DoubleFactorAnalysisExtraction, Rotation Class

Class

DoubleFactorAnalysis

performs a factor analysis on a symmetric matrix of data, assumed to be either a correlation or covariance matrix, using specified factor extraction and rotation algorithms. The analysis consists of 2 steps: First, factors are extracted from the symmetric matrix data, second, the factors are rotated in order to maximize the relationship between the variables and some of the factors.

Inheritance Hierarchy

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

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

Syntax

C++

Copy

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

<SerializableAttribute>
Public Class DoubleFactorAnalysis(Of Extraction As {New, IFactorExtraction}, Rotation As {New, IFactorRotation})
	Implements ICloneable

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

[<SerializableAttribute>]
type DoubleFactorAnalysis<'Extraction, 'Rotation when 'Extraction : new() and IFactorExtraction when 'Rotation : new() and IFactorRotation> = 
    class
        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.

The DoubleFactorAnalysisExtraction, Rotation type exposes the following members.

Constructors

	Name	Description
	DoubleFactorAnalysisExtraction, Rotation(DoubleFactorAnalysisExtraction, Rotation)	Copy constructor. Initializes self with the state of other.
	DoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix)	Constructs a C# Copy DoubleFactorAnalysis object from the given matrix data. Factors are extracted from the matrix of varaible relations (correlation or covariance) and then rotated 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. Variance estimates will be unbiased.
	DoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, Extraction)	Constructs a C# Copy DoubleFactorAnalysis object from the given matrix data. Factors are extracted from the matrix of varaible relations (correlation or covariance) and then rotated 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. Variance estimates will be unbiased.
	DoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType)	Constructs a C# Copy DoubleFactorAnalysis object from the given matrix data. Factors are extracted from the matrix of varaible relations (correlation or covariance) and then rotated 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.
	DoubleFactorAnalysisExtraction, Rotation(BiasType, Extraction, Rotation)	Constructs a C# Copy DoubleFactorAnalysis object with the given factor analysis options. No data is specified. The constructor is used by deriving classes to set up a factor analysis on a particular correlation or covaraince matrix. Construction is followed by a call to the C# Copy Analyze method on the resulting object.
	DoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType, Extraction)	Constructs a C# Copy DoubleFactorAnalysis object from the given matrix data. Factors are extracted from the matrix of varaible relations (correlation or covariance) and then rotated 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.
	DoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType, Extraction, Rotation)	Constructs a C# Copy DoubleFactorAnalysis object from the given matrix data. Factors are extracted from the matrix of varaible relations (correlation or covariance) and then rotated to maximize the relationship between the variables and some of the factors.

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Properties

	Name	Description
	CumulativeVarianceProportions	Gets the cumulative variance proportions.
	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.
	FactorExtraction	Gets the object that performs the factor extraction.
	FactorRotation	Gets the object that performs the factor rotation.
	Factors	Gets the extracted factors. Each column of the matrix is a factor.
	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.
	MatrixData	Gets the matrix data from which factors were extracted. This is either the correlation matrix of the covariance matrix.
	NumberOfFactors	The number of factors extracted.
	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.
	RotatedSumOfSquaredLoadings	Gets the sum of squared loadings for each rotated extracted factor.
	SumOfSquaredLoadings	Gets the sum of squared loadings for each extracted factor.
	VarianceProportions	Gets a vector of proportion of variance explained by each factor. The ith entry corresoponds to the ith factor.

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Methods

	Name	Description
	AdjustFactorSigns	Adjusts the signs of the factors according to the convention that the sum of all factor components should be non-negative. Implemented to match SPSS output.
	Analyze	Performs a factor analysis on the given symmetric covariance or correlation matrix for the data being analyzed.
	Clone	Returns a deep copy of self.
	ComputeCovarianceMatrix	Computes the covaraince matrix for the given data and bias type. The result is returned as a symmetric matrix object.
	Rotate	Performs factor rotation using the C# Copy factorRotation_ field.
	SortRotatedFactorsAndLoadings	Sorts the rotated factor and rotated sum of squared loadings matrices in order of descending variance of the rotated factors. Done mostly to match the output of SPSS. The result is stored in the C# Copy rotatedFactorMatrix_ field.
	StandardizeData	Computes the standardized data - means 0 and variances 1.

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Fields

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

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Remarks

Use the class

Copy

NoRotation

if factor rotation is not desired. To perform factor analysis using the correlation matrix of case data use class

Copy

FactorAnalysisCorrelation

. To perform factor analysis using the covariance matrix of case data use class

Copy

FactorAnalysisCovariance

Reference

CenterSpace.NMath.Core Namespace