# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.factoranalysis

## 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.
• 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

Returns:
• #### 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