FactorAnalysisCovarianceExtraction, Rotation Class

Class FactorAnalysisCovariance performs a factor analysis on a set of case data using the covariance matrix and specified factor extraction and rotation algorithms.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreDoubleFactorAnalysisExtraction, Rotation
CenterSpace.NMath.CoreFactorAnalysisCovarianceExtraction, Rotation

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4

Syntax

C++

Copy

public class FactorAnalysisCovariance<Extraction, Rotation> : DoubleFactorAnalysis<Extraction, Rotation>, 
	ICloneable
where Extraction : new(), IFactorExtraction
where Rotation : new(), IFactorRotation

Public Class FactorAnalysisCovariance(Of Extraction As {New, IFactorExtraction}, Rotation As {New, IFactorRotation})
	Inherits DoubleFactorAnalysis(Of Extraction, Rotation)
	Implements ICloneable

generic<typename Extraction, typename Rotation>
where Extraction : gcnew(), IFactorExtraction
where Rotation : gcnew(), IFactorRotation
public ref class FactorAnalysisCovariance : public DoubleFactorAnalysis<Extraction, Rotation>, 
	ICloneable

type FactorAnalysisCovariance<'Extraction, 'Rotation when 'Extraction : new() and IFactorExtraction when 'Rotation : new() and IFactorRotation> = 
    class
        inherit DoubleFactorAnalysis<'Extraction, 'Rotation>
        interface ICloneable
    end

Type Parameters

Extraction

Type implementing the

Copy

IFactorExtraction

interface which extracts the factors.

Rotation

Type implementing the

Copy

IFactorRotation

interface for factor rotation.

Remarks

Use the class

Copy

NoRotation

if factor rotation is not desired.

The FactorAnalysisCovarianceExtraction, Rotation type exposes the following members.

Constructors

	Name	Description
	FactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix)	Constructs a C# Copy FactorAnalysisCovariance object from the given case data by forming the covariance matrix for the variables, extracting the factors from the covariance matrix based on the covariance between the variables and rotating the factors to maximize the relationship between the variables and some of the factors. Factor rotation will be performed by an instance of the C# Copy Rotation class type parameter constructed with no arguments. By default, unbiased estimates of the case data variable variance are used.
	FactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, Extraction)	Constructs a C# Copy FactorAnalysisCovariance object from the given case data by forming the covariance matrix for the variables, extracting the factors from the covariance matrix based on the covariance between the variables and rotating the factors to maximize the relationship between the variables and some of the factors. Factor rotation will be performed by an instance of the C# Copy Rotation class type parameter constructed with no arguments. By default, unbiased estimates of the case data variable variance are used.
	FactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, BiasType)	Constructs a C# Copy FactorAnalysisCovariance object from the given case data by forming the covariance matrix for the variables, extracting the factors from the covariance matrix based on the covariance between the variables and rotating the factors to maximize the relationship between the variables and some of the factors. Factor extraction will be performed by an instance of the C# Copy Extraction class type parameter constructed with no arguments, and factor rotation will be performed by an instance of the C# Copy Rotation class type parameter constructed with no arguments.
	FactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, BiasType, Extraction)	Constructs a C# Copy FactorAnalysisCovariance object from the given case data by forming the covariance matrix for the variables, extracting the factors from the covariance matrix based on the covariance the variables and rotating the factors to maximize the relationship between the variables and some of the factors. Factor rotation will be performed by an instance of the C# Copy Rotation class type parameter constructed with no arguments.
	FactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, BiasType, Extraction, Rotation)	Constructs a C# Copy FactorAnalysisCovariance object from the given case data by forming the covariance matrix for the variables, extracting the factors from the covariance matrix based on the covariance between the variables and rotating the factors to maximize the relationship between the variables and some of the factors.

