xF A C T O R Unrestricted Factor Analysis Release Version 11.05.01 x64bits July, 2021 Rovira i Virgili University Tarragona, SPAIN Programming: Urbano Lorenzo-Seva Mathematical Specification: Urbano Lorenzo-Seva Pere J. Ferrando -------------------------------------------------------------------------------- DETAILS OF ANALYSIS Participants' scores data file : D:\PENELITIAN AWAL UNTUK PUBLIKASI DISERTASI\studi 1 EFA\friendship.dat Variable labels file : D:\PENELITIAN AWAL UNTUK PUBLIKASI DISERTASI\studi 1 EFA\Label other.txt Method to handle missing values : Hot-Deck Multiple Imputation in Exploratory Factor Analysis (Lorenzo-Seva & Van Ginkel, 2016) Missing code value : 999 Number of participants : 112 Number of variables : 8 Variables included in the analysis : ALL Variables excluded in the analysis : NONE Number of factors : 1 Number of second order factors : 0 Procedure for determining the number of dimensions : Optimal implementation of Parallel Analysis (PA) (Timmerman, & Lorenzo-Seva, 2011) Dispersion matrix : Polychoric Correlations Robust analyses : Bias-corrected and accelerated (BCa; Lambert, Wildt & Durand, 1991) Number of bootstrap samples : 500 Asymptotic Covariance/Variance matrix : estimated using bootstrap sampling Bootstrap confidence intervals : 95% Method for factor extraction : Robust Unweighted Least Squares (RULS) Correction for robust Chi square : Robust Mean and Variance-scaled (Asparouhov & Muthen, 2010) Rotation to achieve factor simplicity : Robust Promin (Lorenzo-Seva & Ferrando, 2019b) Clever rotation start : Weighted Varimax Number of random starts : 100 Maximum mumber of iterations : 1000 Convergence value : 0.00001000 Factor scores estimates : Estimates based on linear model -------------------------------------------------------------------------------- UNIVARIATE DESCRIPTIVES Variable Mean Confidence Interval Variance Skewness Kurtosis (95%) (Zero centered) O1 4.929 ( 4.48 5.38) 3.406 -0.737 -0.440 O2 4.911 ( 4.48 5.35) 3.206 -0.655 -0.538 O3 5.446 ( 5.07 5.83) 2.461 -1.188 0.832 O4 5.098 ( 4.71 5.49) 2.535 -0.845 0.294 O5 4.589 ( 4.17 5.01) 2.956 -0.610 -0.466 O6 5.116 ( 4.70 5.54) 2.995 -0.869 -0.239 O7 5.455 ( 5.06 5.85) 2.694 -1.161 0.557 O8 4.089 ( 3.65 4.53) 3.313 -0.035 -0.979 Polychoric correlation is advised when the univariate distributions of ordinal items are asymmetric or with excess of kurtosis. If both indices are lower than one in absolute value, then Pearson correlation is advised. You can read more about this subject in: Muthén, B., & Kaplan D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171-189. doi:10.1111/j.2044-8317.1985.tb00832.x Muthén, B., & Kaplan D. (1992). A comparison of some methodologies for the factor analysis of non-normal Likert variables: A note on the size of the model. British Journal of Mathematical and Statistical Psychology, 45, 19-30. doi:10.1111/j.2044-8317.1992.tb00975.x BAR CHARTS FOR ORDINAL VARIABLES Variable 1 Value Freq | 1 9 | ************* 2 7 | ********** 3 7 | ********** 4 15 | ********************** 5 23 | ********************************** 6 24 | *********************************** 7 27 | **************************************** +-----------+---------+---------+-----------+ 0 6.8 13.5 20.3 27.0 Variable 2 Value Freq | 1 7 | ********** 2 7 | ********** 3 11 | **************** 4 15 | *********************** 5 21 | ******************************** 6 26 | **************************************** 7 25 | ************************************** +-----------+---------+---------+-----------+ 0 6.5 13.0 19.5 26.0 Variable 3 Value Freq | 1 4 | **** 2 4 | **** 3 6 | ****** 4 10 | *********** 5 20 | ********************** 6 36 | **************************************** 7 32 | *********************************** +-----------+---------+---------+-----------+ 