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Related Experiment Videos

Bootstrap-corrected ADF test statistics in covariance structure analysis

Y F Yung1, P M Bentler

  • 1Department of Psychology, University of California, Los Angeles 90024-1563.

The British Journal of Mathematical and Statistical Psychology
|May 1, 1994
PubMed
Summary
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The asymptotically distribution-free (ADF) test statistic for covariance structure analysis (CSA) performs poorly due to weight matrix estimation issues. Bootstrap corrections improve ADF test statistic accuracy, even with non-normal data.

Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • The asymptotically distribution-free (ADF) test statistic is crucial for covariance structure analysis (CSA).
  • Previous simulation studies indicated poor performance of the ADF test statistic, leading to incorrect model adequacy decisions in psychological research.
  • This poor performance was suspected to stem from issues in estimating the weight matrix (W = gamma -1).

Purpose of the Study:

  • To investigate the reasons behind the poor performance of the ADF test statistic in CSA.
  • To propose and evaluate bootstrap procedures for correcting the ADF test statistic.
  • To demonstrate the effectiveness of bias-corrected ADF test statistics in improving model adequacy decisions.

Main Methods:

  • The study analyzed the estimation of the weight matrix (W = gamma -1) in ADF theory.

Related Experiment Videos

  • Bootstrap procedures, specifically Hall's bias reduction perspective, were applied to correct the ADF test statistic.
  • Confirmatory factor-analytic models with 15 variables and 3 factors were used in simulations.

    • Main Results:

    • Inadequate estimation of the weight matrix was confirmed as the cause of the ADF test statistic's poor performance.
    • Bootstrap correction of additive bias significantly improved the ADF test statistic's tail behavior.
    • Desired tail behavior was achieved with a sample size of 500, even with non-multivariate normal distributions and dependent latent factors.

    Conclusions:

    • The proposed bootstrap correction method effectively addresses the performance issues of the ADF test statistic in CSA.
    • This correction enhances the reliability of decisions regarding the adequacy of psychological process models.
    • The findings support the revival and practical application of ADF theory in covariance structure analysis.