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Related Experiment Videos

Standard errors in covariance structure models: asymptotics versus bootstrap.

Ke-Hai Yuan1, Kentaro Hayashi

  • 1Department of Psychology, University of Notre Dame, IN 46556, USA. kyuan@nd.edu

The British Journal of Mathematical and Statistical Psychology
|October 28, 2006
PubMed
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Standard error (SE) estimates in covariance structure analysis can be inconsistent when models are misspecified. This study examines bootstrap SE estimates, finding them consistent and a reliable alternative to asymptotic methods for misspecified models.

Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Standard error (SE) estimates in covariance structure analysis rely on the assumption of a correctly specified model.
  • Real-world models are approximations, making model misspecification a common issue in practice.
  • Understanding the consistency of SE estimates under misspecification is crucial for reliable statistical inference.

Purpose of the Study:

  • To investigate the consistency of standard software-provided SE estimates when covariance structure models are misspecified.
  • To compare the performance of bootstrap-based SE estimates against traditional asymptotic methods under model misspecification.
  • To identify conditions under which bootstrap SE estimates remain consistent.

Main Methods:

  • Analysis of commonly used formulae for SE estimates in covariance structure analysis.

Related Experiment Videos

  • Application of bootstrap procedures to obtain nonparametric SE estimates.
  • Comparison of bootstrap SE estimates with asymptotic estimates using numerical examples.
  • Investigation of asymptotic variance-covariance matrices and their validity.

    • Main Results:

    • Standard asymptotic SE estimates may be inconsistent when covariance structure models are misspecified.
    • Bootstrap procedures offer nonparametric SE estimates that inherently account for distribution violations and model misspecification.
    • Conditions for the consistency of bootstrap SE estimates were identified and discussed.
    • Numerical examples demonstrated the relationships and validity of different SE and covariance matrix estimation methods.

    Conclusions:

    • Bootstrap estimates of standard errors are consistent and reliable even when covariance structure models are misspecified.
    • The findings highlight the robustness of bootstrap methods in the presence of model misspecification.
    • Researchers should consider bootstrap methods for more accurate SE estimation in practical covariance structure analysis.