0 9.0 18.0 27.0 36.0 Variable 4 Value Freq | 1 6 | ******** 2 1 | * 3 11 | ************** 4 14 | ****************** 5 30 | **************************************** 6 26 | ********************************** 7 24 | ******************************** +-----------+---------+---------+-----------+ 0 7.5 15.0 22.5 30.0 Variable 5 Value Freq | 1 9 | ************ 2 8 | ********** 3 10 | ************* 4 17 | ********************** 5 30 | **************************************** 6 25 | ********************************* 7 13 | ***************** +-----------+---------+---------+-----------+ 0 7.5 15.0 22.5 30.0 Variable 6 Value Freq | 1 5 | ****** 2 8 | ********* 3 10 | ************ 4 8 | ********* 5 22 | ************************** 6 33 | **************************************** 7 26 | ******************************* +-----------+---------+---------+-----------+ 0 8.3 16.5 24.8 33.0 Variable 7 Value Freq | 1 4 | **** 2 6 | ****** 3 5 | ***** 4 10 | *********** 5 18 | ******************** 6 33 | ************************************ 7 36 | **************************************** +-----------+---------+---------+-----------+ 0 9.0 18.0 27.0 36.0 Variable 8 Value Freq | 1 11 | ***************** 2 13 | ******************** 3 22 | *********************************** 4 15 | ************************ 5 25 | **************************************** 6 12 | ******************* 7 14 | ********************** +-----------+---------+---------+-----------+ 0 6.3 12.5 18.8 25.0 -------------------------------------------------------------------------------- MULTIVARIATE DESCRIPTIVES Analysis of the Mardia's (1970) multivariate asymmetry skewness and kurtosis. Coefficient Statistic df P Skewness 28.467 531.392 120 1.0000 SKewness corrected for small sample 28.467 548.864 120 1.0000 Kurtosis 128.510 20.293 0.0000** ** Significant at 0.05 -------------------------------------------------------------------------------- STANDARIZED VARIANCE / COVARIANCE MATRIX (POLYCHORIC CORRELATION) (Polychoric algorithm: Bayes modal estimation; Choi, Kim, Chen, & Dannels, 2011) Variable 1 2 3 4 5 6 7 8 V 1 1.000 V 2 0.972 1.000 V 3 0.682 0.664 1.000 V 4 0.590 0.554 0.751 1.000 V 5 0.669 0.668 0.660 0.734 1.000 V 6 0.585 0.594 0.619 0.684 0.757 1.000 V 7 0.516 0.534 0.705 0.719 0.678 0.797 1.000 V 8 0.458 0.453 0.459 0.573 0.570 0.606 0.524 1.000 -------------------------------------------------------------------------------- BIAS-CORRECTED (BC) BOOTSTRAP 95% CONFIDENCE INTERVALS FOR CORRELATIONS BETWEEN VARIABLES Variables Value Confidence Interval v 1 -- v 2 0.972* ( 0.925 0.991) v 1 -- v 3 0.682* ( 0.499 0.796) v 1 -- v 4 0.590* ( 0.388 0.725) v 1 -- v 5 0.669* ( 0.462 0.801) v 1 -- v 6 0.585* ( 0.366 0.747) v 1 -- v 7 0.516* ( 0.270 0.673) v 1 -- v 8 0.458* ( 0.279 0.630) v 2 -- v 3 0.664* ( 0.458 0.778) v 2 -- v 4 0.554* ( 0.335 0.688) v 2 -- v 5 0.668* ( 0.453 0.820) v 2 -- v 6 0.594* ( 0.352 0.740) v 2 -- v 7 0.534* ( 0.292 0.681) v 2 -- v 8 0.453* ( 0.257 0.617) v 3 -- v 4 0.751* ( 0.601 0.858) v 3 -- v 5 0.660* ( 0.507 0.771) v 3 -- v 6 0.619* ( 0.445 0.750) v 3 -- v 7 0.705* ( 0.530 0.808) v 3 -- v 8 0.459* ( 0.244 0.646) v 4 -- v 5 0.734* ( 0.577 0.827) v 4 -- v 6 0.684* ( 0.524 0.804) v 4 -- v 7 0.719* ( 0.583 0.822) v 4 -- v 8 0.573* ( 0.355 0.740) v 5 -- v 6 0.757* ( 0.586 0.867) v 5 -- v 7 0.678* ( 0.517 0.793) v 5 -- v 8 0.570* ( 0.385 0.717) v 6 -- v 7 0.797* ( 0.637 0.902) v 6 -- v 8 0.606* ( 0.404 0.744) v 7 -- v 8 0.524* ( 0.294 0.702) * Significantly different from zero at population -------------------------------------------------------------------------------- ADEQUACY OF THE POLYCHORIC CORRELATION MATRIX Determinant of the matrix = 0.000255927644703 Bartlett's statistic = 889.1 (df = 28; P = 0.000010) Kaiser-Meyer-Olkin (KMO) test = 0.85405 (good) Bootstrap 95% confidence interval of KMO = ( 0.369 0.860) NORMED ITEM-MSA INDICES Items Quartile of Sum Relative difficulty Normed MSA Bootstrap 95% response scores index Confidence interval O8 1 0.58418 **0.95011 ( 0.253 0.967) O5 2 0.65561 **0.93713 ( 0.366 0.968) O2 2 0.70153 **0.74898 ( 0.332 0.790) O1 2 0.70408 **0.74908 ( 0.330 0.792) O4 2 0.72832 **0.87734 ( 0.338 0.938) O6 2 0.73087 **0.87680 ( 0.356 0.911) O3 3 0.77806 **0.91605 ( 0.348 0.956) O7 3 0.77934 **0.85314 ( 0.332 0.913) ** Number of items proposed to be removed: 8 Values of MSA below .50 suggest that the item does not measure the same domain as the remaining items in the pool, and so that it should be removed. At the same time, for a normal-range test, an optimal pool of items should have a large spread of Relative difficulty indices, and each quartile should have a similar number of items. When removing items from the pool, all these aspects should be taken into account. Sometimes, the conclusion is that new items should be added to the pool of items. -------------------------------------------------------------------------------- EXPLAINED VARIANCE BASED ON EIGENVALUES Variable Eigenvalue Proportion of Cumulative Proportion Variance of Variance 1 5.46335 0.68292 0.68292 2 0.87966 0.10996 3 0.57290 0.07161 4 0.40018 0.05002 5 0.31001 0.03875 6 0.19259 0.02407 7 0.15643 0.01955 8 0.02487 0.00311 -------------------------------------------------------------------------------- PARALLEL ANALYSIS (PA) BASED ON MINIMUM RANK FACTOR ANALYSIS (Timmerman & Lorenzo-Seva, 2011) Implementation details: Correlation matrices analized: Polychoric correlation matrices Number of random correlation matrices: 500 Method to obtain random correlation matrices: Permutation of the raw data (Buja & Eyuboglu, 1992) Variable Real-data Mean of random 95 percentile of random % of variance % of variance % of variance 1 77.6183* 25.6689 30.3964 2 12.0693 21.3765 24.5319 3 4.4891 17.4695 19.9449 4 3.7732 13.9830 16.0903 5 1.0908 10.6734 13.2212 6 0.9029 7.1188 9.9159 7 0.0563 3.7099 6.5721 * Advised number of dimensions: 1 -------------------------------------------------------------------------------- CLOSENESS TO UNIDIMENSIONALITY ASSESSMENT Ferrando & Lorenzo-Seva (2018) ITEM-LEVEL ASSESSMENT Variable I-UniCo Bootstrap 95% Confidence intervals I-ECV Bootstrap 95% Confidence intervals I-REAL BC Bootstrap 95% Confidence intervals O1 0.937 ( 0.732 0.985) 0.728 ( 0.518 0.851) 0.516 ( 0.373 0.676) O2 0.932 ( 0.702 0.982) 0.720 ( 0.496 0.840) 0.525 ( 0.394 0.697) O3 1.000 ( 1.000 1.000) 1.000 ( 0.999 1.000) 0.014 ( 0.001 0.029) O4 0.997 ( 0.936 1.000) 0.926 ( 0.727 0.991) 0.238 ( 0.086 0.466) O5 1.000 ( 0.997 1.000) 0.991 ( 0.925 1.000) 0.080 ( 0.002 0.233) O6 0.994 ( 0.909 1.000) 0.904 ( 0.686 0.987) 0.279 ( 0.104 0.495) O7 0.988 ( 0.905 1.000) 0.866 ( 0.680 0.982) 0.320 ( 0.097 0.514) O8 0.998 ( 0.946 1.000) 0.944 ( 0.745 1.000) 0.154 ( 0.004 0.335) OVERALL ASSESSMENT UniCo = 0.981 BC BOOTSTRAP 95% CONFIDENCE INTERVALS = ( 0.944 0.993) ECV = 0.868 BC BOOTSTRAP 95% CONFIDENCE INTERVALS = ( 0.796 0.915) MIREAL = 0.266 BC BOOTSTRAP 95% CONFIDENCE INTERVALS = ( 0.177 0.313) A value of UniCo (Unidimensional Congruence) and I-Unico (Item Unidimensional Congruence) larger than 0.95 suggests that data can be treated as essentially unidimensional. A value of ECV (Explained Common Variance) and I-ECV (Item Explained Common Variance) larger than 0.85 suggests that data can be treated as essentially unidimensional. A value of MIREAL (Mean of Item REsidual Absolute Loadings) and I-REAL (Item REsidual Absolute Loadings) lower than 0.300 suggests that data can be treated as essentially