FA: Factor Analysis (FA).

Description

Performs factorial analysis (FA) in a data set.

Usage

FA(data, method = "PC", type = 2, nfactor = 1, rotation = "None",
   scoresobs = "Bartlett", converg = 1e-5, iteracao = 1000, 
   testfit = TRUE)

Value

mtxMC: Matrix of correlation / covariance.
mtxAutvlr: Matrix of eigenvalues.
mtxAutvec: Matrix of eigenvectors.
mtxvar: Matrix of variances and proportions.
mtxcarga: Matrix of factor loadings.
mtxvaresp: Matrix of specific variances.
mtxcomuna: Matrix of commonalities.
mtxresidue: Matrix of residues.
vlrsqrs: Upper limit value for sum of squares of the residues.
vlrsqr: Sum of squares of the residues.
mtxresult: Matrix with all associated results.
mtxscores: Matrix with scores of the observations.
coefscores: Matrix with the scores of the coefficients of the factors.

Arguments

data: Data to be analyzed.
method: Method of analysis:
"PC" - Principal Components (default),
"PF" - Principal Factor,
"ML" - Maximum Likelihood.
type: 1 for analysis using the covariance matrix,
2 for analysis using the correlation matrix (default).
rotation: Type of rotation: "None" (default), "Varimax" and "Promax".
nfactor: Number of factors (default = 1).
scoresobs: Type of scores for the observations: "Bartlett" (default) or "Regression".
converg: Limit value for convergence to sum of the squares of the residuals for Maximum likelihood method (default = 1e-5).
iteracao: Maximum number of iterations for Maximum Likelihood method (default = 1000).
testfit: Tests the model fit to the method of Maximum Likelihood (default = TRUE).

Author

Paulo Cesar Ossani

Marcelo Angelo Cirillo

References

Mingot, S. A. Analise de dados atraves de metodos de estatistica multivariada: uma abordagem aplicada. Belo Horizonte: UFMG, 2005. 297 p.

Kaiser, H. F.The varimax criterion for analytic rotation in factor analysis. Psychometrika 23, 187-200, 1958.

Rencher, A. C. Methods of multivariate analysis. 2th. ed. New York: J.Wiley, 2002. 708 p.

Ferreira, D. F. Estatistica Multivariada. 2a ed. revisada e ampliada. Lavras: Editora UFLA, 2011. 676 p.

Examples

Run this code

data(DataQuan) # data set

data <- DataQuan[,2:ncol(DataQuan)]

rownames(data) <- DataQuan[,1]

res <- FA(data, method = "PC", type = 2, nfactor = 3, rotation = "None",
          scoresobs = "Bartlett", converg = 1e-5, iteracao = 1000, 
          testfit = TRUE) 

print("Matrix with all associated results:"); round(res$mtxresult,3)

print("Sum of squares of the residues:"); round(res$vlrsqr,3)

print("Matrix of the factor loadings.:"); round(res$mtxcarga,3)

print("Matrix with scores of the observations:"); round(res$mtxscores,3)

print("Matrix with the scores of the coefficients of the factors:"); round(res$coefscores,3)

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