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On latent-variable model misspecification in structural measurement error models for binary response.

Xianzheng Huang1, Joshua M Tebbs

  • 1Department of Statistics, University of South Carolina, Columbia, South Carolina 29208, USA. huang@stat.sc.edu

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Summary
This summary is machine-generated.

Pooling binary responses in structural measurement error models enhances robustness to covariate errors and potential model misspecification. This approach can yield improved parameter estimators, even with information loss.

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Structural measurement error models are crucial for analyzing data with inaccuracies in measured variables.
  • Binary response data are common in health and social sciences, but measurement error poses challenges.
  • Latent-variable model misspecification can significantly impact the reliability of statistical estimates.

Purpose of the Study:

  • To evaluate the robustness of pooled binary responses in structural measurement error models against covariate measurement error and model misspecification.
  • To compare the performance of estimators from pooled versus individual binary responses.
  • To develop a novel diagnostic method for detecting latent-variable model misspecification in structural measurement error models.

Main Methods:

  • Development and application of structural measurement error models for binary outcomes.
  • Comparison of likelihood-based estimators using pooled versus individual binary responses.
  • Simulation studies to assess model performance under various conditions.
  • Application of methods to real-world data from the Framingham Heart Study.

Main Results:

  • Likelihood-based estimators from pooled binary responses demonstrate greater robustness to covariate measurement error when latent-variable models are misspecified.
  • Pooling binary responses can lead to improved parameter estimators in terms of mean-squared error, despite potential information loss.
  • A new diagnostic tool was developed to identify latent-variable model misspecification in structural measurement error models with individual binary responses.

Conclusions:

  • Pooling binary responses offers a more robust approach for structural measurement error models, particularly when dealing with covariate errors and potential model misspecification.
  • The developed diagnostic method aids in ensuring the validity of structural measurement error models.
  • Findings support the use of pooled binary responses for enhanced reliability in statistical analyses.