unidimensional. -------------------------------------------------------------------------------- ROBUST GOODNESS OF FIT STATISTICS Root Mean Square Error of Approximation (RMSEA) = 0.129; BC Bootstrap 95% confidence interval = ( 0.0416 0.1942) (larger than 0.100 : poor) Estimated Non-Centrality Parameter (NCP) = 5.550 Degrees of Freedom = 20 Test of Approximate Fit H0 : RMSEA < 0.05; P = 0.748 Minimum Fit Function Chi Square with 20 degrees of freedom = 24.595 (P = 0.224933) Robust Mean and Variance-Adjusted Chi Square with 20 degrees of freedom = 57.130 (P = 0.000023) Chi-Square for independence model with 28 degrees of freedom = 1291.411 Non-Normed Fit Index (NNFI; Tucker & Lewis) = 0.959; BC Bootstrap 95% confidence interval = ( 0.885 0.993) Comparative Fit Index (CFI) = 0.971; BC Bootstrap 95% confidence interval = ( 0.918 0.995) (between 0.950 and 0.990 : close) Schwarz’s Bayesian Information Criterion (BIC) = 132.626; BC Bootstrap 95% confidence interval = ( 99.346 179.236) Goodness of Fit Index (GFI) = 0.986; BC Bootstrap 95% confidence interval = ( 0.968 0.995) Adjusted Goodness of Fit Index (AGFI) = 0.980; BC Bootstrap 95% confidence interval = ( 0.956 0.993) Goodness of Fit Index without diagonal values (GFI) = 0.981; BC Bootstrap 95% confidence interval = ( 0.955 0.994) Adjusted Goodness of Fit Index without diagonal values(AGFI) = 0.973; BC Bootstrap 95% confidence interval = ( 0.937 0.992) EIGENVALUES OF THE REDUCED CORRELATION MATRIX Variable Eigenvalue 1 5.115458571 2 0.510797604 3 0.137650463 4 0.026192772 5 -0.027814290 6 -0.137431297 7 -0.173480866 8 -0.335918289 -------------------------------------------------------------------------------- UNROTATED LOADING MATRIX Variable F 1 Communality O1 0.802 0.644 O2 0.796 0.634 O3 0.818 0.670 O4 0.829 0.687 O5 0.857 0.735 O6 0.835 0.697 O7 0.803 0.645 O8 0.635 0.404 EXPLAINED VARIANCE AND RELIABILITY OF EAP SCORES Ferrando & Lorenzo-Seva (2016) Factor Variance EAP Reliability Factor Determinacy Index 1 5.115 0.939 0.969 -------------------------------------------------------------------------------- CONSTRUCT REPLICABILITY: GENERALIZED H (G-H) INDEX Hancock & Mueller (2000) Factor H-Latent BC Bootstrap 95 % Confidence intervals H-Observed BC Bootstrap 95 % Confidence intervals F 1 0.939 ( 0.886 0.955) 0.873 ( 0.822 0.903) The H index evaluates how well a set of items represents a common factor. It is bounded between 0 and 1 and approaches unity as the magnitude of the factor loadings and/or the number of items increase. High H values (>.80) suggest a well defined latent variable, which is more likely to be stable across studies, whereas low H values suggest a poorly defined latent variable, which is likely to change across studies. H-Latent assesses how well the factor can be identified by the continuous latent response variables that underlie the observed item scores, whereas H-Observed assesses how well it can be identified from the observed item scores. -------------------------------------------------------------------------------- QUALITY AND EFFECTIVENESS OF FACTOR SCORE ESTIMATES Ferrando & Lorenzo-Seva (2018) F 1 Factor Determinacy Index (FDI) 0.969 EAP marginal reliability 0.939 Sensitivity ratio (SR) 3.916 Expected percentage of true differences (EPTD) 94.6% The sensitivity ratio (SR) can be interpreted as the number of different factor levels than can be differentiated on the basis of the factor score estimates. The expected percentage of true differences (EPTD) is the estimated percentage of differences between the observed factor score estimates that are in the same direction as the corresponding true differences. If factor scores are to be used for individual assessment, FDI values above .90, marginal reliabilities above .80, SR above 2, and EPTDs above 