Factor- Version 9.2 (the latest version)

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Factor is a program developed to fit the Exploratory Factor Analysis model. Below we describe the methods used.

Univariate and multivariate descriptives of variables:

    Univariate mean, variance, skewness, and kurtosis
    Multivariate skewness and kurtosis (Mardia, 1970)
    Var charts for ordinal variables

Dispersion matrices:

    User defined tipo matrix
    Covariance matrix
    Pearson correlation matrix
    Polychoric correlation matrix (Polychoric algorithm: Olsson ,1979a, 1979b; Tetrachoric algorithm: Bonett & Price, 2005) with smoothing algorithm (Devlin, Gnanadesikan, & Kettenring, 1975; Devlin, Gnanadesikan, & Kettenring, 1981)

Procedures for determining the number of factors/components to be retained:

    MAP: Minimum Average Partial Test (Velicer, 1976)
    PA: Parallel Analysis (Horn, 1965)
    Optimal PA. It is an implementation of Parallel Analysis where it is computed based on the same type of correlation matrix (i.e., Pearson or polychoric correlation) and the same type of underlying dimensions (i.e., components of factor) as defined for the whole analysis (Timmerman & Lorenzo-Seva, 2011)
    Hull method for selecting the number of common factors: this method aims to find a model with an optimal balance between model fit and number of parameters (Lorenzo-Seva & Timmerman, 2011)

Factor and component analysis:

    PCA: Principal Component Analysis
    ULS: Unweighted Least Squares factor analysis (also MINRES and PAF)
    EML: Exploratory Maximum Likelihood factor analysis
    MRFA: Minimum Rank Factor Analysis (ten Berge, & Kiers, 1991)
    Item Test Theory parameterization of factor solution
    Semi-confirmatory factor analysis based on orthogonal and oblique rotation to a (partially) specified target (Browne, 1972a, 1972b)
    Schmid-Leiman second-order solution (1957)
    Factor scores for continuous data (ten Berge, Krijnen, Wansbeek, & Shapiro, 1999), and expected a-posteriori (EAP) estimation of latent trait scores for ordinal data
    Person fit indices (Ferrando, 2009)

In ULS factor analysis, the Heywood case correction described in Mulaik (1972, page 153) is included: when an update has sum of squares larger than the observed variance of the variable, that row is updated by constrained regression using the procedure proposed by ten Berge and Nevels (1977).

Some of the rotation methods to obtain simplicity are:

    Quartimax (Neuhaus & Wrigley, 1954)
    Varimax (Kaiser, 1958)
    Weighted Varimax (Cureton & Mulaik, 1975)
    Orthomin (Bentler, 1977)
    Direct Oblimin (Clarkson & Jennrich, 1988)
    Weighted Oblimin (Lorenzo-Seva, 2000)
    Promax (Hendrickson & White, 1964)
    Promaj (Trendafilov, 1994)
    Promin (Lorenzo-Seva, 1999)
    Simplimax (Kiers, 1994)

Some of the indices used in the analysis are:

    Test on the dispersion matrix: Determinant, Bartlett's test and Kaiser-Meyer-Olkin (KMO)
    Goodness of fit statistics: Chi-Square Non-Normed Fit Index (NNFI; Tucker & Lewis); Comparative Fit Index (CFI); Goodness of Fit Index (GFI); Adjusted Goodness of Fit Index (AGFI); Root Mean Square Error of Approximation (RMSEA); and Estimated Non-Centrality Parameter (NCP)
    Reliabilities of rotated components (ten Berge & Hofstee, 1999)
    Simplicity indices: Bentler’s Simplicity index (1977) and Loading Simplicity index (Lorenzo-Seva, 2003)
    Mean, variance and histogram of fitted and standardized residuals. Automatic detection of large standardized residuals.
    The greatest lower bound (glb) to reliability (Woodhouse & Jackson, 1977). The greatest lower bound (glb) to reliability represents the smallest reliability possible given observed covariance matrix under the restriction that the sum of error variances is maximized for errors that correlate 0 with other variables (Ten Berge, Snijders, & Zegers, 1981).
    McDonald's Omega. Omega can be interpreted as the square of the correlation between the scale score and the latent common to all the indicators in the infinite universe of indicators of which the scale indicators are a subset (McDonald, 1999, page 89).
    Congruence index to assess the congruence between the rotated loading matrix and the user provided target matrix (Lorenzo-Seva, & ten Berge, 2006).


http://psico.fcep.urv.es/utilitats/factor/index.html