public class FactorAnalysis : TransformationModel

Public Class FactorAnalysis
	Inherits TransformationModel

public ref class FactorAnalysis : public TransformationModel

type FactorAnalysis =  
    class
        inherit TransformationModel
    end

The FactorAnalysis type exposes the following members.

	Name	Description
	FactorAnalysis(MatrixDouble)	Constructs a new factor analysis object.
	FactorAnalysis(Matrix)	Constructs a new factor analysis object.
	FactorAnalysis(NumericalVariable)	Constructs a new factor analysis object.
	FactorAnalysis(VectorDouble)	Constructs a new factor analysis object.
	FactorAnalysis(DataTable, String)	Constructs a new factor analysis object.
	FactorAnalysis(IDataFrame, String)	Constructs a new FactorAnalysis.
	FactorAnalysis(IDataFrame, String)	Constructs a new FactorAnalysis.
	FactorAnalysis(SymmetricMatrixDouble, FactorMethod)	Constructs a new factor analysis object.
	FactorAnalysis(SymmetricMatrix, FactorMethod)	Constructs a new factor analysis object.
	FactorAnalysis(VariableCollection, String)	Constructs a new FactorAnalysis.

	Name	Description
	BaseFeatureIndex	Gets an index containing the keys of the columns that are required inputs to the model. (Inherited from Model.)
	Communalities	Gets a vector containing the proportion of the common variance of each variable associated with the factors.
	Computed	Gets whether the regression model has been computed. (Inherited from Model.)
	CumulativeVarianceExplained	Gets a vector containing the variance explained by each factor.
	Data	Gets an object that contains all the data used as input to the model. (Inherited from Model.)
	DependentVariables	Gets the collection of dependent variables associated with this model. (Inherited from Model.)
	Eigenvalues	Gets a vector containing the eigenvalues corresponding to the factors.
	ExtractionMethod	Gets or sets the method for extracting factors.
	ExtractionPhaseMaxIterations	Gets or sets the maximum number of iterations allowed for factor extraction.
	ExtractionPhaseTolerance	Gets or sets the difference in successive approximations of the communalities that signals convergence when extracting the factors.
	FactorCorrelationMatrix	Gets a matrix that contains the correlations between the factors.
	FactorCountMethod	Gets or sets a value that specifies how the number of factors is determined.
	FactorScoreCoefficientMatrix	Gets the matrix of factor score coefficients.
	FactorScoreMethod	Gets or sets the method for computing factor score coefficients.
	FactorThreshold	Gets or sets the threshold value for automatically determining the number of factors to be extracted.
	FactorTransformationMatrix	Gets the matrix that transforms the original factors to the rotated factors.
	Features	Gets a matrix that contains the features. (Inherited from TransformationModel.)
	IndependentVariables	Gets the collection of independent variables associated with this model. (Inherited from Model.)
	InitialCommunalities	Gets a vector containing the initial values of the communalities.
	InputSchema	Gets the schema for the features used for fitting the model. (Inherited from Model.)
	IsObliqueRotation	Gets whether the factor rotation is oblique.
	IsOrthogonalRotation	Gets whether the factor rotation is orthogonal.
	LoadingsMatrix	Gets the matrix of unrotated factor loadings.
	MaxDegreeOfParallelism	Gets or sets the maximum degree of parallelism enabled by this instance. (Inherited from Model.)
	Method	Gets or sets whether the factor analysis is based on a correlation matrix or a covariance matrix.
	ModelSchema	Gets the collection of variables used in the model. (Inherited from Model.)
	ModelSubset	Returns an array of indexes of final model features in the set of input features. (Inherited from Model.)
	NumberOfFactors	Gets or sets the number of factors to be extracted.
	NumberOfObservations	Gets the number of observations the model is based on. (Inherited from MultivariateModel.)
	ParallelOptions	Gets or sets an object that specifies how the calculation of the model should be parallelized. (Inherited from Model.)
	PatternMatrix	Gets the matrix of contributions of each factor to the variance of each variable.
	PromaxPower	Gets or sets the exponent used in promax rotation.
	RotatedLoadingsMatrix	Gets the matrix of rotated factor loadings, the correlations between factors and variables after rotation.
	RotationMethod	Gets or sets the method for rotating factors.
	RotationPhaseMaxIterations	Gets or sets the maximum number of iterations allowed for factor rotation.
	RotationPhaseTolerance	Gets or sets the threshold value of the convergence measure for factor rotations.
	Standardize	Gets or sets whether the variables should be standardized before the clustering is computed.
	Status	Gets the status of the model, which determines which information is available. (Inherited from Model.)
	StructureMatrix	Gets the matrix of the correlations between factors and variables.
	SupportsWeights	Indicates whether the model supports case weights. (Inherited from Model.)
	Uniqueness	Gets a vector containing the proportion of the common variance of each variable not associated with the factors.
	VarianceExplained	Gets a vector containing the variance explained by each factor.
	Weights	Gets or sets the actual weights. (Inherited from Model.)