90% are recommended. -------------------------------------------------------------------------------- BIAS-CORRECTED AND ACCELERATED (BCa) BOOTSTRAP 95% CONFIDENCE INTERVALS FOR LOADING VALUES Variable F 1 BCa Confidence Interval O1 0.802 ( 0.599 0.880) O2 0.796 ( 0.577 0.870) O3 0.818 ( 0.682 0.894) O4 0.829 ( 0.725 0.893) O5 0.857 ( 0.773 0.914) O6 0.835 ( 0.685 0.912) O7 0.803 ( 0.647 0.884) O8 0.635 ( 0.465 0.773) -------------------------------------------------------------------------------- GREATEST LOWER BOUND (GLB) TO RELIABILITY Woodhouse & Jackson (1977) WARNING: The GLB and Omega can only be trusted in large samples, preferably 1,000 cases or more, due to a positive sampling bias (ten Berge & Socan, 2004). Greatest Lower Bound to Reliability = 0.968474 McDonald's ordinal Omega = 0.933801 Standardized Cronbach's alpha = 0.932888 Total observed variance = 8.000 Total Common Variance = 6.627 ASSOCIATED COMMUNALITIES Variable Communality O1 0.987940 O2 0.993091 O3 0.783057 O4 0.879793 O5 0.750739 O6 0.926610 O7 0.833269 O8 0.472746 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). Omega can be interpreted as the square of the correlation between the scale score and the latent variable common to all the indicators in the infinite universe of indicators of which the scale indicators are a subset (McDonald, 1999, page 89). -------------------------------------------------------------------------------- DISTRIBUTION OF RESIDUALS Number of Residuals = 28 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.1287 Median Fitted Residual = -0.0105 Largest Fitted Residual = 0.3331 Mean Fitted Residual = -0.0000 Variance Fitted Residual = 0.0079 Root Mean Square of Residuals (RMSR) = 0.0890 BC Bootstrap 95% confidence interval of RMSR = ( 0.052 0.121) Expected mean value of RMSR for an acceptable model = 0.0949 (Kelley's criterion) (Kelley, 1935,page 13; see also Harman, 1962, page 21 of the 2nd edition) Weighted Root Mean Square Residual (WRMR) = 0.4501 (values under 1.0 have been recommended to represent good fit; Yu & Muthen, 2002) BC Bootstrap 95% confidence interval of WRMR = ( 0.269 0.739) Histogram for fitted residuals Value Freq | -0.1287 3 | ********** -0.0517 10 | ************************************ 0.0252 11 | **************************************** 0.1022 3 | ********** 0.1792 0 | 0.2562 0 | 0.3331 1 | *** +-----------+---------+---------+-----------+ 0 2.8 5.5 8.3 11.0 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -1.36 Median Standardized Residual = -0.11 Largest Standardized Residual = 3.51 Mean Standardized Residual = -0.00 Stemleaf Plot for Standardized Residuals -1 | 411 -0 | 987766542211 0 | 11233455688 1 | 3 2 | 3 | 5 Largest Positive Standardized Residuals Residual for Var 2 and Var 1 3.51 -------------------------------------------------------------------------------- DESCRIPTIVES RELATED TO MISSING DATA Missing value code : 999 No missing data was observed in your data -------------------------------------------------------------------------------- References Asparouhov, T., & Muthen, B. (2010). Simple second order chi-square correction. Unpublished manuscript. Available at https://www.statmodel.com/download/WLSMV_new_chi21.pdf. Buja, A., & Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509-540. doi:10.1207/s15327906mbr2704_2 Ferrando, P. J., & Lorenzo-Seva U. (2018). Assessing the quality and appropriateness of factor solutions and factor score estimates in exploratory item factor analysis. Educational and Psychological Measurement, 78, 762-780. doi:10.1177/0013164417719308 Hancock, G.R., &Mueller, R.O. (2000). Rethinking construct reliability within latent variable systems.In R.Cudek, S.H.C.duToit & D.F.Sorbom(Eds.), Structural equation modeling : Present and