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DoubleFactorAnalysisExtraction, Rotation Class

Class
C#
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

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4
Syntax
[SerializableAttribute]
public class DoubleFactorAnalysis<Extraction, Rotation> : ICloneable
where Extraction : new(), IFactorExtraction
where Rotation : new(), IFactorRotation

Type Parameters

Extraction
Type implementing the
C#
IFactorExtraction
interface which extracts the factors.
Rotation
Type implementing the
C#
IFactorRotation
interface for factor rotation.

The DoubleFactorAnalysisExtraction, Rotation type exposes the following members.

Constructors
 NameDescription
Protected methodDoubleFactorAnalysisExtraction, Rotation(DoubleFactorAnalysisExtraction, Rotation) Copy constructor. Initializes self with the state of other.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix) Constructs a
C#
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#
Extraction
class type parameter constructed with no arguments, and factor rotation will be performed by an instance of the
C#
Rotation
class type parameter constructed with no arguments. Variance estimates will be unbiased.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, Extraction) Constructs a
C#
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#
Rotation
class type parameter constructed with no arguments. Variance estimates will be unbiased.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType) Constructs a
C#
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#
Extraction
class type parameter constructed with no arguments, and factor rotation will be performed by an instance of the
C#
Rotation
class type parameter constructed with no arguments.
Protected methodDoubleFactorAnalysisExtraction, Rotation(BiasType, Extraction, Rotation) Constructs a
C#
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#
Analyze
method on the resulting object.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType, Extraction) Constructs a
C#
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#
Rotation
class type parameter constructed with no arguments.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType, Extraction, Rotation) Constructs a
C#
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
 NameDescription
Public propertyCumulativeVarianceProportions Gets the cumulative variance proportions.
Public propertyExtractedCommunalities 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.
Public propertyFactorExtraction Gets the object that performs the factor extraction.
Public propertyFactorRotation Gets the object that performs the factor rotation.
Public propertyFactors Gets the extracted factors. Each column of the matrix is a factor.
Public propertyInitialCommunalities 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.
Public propertyMatrixData Gets the matrix data from which factors were extracted. This is either the correlation matrix of the covariance matrix.
Public propertyNumberOfFactors The number of factors extracted.
Public propertyRotatedFactors Gets the rotated factors (will be the same as
C#
Factors
property if
C#
NoRotation
is the rotation class parameter type). Each column of the matrix is a factor.
Public propertyRotatedSumOfSquaredLoadings Gets the sum of squared loadings for each rotated extracted factor.
Public propertySumOfSquaredLoadings Gets the sum of squared loadings for each extracted factor.
Public propertyVarianceProportions Gets a vector of proportion of variance explained by each factor. The ith entry corresoponds to the ith factor.
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Methods
 NameDescription
Public methodStatic memberAdjustFactorSigns 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.
Public methodAnalyze Performs a factor analysis on the given symmetric covariance or correlation matrix for the data being analyzed.
Public methodClone Returns a deep copy of self.
Public methodStatic memberComputeCovarianceMatrix Computes the covaraince matrix for the given data and bias type. The result is returned as a symmetric matrix object.
Protected methodRotate Performs factor rotation using the
C#
factorRotation_
field.
Protected methodSortRotatedFactorsAndLoadings 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#
rotatedFactorMatrix_
field.
Public methodStatic memberStandardizeData Computes the standardized data - means 0 and variances 1.
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Fields
 NameDescription
Protected fieldbias_ The bias type for all variance estimates.
Protected fieldfactorExtraction_ Factor extraction algorithm.
Protected fieldfactorMatrix_ The extracted factors.
Protected fieldfactorRotation_ Factor rotation algorithm.
Protected fieldmatrixData_ Matrix data being analyzed (correlation or covariance).
Protected fieldnoRotation_ Boolean variable indicating whether or not factor rotation was requested.
Protected fieldnumberOfFactors_ Number of factors to be extracted.
Protected fieldrotatedFactorMatrix_ The rotated factors.
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Remarks
Use the class
C#
NoRotation
if factor rotation is not desired. To perform factor analysis using the correlation matrix of case data use class
C#
FactorAnalysisCorrelation
. To perform factor analysis using the covariance matrix of case data use class
C#
FactorAnalysisCovariance
See Also