	Name	Description
	Compute	Computes the model. (Inherited from Model.)
	Compute(ParallelOptions)	Computes the model. (Inherited from Model.)
	ComputeModel	Computes the model. (Inherited from Model.)
	ComputeModel(ParallelOptions)	Computes the factor analysis. (Overrides ModelComputeModel(ParallelOptions).)
	ComputeModel(ModelInput, ParallelOptions)	Computes the factor analysis. (Overrides ModelComputeModel(ModelInput, ParallelOptions).)
	Contains	Returns whether another UnivariateModel is nested within this instance. (Inherited from Model.)
	Equals	Determines whether the specified Object is equal to the current Object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	Fit	Fits the model to the data. (Inherited from Model.)
	Fit(ParallelOptions)	Fits the model to the data. (Inherited from Model.)
	FitCore	Computes the model to the specified input using the specified parallelization options. (Inherited from Model.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetRotatedFactors	Gets a read-only collection of the factors after rotation.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	GetUnrotatedFactors	Gets a read-only collection of the factors before rotation.
	InverseTransform	Applies the inverse transformation to a set of observations. (Overrides TransformationModelInverseTransform(MatrixDouble).)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ResetComputation	Clears all computed model parameters. (Inherited from Model.)
	SetDataSource	Uses the specified data frame as the source for all input variables. (Inherited from Model.)
	Summarize	Returns a string containing a human-readable summary of the object using default options. (Inherited from Model.)
	Summarize(SummaryOptions)	Returns a string containing a human-readable summary of the object using the specified options. (Inherited from Model.)
	ToString	Returns a string that represents the current object. (Inherited from Model.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	Transform	Applies the transformation to a set of observations. (Overrides TransformationModelTransform(MatrixDouble).)

Use the FactorAnalysis class to perform a factor analysis on a set of variables or directly on a correlation matrix or a covariance matrix.

The number of factors can be set in advance, or may be determined automatically based on the eigenvalues of the correlation matrix.

The ExtractionMethod property determines the algorithm for determining the factors. It is of type FactorExtractionMethod. A variety of factor extraction methods is available: principal components, principal axis, maximum likelihood, unweighted least squares (ULS), generalized least squares (GLS), alpha factoring, and image factoring. Several extraction methods use an iterative process. You can set the tolerance and iteration limit for this phase using the ExtractionPhaseTolerance and ExtractionPhaseMaxIterations properties, respectively.

After the factors have been determined, they may be rotated. Again, a number of methods are available, including orthogonal (varimax, equamax, quartimax) and oblique (promax). The default is varimax. The method is specified by the RotationMethod property, which is of type FactorRotationMethod. Factor rotation is usually an iterative process. You can set the tolerance and iteration limit for this phase using the RotationPhaseTolerance and RotationPhaseMaxIterations properties, respectively.

Once the analysis is complete, the Communalities property contains the communalities of the variables, while the Uniqueness property contains its complement. The LoadingsMatrix property returns a matrix whose columns are the correlations of the factor with the corresponding variables before rotation. The FactorScoreCoefficientMatrix contains the coefficients of the factor scores.

Depending on whether the rotation is orthogonal or oblique, a number of properties are available. For orthogonal rotations, the RotatedLoadingsMatrix returns the loadings matrix after rotation. For oblique rotations, the PatternMatrix property contains the matrix of contributions of each factor to the variance of each variable. The StructureMatrix contains the matrix of correlations between factors and variables. For orthogonal rotations, both these matrices are equal and the same as the RotatedLoadingsMatrix.

Numerical Libraries

Reference