com.numericalmethod.suanshu.stats.factoranalysis

Class FAEstimator

java.lang.Object

com.numericalmethod.suanshu.stats.test.HypothesisTest

com.numericalmethod.suanshu.stats.factoranalysis.FAEstimator

All Implemented Interfaces:

java.io.Serializable

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

, Serialized Form

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Method Summary

Modifier and Type	Method and Description
int	dof() Get the degree of freedom in the factor analysis model.
java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
ImmutableMatrix	loadings() Get the rotated loading matrix.
double	logLikelihood() Get the log-likelihood value.
ImmutableVector	psi() Get the estimated (optimal) psi, E(ee'), p.
double	pValue() Calculate the p-value of the test statistics, given the degree of freedom.
ImmutableMatrix	scores() Get 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, 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()

Get the estimated (optimal) psi, E(ee'), p. 6.

Returns:

the psi vector

loadings

public ImmutableMatrix loadings()

Get the rotated loading matrix.

Returns:

the rotated matrix of loadings

dof

public int dof()

Get the degree of freedom in the factor analysis model.

Returns:

the degree of freedom

logLikelihood

public double logLikelihood()

Get the log-likelihood value.

Returns:

the log-likelihood

scores

public ImmutableMatrix scores()

Get 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 java.lang.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

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public java.lang.String getAlternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

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.

Overrides:

statistics in class HypothesisTest

Returns:

the test statistics

See Also:

Wikipedia: Test statistic

pValue

public double pValue()

Calculate the p-value of the test statistics, given the degree of freedom.

Overrides:

pValue in class HypothesisTest

Returns:

the p-value

See Also:

Wikipedia: P-value