Numerical Components for .NET
Namespace: Extreme.Statistics.MultivariateAssembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 4.2.11333.0 (4.2.12253.0)
public class FactorAnalysis : MultivariateModel
Public Class FactorAnalysis _
public ref class FactorAnalysis : public MultivariateModel
type FactorAnalysis =
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
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
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
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