# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.factor.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 Summary

All Methods
Modifier and Type Method and Description
int dof()
Gets the degree of freedom in the factor analysis model.
String getAlternativeHypothesis()
Get the description of the alternative hypothesis.
String getNullHypothesis()
Get a description of the null hypothesis.
ImmutableMatrix loadings()
double logLikelihood()
Gets the log-likelihood value.
ImmutableVector psi()
Gets the estimated (optimal) psi, E(ee'), p.
double pValue()
Calculates the p-value of the test statistics, given the degree of freedom.
ImmutableMatrix scores()
Gets the matrix of scores, computed using either Thompson's (1951) scores, or Bartlett's (1937) weighted least-squares scores.
double statistics()
Get the test statistics of the factor analysis.
• ### Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, nGroups, nObs, oneSidedPvalue
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Method Detail

• #### psi

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

public ImmutableMatrix loadings()
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
• #### getNullHypothesis

public String getNullHypothesis()
Description copied from class: HypothesisTest
Get a description of the null hypothesis.
Specified by:
getNullHypothesis in class HypothesisTest
Returns:
the null hypothesis description
Wikipedia: Null hypothesis
• #### getAlternativeHypothesis

public String getAlternativeHypothesis()
Description copied from class: HypothesisTest
Get the description of the alternative hypothesis.
Specified by:
getAlternativeHypothesis in class HypothesisTest
Returns:
the alternative hypothesis description
Wikipedia: Alternative hypothesis
• #### 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
public double pValue()
pValue in class HypothesisTest