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Properties

	Name	Description
	CaseData	Gets the case data being analyzed.
	CumulativeVarianceProportions	Gets the cumulative variance proportions. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	ExtractedCommunalities	This is the proportion of each variable's variance that can be explained by the extracted factors jointly. The ith entry corresponds to the ith variable. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	FactorExtraction	Gets the object that performs the factor extraction. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	FactorRotation	Gets the object that performs the factor rotation. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	Factors	Gets the extracted factors. Each column of the matrix is a factor. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	InitialCommunalities	This is the proportion of each variable's variance that can be explained by the factors jointly. The ith entry corresponds to the ith variable. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	MatrixData	Gets the matrix data from which factors were extracted. This is either the correlation matrix of the covariance matrix. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	NumberOfFactors	The number of factors extracted. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	RescaledExtractedCommunalities	This is the proportion of each variable's variance that can be explained by the extracted rescaled factors jointly. The ith entry corresponds to the ith variable.
	RescaledFactors	Gets the matrix of extracted factors which have been scaled by dividing by the standard deviation of the case data variables. Explicitly - The ith rescaled factor is the ith factor scaled by dividing each factor component by the standard deviation of the ith column of the case data being analyzed.
	RescaledRotatedSumOfSquaredLoadings	Gets the sum of squared loadings for each rescaled rotated extracted factor.
	RescaledSumOfSquaredLoadings	Gets the sum of squared loadings for each rescaled extracted factor.
	RotatedFactors	Gets the rotated factors (will be the same as C# Copy Factors property if C# Copy NoRotation is the rotation class parameter type). Each column of the matrix is a factor. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	RotatedRescaledFactors	Gets the matrix of rotated factors which have been scaled by dividing by the standard deviation of the case data variables. Explicitly - The ith rescaled rotated factor is the ith rotated factor scaled by dividing each factor component by the standard deviation of the ith column of the case data being analyzed.
	RotatedSumOfSquaredLoadings	Gets the sum of squared loadings for each rotated extracted factor. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	SumOfSquaredLoadings	Gets the sum of squared loadings for each extracted factor. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	VarianceProportions	Gets a vector of proportion of variance explained by each factor. The ith entry corresoponds to the ith factor. (Inherited from DoubleFactorAnalysisExtraction, Rotation)

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Methods

	Name	Description
	Analyze	Performs a factor analysis on the given symmetric covariance or correlation matrix for the data being analyzed. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	Clone	Returns a deep copy of self.
	FactorScoreCoefficients	Gets the coefficients by which the variables are multiplied to obtain factor scores. The coefficients are computed using an instance of the class C# Copy RegressionFactorScores .
	FactorScoreCoefficients(IFactorScores)	Gets the coefficients by which the variables are multiplied to obtain factor scores.
	FactorScores	Gets the matrix of factor scores. The score for a given factor is a linear combination of all of the measures, weighted by the corresponding factor loading. The scores are computed using an instance of the class C# Copy RegressionFactorScores
	FactorScores(IFactorScores)	Gets the matrix of factor scores using the provided algorithm to compute them. The score for a given factor is a linear combination of all of the measures, weighted by the corresponding factor loading.
	Rotate	Performs factor rotation using the C# Copy factorRotation_ field. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	SortRotatedFactorsAndLoadings	Rotated raw rotated factors and raw sum of squared loadings are sorted by the variable variances of the scaled rotated factors. (Overrides DoubleFactorAnalysisExtraction, RotationSortRotatedFactorsAndLoadings(DoubleMatrix))

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Fields

	Name	Description
	bias_	The bias type for all variance estimates. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	factorExtraction_	Factor extraction algorithm. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	factorMatrix_	The extracted factors. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	factorRotation_	Factor rotation algorithm. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	matrixData_	Matrix data being analyzed (correlation or covariance). (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	noRotation_	Boolean variable indicating whether or not factor rotation was requested. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	numberOfFactors_	Number of factors to be extracted. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	rotatedFactorMatrix_	The rotated factors. (Inherited from DoubleFactorAnalysisExtraction, Rotation)

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Remarks

The analysis consists of 3 steps: First, a covariance matrix is generated for all the variables. Second, factors are extracted from the covariance matrix based on the covariance between variables. Third, the factors are rotated in order to maximize the relationship between the variables and some of the factors.

Reference

CenterSpace.NMath.Core Namespace