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1 results

  • Tests for Linear Trend in the Smallest Eigenvalues of the Correlation Matrix

  • Peter M. Bentler, Ke-Hai Yuan
  • Journal:
    Psychometrika / Volume 63 / Issue 2 / June 1998
    Published online by Cambridge University Press:
    01 January 2025, pp. 131-144

  • A test for linear trend among a set of eigenvalues of a correlation matrix is developed. As a technical implementation of Cattell's scree test, this is a generalization of Anderson's test for the equality of eigenvalues, and extends Bentler and Yuan's work on linear trends in eigenvalues of a covariance matrix. The power of minimum x2 and maximum likelihood ratio tests are compared. Examples show that the linear trend hypothesis is more realistic than the standard hypothesis of equality of eigenvalues, and that the hypothesis is compatible with standard decisions on the number of factors or components to retain in data analysis.