NameFull: Lix, Lisa M.
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            – D: 01
              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
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              Value: 78
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            – TitleFull: British Journal of Mathematical & Statistical Psychology
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