future(pp. 195 - 216).Lincolnwood, IL : Scientific Software. Harman, H. H. (1962). Modern Factor Analysis, 2nd Edition. University of Chicago Press, Chicago. Kelley, T. L. (1935). Essential Traits of Mental Life, Harvard Studies in Education, vol. 26. Harvard University Press, Cambridge. Lambert, Z.V., Wildt, A.R., & Durand, R.M. (1991). Approximating confidence intervals for factor loadings. Multivariate behavioral research, 26(3), 421 - 434. doi:10.1207/s15327906mbr2603_3 Lorenzo-Seva, U., & Ferrando, P.J. (2019b). Robust Promin: a method for diagonally weighted factor rotation. LIBERABIT, Revista Peruana de Psicología, 25, 99-106. doi:10.24265/liberabit.2019.v25n1.08 Lorenzo-Seva, U., & Van Ginkel, J. R. (2016). Multiple Imputation of missing values in exploratory factor analysis of multidimensional scales: estimating latent trait scores. Anales de Psicología/Annals of Psychology, 32(2), 596-608. doi:10.6018/analesps.32.2.215161 McDonald, R.P. (1999). Test theory: A unified treatment. Mahwah, NJ: Lawrence Erlbaum. Mardia, K. V. (1970). Measures of multivariate skewnees and kurtosis with applications. Biometrika, 57, 519-530. doi:10.2307/2334770 Olsson, U. (1979a). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44, 443-460. doi:10.1007/bf02296207 Olsson, U. (1979b). On the robustness of factor analysis against crude classification of the observations. Multivariate Behavioral Research, 14, 485-500. doi:10.1207/s15327906mbr1404_7 Mislevy, R.J., & Bock, R.D. (1990). BILOG 3 Item analysis and test scoring with binary logistic models. Mooresville: Scientific Software. Ten Berge, J.M.F., Snijders, T.A.B. & Zegers, F.E. (1981). Computational aspects of the greatest lower bound to reliability and constrained minimum trace factor analysis. Psychometrika, 46, 201-213. doi:10.1007/bf02293900 Ten Berge, J.M.F., & Socan, G. (2004). The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality. Psychometrika, 69, 613-625. doi:10.1007/bf02289858 Timmerman, M. E., & Lorenzo-Seva, U. (2011). Dimensionality Assessment of Ordered Polytomous Items with Parallel Analysis. Psychological Methods, 16, 209-220. doi:10.1037/a0023353 Woodhouse, B. & Jackson, P.H. (1977). Lower bounds to the reliability of the total score on a test composed of nonhomogeneous items: II. A search procedure to locate the greatest lower bound. Psychometrika, 42, 579-591. doi:10.1007/bf02295980 Yu, C., & Muthen, B. (2002, April). Evaluation of model fit indices for latent variable models with categorical and continuous outcomes. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, L.A. FACTOR is based on CLAPACK. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., & Sorensen, D. (1999). LAPACK Users' Guide. Society for Industrial and Applied Mathematics. Philadelphia, PA FACTOR can be refered as: Ferrando, P.J., & Lorenzo-Seva, U. (2017). Program FACTOR at 10: origins, development and future directions. Psicothema, 29(2), 236-241. doi: 10.7334/psicothema2016.304 Lorenzo-Seva, U., & Ferrando, P.J. (2013). FACTOR 9.2 A comprehensive program for fitting exploratory and semiconfirmatory factor analysis and IRT models. Applied Psychological Measurement, 37(6), 497-498. doi:10.1177/0146621613487794 Lorenzo-Seva, U., & Ferrando, P.J. (2006). FACTOR: A computer program to fit the exploratory factor analysis model. Behavioral Research Methods, 38(1), 88-91. 10.3758/bf03192753 For further information and new releases go to: psico.fcep.urv.cat/utilitats/factor -------------------------------------------------------------------------------- FACTOR completed Computing time : 37.78 minutes. Matrices generated : 558409303 Our last advice: Distrust 5% of statistics, and 95% of statisticians. (Cal desconfiar un 5% de l'estadistica, i un 95% de l'estadistic.)