Psychological Test Toolbox is a program developed to fit the Exploratory Factor Analysis model controlling Social Desirability and Acquiescence, based on the method described on Ferrando, Lorenzo-Seva, & Chico (2009). Below we describe the methods used.
Univariate descriptives of variables:
- Univariate mean, variance, skewness, and kurtosis
- Var charts for ordinal variables
- User defined type 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)
The Procedure for determining the number of factors/components to be retained:
- Optimal PA. It is an implementation of Parallel Analysis (Horn, 1965) 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)
Factor and component analysis:
- ULS: Unweighted Least Squares factor analysis (also MINRES and PAF)
- MRFA: Minimum Rank Factor Analysis (ten Berge, & Kiers, 1991)
- Semi-confirmatory factor analysis based on orthogonal and oblique rotation to a (partially) specified target (Browne, 1972a, 1972b)
- Factor scores for continuous data (ten Berge, Krijnen, Wansbeek, & Shapiro, 1999), and expected a-posteriori (EAP) estimation of latent trait scores for ordinal data
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).
The rotation methods to obtain simplicity are:
- Varimax (Kaiser, 1958)
- Promin (Lorenzo-Seva, 1999)
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: Goodness of Fit Index (GFI) and Root Mean Square Error of Approximation (RMSEA)
- 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.
- Congruence index to assess the congruence between the rotated loading matrix and the user provided target matrix (Lorenzo-Seva, & ten Berge, 2006).