FactorAnalysisCorrelationExtraction, Rotation Class

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

Inheritance Hierarchy

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

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

Syntax

C++

Copy

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

Public Class FactorAnalysisCorrelation(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 FactorAnalysisCorrelation : public DoubleFactorAnalysis<Extraction, Rotation>, 
	ICloneable

type FactorAnalysisCorrelation<'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 FactorAnalysisCorrelationExtraction, Rotation type exposes the following members.

Constructors

	Name	Description
	FactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix)	Constructs a C# Copy FactorAnalysisCorrelation object from the given case data by forming the correlation matrix for the variables, extracting the factors from the correlation matrix based on the correlation coefficients of 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. By default, unbiased estimates of the case data variable variance are used.
	FactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, Extraction)	Constructs a C# Copy FactorAnalysisCorrelation object from the given case data by forming the correlation matrix for the variables, extracting the factors from the correlation matrix based on the correlation coefficients of 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.
	FactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType)	Constructs a C# Copy FactorAnalysisCorrelation object from the given case data by forming the correlation matrix for the variables, extracting the factors from the correlation matrix based on the correlation coefficients of 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.
	FactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType, Extraction)	Constructs a C# Copy FactorAnalysisCorrelation object from the given case data by forming the correlation matrix for the variables, extracting the factors from the correlation matrix based on the correlation coefficients of 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.
	FactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType, Extraction, Rotation)	Constructs a C# Copy FactorAnalysisCorrelation object from the given case data by forming the correlation matrix for the variables, extracting the factors from the correlation matrix based on the correlation coefficients of 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)
	Means	Gets the vector of variable means. This is the column means of the case data being analyzed.
	NumberOfFactors	The number of factors extracted. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	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)
	RotatedSumOfSquaredLoadings	Gets the sum of squared loadings for each rotated extracted factor. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	StandardDeviations	Gets the vector of variable standard deviations. This is the column standard deviations of the case data being analyzed.
	StandardizedCaseData	Gets the case data standardized to have zero mean and unit variance.
	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	Overrides the object Clone method.
	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	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. (Inherited from DoubleFactorAnalysisExtraction, Rotation)

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Fields

	Name	Description
	bias_	The bias type for all variance estimates. (Inherited from DoubleFactorAnalysisExtraction, Rotation)
	caseData_	The orginal data to be analyzed. Each row is a case and each column a variable.
	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)
	means_	Variable means. This the vector of column means of the case data.
	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)
	standardDeviations_	Variable standard deviations. This is the vector of column standard deviations of the case data.
	standardizedCaseData_	The data normalized to have zero mean and unit variance.

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Remarks

The analysis consists of 3 steps: First, a correlation matrix is generated for all the variables. Second, factors are extracted from the correlation matrix based on the correlation coefficients of the 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