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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: 7.3
Syntax
public class FactorAnalysisCovariance<Extraction, Rotation> : DoubleFactorAnalysis<Extraction, Rotation>, 
	ICloneable
where Extraction : new(), IFactorExtraction
where Rotation : new(), IFactorRotation

Type Parameters

Extraction
Type implementing the
IFactorExtraction
interface which extracts the factors.
Rotation
Type implementing the
IFactorRotation
interface for factor rotation.
Remarks
Use the class
NoRotation
if factor rotation is not desired.

The FactorAnalysisCovarianceExtraction, Rotation type exposes the following members.

Constructors
  NameDescription
Public methodFactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix)
Constructs a
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
Rotation
class type parameter constructed with no arguments. By default, unbiased estimates of the case data variable variance are used.
Public methodFactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, BiasType)
Constructs a
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
Extraction
class type parameter constructed with no arguments, and factor rotation will be performed by an instance of the
Rotation
class type parameter constructed with no arguments.
Public methodFactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, Extraction)
Constructs a
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
Rotation
class type parameter constructed with no arguments. By default, unbiased estimates of the case data variable variance are used.
Public methodFactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, BiasType, Extraction)
Constructs a
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
Rotation
class type parameter constructed with no arguments.
Public methodFactorAnalysisCovarianceExtraction, Rotation(DoubleMatrix, BiasType, Extraction, Rotation)
Constructs a
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
  NameDescription
Public propertyCaseData
Gets the case data being analyzed.
Public propertyCumulativeVarianceProportions
Gets the cumulative variance proportions.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
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.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyFactorExtraction
Gets the object that performs the factor extraction.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyFactorRotation
Gets the object that performs the factor rotation.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyFactors
Gets the extracted factors. Each column of the matrix is a factor.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
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.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyMatrixData
Gets the matrix data from which factors were extracted. This is either the correlation matrix of the covariance matrix.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyNumberOfFactors
The number of factors extracted.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyRescaledExtractedCommunalities
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.
Public propertyRescaledFactors
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.
Public propertyRescaledRotatedSumOfSquaredLoadings
Gets the sum of squared loadings for each rescaled rotated extracted factor.
Public propertyRescaledSumOfSquaredLoadings
Gets the sum of squared loadings for each rescaled extracted factor.
Public propertyRotatedFactors
Gets the rotated factors (will be the same as
Factors
property if
NoRotation
is the rotation class parameter type). Each column of the matrix is a factor.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyRotatedRescaledFactors
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.
Public propertyRotatedSumOfSquaredLoadings
Gets the sum of squared loadings for each rotated extracted factor.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertySumOfSquaredLoadings
Gets the sum of squared loadings for each extracted factor.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public propertyVarianceProportions
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
  NameDescription
Public methodAnalyze
Performs a factor analysis on the given symmetric covariance or correlation matrix for the data being analyzed.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Public methodClone
Returns a deep copy of self.
Public methodFactorScoreCoefficients
Gets the coefficients by which the variables are multiplied to obtain factor scores. The coefficients are computed using an instance of the class
RegressionFactorScores
.
Public methodFactorScoreCoefficients(IFactorScores)
Gets the coefficients by which the variables are multiplied to obtain factor scores.
Public methodFactorScores
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
RegressionFactorScores
Public methodFactorScores(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.
Protected methodRotate
Performs factor rotation using the
factorRotation_
field.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected methodSortRotatedFactorsAndLoadings
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
  NameDescription
Protected fieldbias_
The bias type for all variance estimates.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldfactorExtraction_
Factor extraction algorithm.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldfactorMatrix_
The extracted factors.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldfactorRotation_
Factor rotation algorithm.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldmatrixData_
Matrix data being analyzed (correlation or covariance).
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldnoRotation_
Boolean variable indicating whether or not factor rotation was requested.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldnumberOfFactors_
Number of factors to be extracted.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Protected fieldrotatedFactorMatrix_
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.
See Also