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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
public class FactorAnalysisCorrelation<Extraction, Rotation> : 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.
Remarks
Use the class
C#
NoRotation
if factor rotation is not desired.

The FactorAnalysisCorrelationExtraction, Rotation type exposes the following members.

Constructors
 NameDescription
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix) Constructs a
C#
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#
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. By default, unbiased estimates of the case data variable variance are used.
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, Extraction) Constructs a
C#
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#
Rotation
class type parameter constructed with no arguments. By default, unbiased estimates of the case data variable variance are used.
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType) Constructs a
C#
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#
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.
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType, Extraction) Constructs a
C#
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#
Rotation
class type parameter constructed with no arguments.
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType, Extraction, Rotation) Constructs a
C#
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
 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 propertyMeans Gets the vector of variable means. This is the column means of the case data being analyzed.
Public propertyNumberOfFactors The number of factors extracted.
(Inherited from DoubleFactorAnalysisExtraction, Rotation)
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.
(Inherited from DoubleFactorAnalysisExtraction, Rotation)
Public propertyRotatedSumOfSquaredLoadings Gets the sum of squared loadings for each rotated extracted factor.
(Inherited from DoubleFactorAnalysisExtraction, Rotation)
Public propertyStandardDeviations Gets the vector of variable standard deviations. This is the column standard deviations of the case data being analyzed.
Public propertyStandardizedCaseData Gets the case data standardized to have zero mean and unit variance.
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 Overrides the object Clone method.
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
C#
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
C#
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
C#
factorRotation_
field.
(Inherited from DoubleFactorAnalysisExtraction, Rotation)
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.
(Inherited from DoubleFactorAnalysisExtraction, Rotation)
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Fields
 NameDescription
Protected fieldbias_ The bias type for all variance estimates.
(Inherited from DoubleFactorAnalysisExtraction, Rotation)
Protected fieldcaseData_ The orginal data to be analyzed. Each row is a case and each column a variable.
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 fieldmeans_ Variable means. This the vector of column means of the case data.
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)
Protected fieldstandardDeviations_ Variable standard deviations. This is the vector of column standard deviations of the case data.
Protected fieldstandardizedCaseData_ 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.
See Also