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A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses.

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  • 1Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, USA.

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Summary
This summary is machine-generated.

This study introduces a tensor decomposition method for latent class analysis, improving computational efficiency and accuracy for large-scale survey data. The new tensor-EM pipeline effectively analyzes complex datasets in social sciences.

Keywords:
EM algorithmclustering consistencylarge-scale latent class analysistensor decompositiontensor power method

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Area of Science:

  • Statistics
  • Data Science
  • Psychometrics

Background:

  • Latent class models are essential in social and behavioral sciences for analyzing categorical data.
  • Traditional methods struggle with large-scale datasets (large N and J) due to computational inefficiency and local optima issues with the EM algorithm.

Purpose of the Study:

  • To develop computationally efficient and theoretically valid methods for latent class analysis on large-scale data.
  • To address the limitations of the Expectation-Maximization (EM) algorithm in large-scale latent class analysis.

Main Methods:

  • Introduced a tensor decomposition perspective for latent class analysis with binary responses.
  • Proposed a two-step approach: moment-based tensor power method followed by EM algorithm initialization.
  • Established theoretical clustering consistency for Maximum Likelihood Estimator (MLE) as N and J approach infinity.

Main Results:

  • The proposed tensor-EM pipeline demonstrates significant improvements in computational efficiency for large-scale data.
  • Simulation studies confirm the accuracy and efficiency of the tensor-EM method.
  • The method was successfully applied to an educational assessment dataset.

Conclusions:

  • The tensor decomposition approach offers a powerful and efficient solution for latent class analysis in the era of big data.
  • This method enhances the reliability and scalability of latent class modeling in psychological, behavioral, and social sciences.