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Bootstrap scree tests: a Monte Carlo simulation and applications to published data.

Sungjin Hong1, Stephen K Mitchell, Richard A Harshman

  • 1University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA. hongsj@uiuc.edu

The British Journal of Mathematical and Statistical Psychology
|May 20, 2006
PubMed
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A new non-parametric bootstrap method for Cattell's scree test is introduced. This approach offers a robust alternative to parametric methods, especially for non-normal data in principal component analysis.

Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • Principal component analysis (PCA) often uses Cattell's scree test to determine the number of components.
  • Existing parametric tests for scree test eigenvalues have limitations when data violate parametric assumptions.
  • A need exists for robust, non-parametric methods to analyze scree test data.

Purpose of the Study:

  • To propose and evaluate a non-parametric bootstrap procedure for Cattell's scree test.
  • To compare the performance of the bootstrap method against parametric linear trend tests.
  • To assess the utility of bias-corrected bootstrap methods for scree test statistics.

Main Methods:

  • A non-parametric bootstrap procedure was developed for Cattell's scree test.

Related Experiment Videos

  • The break in the scree trend was defined using linear slopes based on consecutive or all post-k eigenvalues.
  • The bias-corrected and accelerated bootstrap method was also examined.
  • Performance was evaluated under various data conditions, including leptokurtic and skewed data.

    • Main Results:

    • Gorsuch and Nelson's bootstrap CNG method demonstrated the best performance, showing consistency and efficiency.
    • The proposed bootstrap method is suitable for situations where parametric assumptions are not met.
    • Bias correction using the bias-corrected and accelerated bootstrap method was found to be unstable and not useful.
    • Comparison with parametric linear trend tests on published datasets showed the bootstrap approach's viability.

    Conclusions:

    • The non-parametric bootstrap method provides a reliable alternative for Cattell's scree test, particularly with non-normal data.
    • The Gorsuch and Nelson bootstrap CNG is recommended for its robustness and efficiency.
    • Parametric assumptions are not always necessary for effective scree test analysis in PCA.