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Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework.

Siliang Zhang1, Yunxiao Chen2

  • 1EAST CHINA NORMAL UNIVERSITY, London, England.

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Summary
This summary is machine-generated.

This study introduces a unified computational framework for latent variable models, addressing complex estimation challenges. The new quasi-Newton stochastic proximal algorithm offers efficient and robust solutions for modern psychometric applications.

Keywords:
Polyak–Ruppert averaginglatent variable modelspenalized estimatorproximal algorithmquasi-Newton methodsstochastic approximation

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Computational Statistics

Background:

  • Latent variable models are crucial in psychometrics.
  • Modern applications involve many latent variables, mixed data types, and parameter constraints/penalties.
  • Existing estimation methods lack a unified framework for these complexities.

Purpose of the Study:

  • To develop a unified computational framework for latent variable model estimation.
  • To propose a novel quasi-Newton stochastic proximal algorithm.
  • To address challenges posed by numerous latent variables, mixed data types, and parameter regularizations.

Main Methods:

  • Unified formulation of the optimization problem.
  • Development of a quasi-Newton stochastic proximal algorithm.
  • Theoretical analysis of algorithm properties.

Main Results:

  • Established theoretical properties of the proposed algorithm.
  • Demonstrated computational efficiency and robustness through simulations.
  • Validated the framework across diverse latent variable model estimation scenarios.

Conclusions:

  • The proposed unified framework and algorithm effectively handle complex latent variable models.
  • The method provides a robust and computationally efficient solution for modern psychometric inference.
  • This work fills a critical gap in computational frameworks for latent variable modeling.