Click or drag to resize

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: 7.3
Syntax
public class FactorAnalysisCorrelation<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 FactorAnalysisCorrelationExtraction, Rotation type exposes the following members.

Constructors
  NameDescription
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix)
Constructs a
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
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. By default, unbiased estimates of the case data variable variance are used.
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType)
Constructs a
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
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 methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, Extraction)
Constructs a
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
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, Extraction)
Constructs a
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
Rotation
class type parameter constructed with no arguments.
Public methodFactorAnalysisCorrelationExtraction, Rotation(DoubleMatrix, BiasType, Extraction, Rotation)
Constructs a
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.
Top
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
Factors
property if
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.)
Top
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
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
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.
(Inherited from DoubleFactorAnalysisExtraction, Rotation.)
Top
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.
Top
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