com.numericalmethod.suanshu.stats.factoranalysis

Class FactorAnalysis

java.lang.Object

com.numericalmethod.suanshu.stats.factoranalysis.FactorAnalysis

All Implemented Interfaces:

java.io.Serializable

public class FactorAnalysis
extends java.lang.Object
implements java.io.Serializable

Factor analysis is a statistical method used to describe variability among observed variables in terms of a potentially lower number of unobserved variables called factors. Factor analysis searches for joint variations in response to unobserved latent variables. The observed variables are modeled as linear combinations of the potential factors, plus "error" terms. The information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Although factor analysis and principal component analysis (PCA) are both dimension reduction techniques, those two are not identical. Because PCA performs a variance-maximizing rotation of the variable space, it takes into account all variability in the variables. In contrast, factor analysis estimates how much of the variability is due to common factors. The two methods become essentially equivalent if the error terms in the factor analysis model can be assumed to all have the same variance.

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.
• K. G. Jöreskog, "Statistical Estimation in Factor Analysis: A New Technique and Its Foundation," Almqvist and Wicksell, 1963.
• 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

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	FactorAnalysis.ScoringRule These are the different ways to compute the factor analysis scores.

Constructor Summary

Constructors

Constructor and Description
FactorAnalysis(Matrix data, int nFactors) Perform factor analysis on the data set, using Bartlett's weighted least-squares scores, and sample correlation matrix.
FactorAnalysis(Matrix data, int nFactors, FactorAnalysis.ScoringRule rule) Perform factor analysis on the data set with a user defined scoring rule.
FactorAnalysis(Matrix data, int nFactors, FactorAnalysis.ScoringRule rule, Matrix S) Perform factor analysis on the data set with a user defined scoring rule and a user defined covariance (or correlation) matrix.

Method Summary

Modifier and Type	Method and Description
FAEstimator	getEstimators(int maxIterations) Get the estimators (estimated psi, loading matrix, degree of freedom, test statistics, p-value, etc) obtained from the factor analysis, given the maximum number of iterations.
FAEstimator	getEstimators(Vector initial, int maxIterations) Get the estimators (estimated psi, loading matrix, degree of freedom, test statistics, p-value, etc) obtained from the factor analysis, given the initial psi and the maximum number of iterations.
int	nFactors() Get the number of factors.
int	nObs() Get the number of observations.
int	nVariables() Get the number of variables in the original data set.
ImmutableMatrix	S() Get the covariance (or correlation) matrix.
FactorAnalysis.ScoringRule	scoringRule() Get the scoring rule.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FactorAnalysis

public FactorAnalysis(Matrix data,
                      int nFactors,
                      FactorAnalysis.ScoringRule rule,
                      Matrix S)

Perform factor analysis on the data set with a user defined scoring rule and a user defined covariance (or correlation) matrix.

Parameters:

data - the data set

nFactors - the number of factors

rule - the scoring rule

S - a covariance (or correlation) matrix, usually taken to be the covariance (or correlation) matrix of the data set. Using a correlation matrix amounts to scaling the original data set.

FactorAnalysis

public FactorAnalysis(Matrix data,
                      int nFactors,
                      FactorAnalysis.ScoringRule rule)

Perform factor analysis on the data set with a user defined scoring rule.

Parameters:

data - the data set

nFactors - the number of factors

rule - the scoring rule

FactorAnalysis

public FactorAnalysis(Matrix data,
                      int nFactors)

Perform factor analysis on the data set, using Bartlett's weighted least-squares scores, and sample correlation matrix.

Parameters:

data - the data set

nFactors - the number of factors

Method Detail

S

public ImmutableMatrix S()

Get the covariance (or correlation) matrix.

Returns:

the covariance (or correlation) matrix

nObs

public int nObs()

Get the number of observations.

Returns:

the number of observations

nVariables

public int nVariables()

Get the number of variables in the original data set.

Returns:

the number of variables in the original data set

nFactors

public int nFactors()

Get the number of factors.

Returns:

the number of factors

scoringRule

public FactorAnalysis.ScoringRule scoringRule()

Get the scoring rule.

Returns:

the scoring rule

getEstimators

public FAEstimator getEstimators(int maxIterations)

Get the estimators (estimated psi, loading matrix, degree of freedom, test statistics, p-value, etc) obtained from the factor analysis, given the maximum number of iterations.

Parameters:

maxIterations - the maximum number of iterations

Returns:

the estimators from the factor analysis

getEstimators

public FAEstimator getEstimators(Vector initial,
                                 int maxIterations)

Get the estimators (estimated psi, loading matrix, degree of freedom, test statistics, p-value, etc) obtained from the factor analysis, given the initial psi and the maximum number of iterations.

Parameters:

initial - the initial values of psi

maxIterations - the maximum number of iterations

Returns:

the estimators from the factor analysis