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Pairwise likelihood estimation and limited-information goodness-of-fit test statistics for binary factor analysis

Haziq Jamil1,2, Irini Moustaki2, Chris Skinner2

  • 1Universiti Brunei Darussalam, Gadong, Brunei Darussalam.

The British Journal of Mathematical and Statistical Psychology
|October 12, 2024
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Summary
This summary is machine-generated.

This study introduces improved methods for analyzing binary data in factor models, enhancing accuracy with complex survey data. New statistical tests are developed and validated for better performance in various sampling scenarios.

Keywords:
complex samplingcomposite likelihoodfactor analysisgoodness‐of‐fit testspairwise likelihood

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Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Factor models are widely used for analyzing latent structures in data.
  • Traditional methods often struggle with binary outcomes and complex survey designs.
  • Pairwise likelihood estimation offers a flexible approach for such data.

Purpose of the Study:

  • To extend pairwise likelihood estimation for factor models with binary data to complex sampling.
  • To introduce and evaluate limited-information goodness-of-fit tests (Pearson chi-squared, Wald) for these models.
  • To improve the computational efficiency of these statistical tests.

Main Methods:

  • Pairwise likelihood estimation adapted for complex survey designs.
  • Development of modified Pearson chi-squared and Wald test statistics.
  • Simulation studies under simple random sampling and unequal probability sampling.

Main Results:

  • The proposed methods effectively handle factor models with binary data under complex sampling.
  • Modified test statistics show improved computational efficiency.
  • The estimation and tests perform well under different sampling schemes.

Conclusions:

  • Pairwise likelihood estimation and new goodness-of-fit tests are valuable tools for factor analysis of binary data, especially with complex survey data.
  • The enhanced methods offer practical advantages in statistical modeling and analysis.
  • The study validates the robustness of the proposed techniques across various sampling designs.