Class FAEstimator


  • public class FAEstimator
    extends HypothesisTest
    These are the estimators (estimated psi, loading matrix, scores, degrees of freedom, test statistics, p-value, etc.) from the factor analysis MLE optimization.
    See Also:
    • M. S. Bartlett, "The Statistical Conception of Mental Factors," The British Journal of Psychology, vol. 28, 97-104, 1937.
    • M. S. Bartlett, "A Note on Multiplying Factors for Various Chi-Squared Approximations," Journal of the Royal Statistical Society, Series B, vol. 16, 296-298, 1954.
    • D. N. Lawley and A. E. Maxwell, "Factor Analysis as a Statistical Method," Second Edition, Butterworths, 1971.
    • G. H. Thomson, "The Factorial Analysis of Human Ability," London University Press, 1951.
    • Wikipedia: Factor analysis
    • Method Detail

      • psi

        public ImmutableVector psi()
        Gets the estimated (optimal) psi, E(ee'), p. 6.
        Returns:
        the psi vector
      • loadings

        public ImmutableMatrix loadings()
        Gets the rotated loading matrix.
        Returns:
        the rotated matrix of loadings
      • dof

        public int dof()
        Gets the degree of freedom in the factor analysis model.
        Returns:
        the degree of freedom
      • logLikelihood

        public double logLikelihood()
        Gets the log-likelihood value.
        Returns:
        the log-likelihood
      • scores

        public ImmutableMatrix scores()
        Gets the matrix of scores, computed using either Thompson's (1951) scores, or Bartlett's (1937) weighted least-squares scores.
        Returns:
        the matrix of scores
      • statistics

        public double statistics()
        Get the test statistics of the factor analysis. Bartlett (1954) has shown that the chi-squared approximation to the distribution can be improved by using a multiplying factor of (N - 1) - (2p + 4k + 5) / 6, which is the same multiplying factor used here and often used in empirical studies. N.B. the same multiplying factor is used in Bartlett's test of sphericity.
        Specified by:
        statistics in class HypothesisTest
        Returns:
        the test statistics
        See Also:
        Wikipedia: Test statistic
      • pValue

        public double pValue()
        Calculates the p-value of the test statistics, given the degree of freedom.
        Specified by:
        pValue in class HypothesisTest
        Returns:
        the p-value
        See Also:
        Wikipedia: P-value