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