Class FAEstimator
- java.lang.Object
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- dev.nm.stat.test.HypothesisTest
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- dev.nm.stat.factor.factoranalysis.FAEstimator
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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
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description intdof()Gets the degree of freedom in the factor analysis model.StringgetAlternativeHypothesis()Get the description of the alternative hypothesis.StringgetNullHypothesis()Get a description of the null hypothesis.ImmutableMatrixloadings()Gets the rotated loading matrix.doublelogLikelihood()Gets the log-likelihood value.ImmutableVectorpsi()Gets the estimated (optimal) psi, E(ee'), p.doublepValue()Calculates the p-value of the test statistics, given the degree of freedom.ImmutableMatrixscores()Gets the matrix of scores, computed using either Thompson's (1951) scores, or Bartlett's (1937) weighted least-squares scores.doublestatistics()Get the test statistics of the factor analysis.-
Methods inherited from class dev.nm.stat.test.HypothesisTest
isNullRejected, nGroups, nObs, oneSidedPvalue
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Method Detail
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psi
public ImmutableVector psi()
Gets the estimated (optimal) psi, E(ee'), p. 6.- Returns:
- the psi vector
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loadings
public ImmutableMatrix loadings()
Gets the rotated loading matrix.- Returns:
- the rotated matrix of loadings
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dof
public int dof()
Gets the degree of freedom in the factor analysis model.- Returns:
- the degree of freedom
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logLikelihood
public double logLikelihood()
Gets the log-likelihood value.- Returns:
- the log-likelihood
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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
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getNullHypothesis
public String getNullHypothesis()
Description copied from class:HypothesisTestGet a description of the null hypothesis.- Specified by:
getNullHypothesisin classHypothesisTest- Returns:
- the null hypothesis description
- See Also:
- Wikipedia: Null hypothesis
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getAlternativeHypothesis
public String getAlternativeHypothesis()
Description copied from class:HypothesisTestGet the description of the alternative hypothesis.- Specified by:
getAlternativeHypothesisin classHypothesisTest- Returns:
- the alternative hypothesis description
- See Also:
- Wikipedia: Alternative hypothesis
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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:
statisticsin classHypothesisTest- Returns:
- the test statistics
- See Also:
- Wikipedia: Test statistic
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pValue
public double pValue()
Calculates the p-value of the test statistics, given the degree of freedom.- Specified by:
pValuein classHypothesisTest- Returns:
- the p-value
- See Also:
- Wikipedia: P-value
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