Click or drag to resize

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

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.3
Syntax
[SerializableAttribute]
public class 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.

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
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
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. Variance estimates will be unbiased.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType)
Constructs a
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
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 methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, Extraction)
Constructs a
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
Rotation
class type parameter constructed with no arguments. Variance estimates will be unbiased.
Protected methodDoubleFactorAnalysisExtraction, Rotation(BiasType, Extraction, Rotation)
Constructs a
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
Analyze
method on the resulting object.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType, Extraction)
Constructs a
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
Rotation
class type parameter constructed with no arguments.
Public methodDoubleFactorAnalysisExtraction, Rotation(DoubleSymmetricMatrix, BiasType, Extraction, Rotation)
Constructs a
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.
Top
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
Factors
property if
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.
Top
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
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
rotatedFactorMatrix_
field.
Public methodStatic memberStandardizeData
Computes the standardized data - means 0 and variances 1.
Top
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.
Top
Remarks
Use the class
NoRotation
if factor rotation is not desired. To perform factor analysis using the correlation matrix of case data use class
FactorAnalysisCorrelation
. To perform factor analysis using the covariance matrix of case data use class
FactorAnalysisCovariance
See Also