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An improved stochastic EM algorithm for large-scale full-information item factor analysis.

Siliang Zhang1, Yunxiao Chen2, Yang Liu3

  • 1Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China.

The British Journal of Mathematical and Statistical Psychology
|December 5, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient stochastic Expectation-Maximization (EM) algorithm for large-scale factor analysis. The enhanced algorithm is scalable, user-friendly, and provides accurate parameter estimation for complex data.

Keywords:
Gibbs samplerfull-information item factor analysismultidimensional item response theoryproximal gradient descentrejection samplingstochastic EM algorithm

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Area of Science:

  • Statistics
  • Psychometrics
  • Computational Statistics

Background:

  • Full-information item factor analysis (FIIFA) is crucial for understanding complex data structures.
  • Traditional methods struggle with large-scale datasets and numerous latent traits.
  • The stochastic EM algorithm offers a potential solution for computational efficiency.

Purpose of the Study:

  • To implement and evaluate an advanced stochastic EM algorithm for large-scale FIIFA.
  • To enhance computational efficiency and ease of use for practitioners.
  • To provide reliable parameter estimation and standard errors for complex latent variable models.

Main Methods:

  • Developed a stochastic EM algorithm incorporating an adaptive-rejection-based Gibbs sampler for the E step.
  • Utilized a proximal gradient descent algorithm for optimization in the M step.
  • Incorporated diagnostic procedures for algorithm convergence and employed the missing-information identity for standard errors.

Main Results:

  • The proposed algorithm demonstrates computational efficiency and is virtually tuning-free.
  • It is scalable to large datasets with multiple latent traits (e.g., >5).
  • Validated through simulation studies and application to the IPIP-NEO personality inventory.

Conclusions:

  • The enhanced stochastic EM algorithm is a powerful and practical tool for large-scale FIIFA.
  • It offers a scalable and user-friendly approach for analyzing complex latent variable models.
  • Potential extensions to other latent variable models are discussed.