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 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()
Gets the rotated loading matrix.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 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:HypothesisTest
Get a description of the null hypothesis.- Specified by:
getNullHypothesis
in classHypothesisTest
- Returns:
- the null hypothesis description
- See Also:
- Wikipedia: Null hypothesis
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getAlternativeHypothesis
public String getAlternativeHypothesis()
Description copied from class:HypothesisTest
Get the description of the alternative hypothesis.- Specified by:
getAlternativeHypothesis
in 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:
statistics
in 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:
pValue
in classHypothesisTest
- Returns:
- the p-value
- See Also:
- Wikipedia: P-value
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