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\VE fam\data fam.dat Variable labels file : D:\PENELITIAN AWAL UNTUK PUBLIKASI DISERTASI\studi 1 EFA\VE fam\fam label.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 Number of nodes used in the graded model : 20 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 Index for detecting correlated residuals : EREC (Expected REsidual correlation direct Change; Ferrando, Hernandez-Dorado & Lorenzo-Seva, 2021) Factor scores estimates : Estimates based on graded model (Nodes = 20) -------------------------------------------------------------------------------- UNIVARIATE DESCRIPTIVES Variable Mean Confidence Interval Variance Skewness Kurtosis (95%) (Zero centered) fam1 5.464 ( 5.02 5.90) 3.284 -1.277 0.679 fam2 5.518 ( 5.05 5.98) 3.643 -1.264 0.369 fam3 5.938 ( 5.59 6.28) 2.023 -1.768 3.042 fam4 5.902 ( 5.55 6.25) 2.089 -1.636 2.391 fam5 5.455 ( 5.02 5.89) 3.266 -1.168 0.357 fam6 5.830 ( 5.47 6.19) 2.248 -1.551 2.002 fam7 5.920 ( 5.55 6.29) 2.342 -1.659 2.015 fam8 4.607 ( 4.17 5.05) 3.274 -0.494 -0.712 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 3 | ** 3 3 | ** 4 10 | ********* 5 17 | *************** 6 27 | ************************* 7 43 | **************************************** +-----------+---------+---------+-----------+ 0 10.8 21.5 32.3 43.0 Variable 2 Value Freq | 1 9 | ******* 2 5 | **** 3 4 | *** 4 8 | ****** 5 11 | ******** 6 25 | ******************** 7 50 | **************************************** +-----------+---------+---------+-----------+ 0 12.5 25.0 37.5 50.0 Variable 3 Value Freq | 1 3 | ** 2 3 | ** 3 1 | 4 6 | **** 5 18 | ************* 6 28 | ********************* 7 53 | **************************************** +-----------+---------+---------+-----------+ 0 13.3 26.5 39.8 53.0 Variable 4 Value Freq | 1 3 | ** 2 2 | * 3 3 | ** 4 9 | ****** 5 13 | ********** 6 30 | *********************** 7 52 | **************************************** +-----------+---------+---------+-----------+ 0 13.0 26.0 39.0 52.0 Variable 5 Value Freq | 1 7 | ****** 2 5 | **** 3 6 | ***** 4 6 | ***** 5 21 | ****************** 6 22 | ******************* 7 45 | **************************************** +-----------+---------+---------+-----------+ 0 11.3 22.5 33.8 45.0 Variable 6 Value Freq | 1 3 | ** 2 4 | *** 3 2 | * 4 7 | ***** 5 19 | ************** 6 26 | ******************** 7 51 | **************************************** +-----------+---------+---------+-----------+ 0 12.8 25.5 38.3 51.0 Variable 7 Value Freq | 1 3 | ** 2 3 | ** 3 6 | **** 4 5 | *** 5 10 | ******* 6 29 | ******************** 7 56 | **************************************** +-----------+---------+---------+-----------+ 0 14.0 28.0 42.0 56.0 Variable 8 Value Freq | 1 8 | ******** 2 13 | ************** 3 8 | ******** 4 12 | ************* 5 36 | **************************************** 6 15 | **************** 7 20 | ********************** +-----------+---------+---------+-----------+ 0 9.0 18.0 27.0 36.0 -------------------------------------------------------------------------------- MULTIVARIATE DESCRIPTIVES Analysis of the Mardia's (1970) multivariate asymmetry skewness and kurtosis. Coefficient Statistic df P Skewness 45.601 851.215 120 1.0000 SKewness corrected for small sample 45.601 879.202 120 1.0000 Kurtosis 160.073 33.497 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 0.945 1.000 V 3 0.681 0.671 1.000 V 4 0.727 0.695 0.955 1.000 V 5 0.826 0.858 0.751 0.792 1.000 V 6 0.718 0.750 0.791 0.791 0.842 1.000 V 7 0.638 0.677 0.734 0.761 0.746 0.934 1.000 V 8 0.572 0.599 0.539 0.578 0.725 0.656 0.615 1.000 -------------------------------------------------------------------------------- BIAS-CORRECTED (BC) BOOTSTRAP 95% CONFIDENCE INTERVALS FOR CORRELATIONS BETWEEN VARIABLES Variables Value Confidence Interval v 1 -- v 2 0.945* ( 0.839 0.982) v 1 -- v 3 0.681* ( 0.474 0.818) v 1 -- v 4 0.727* ( 0.539 0.848) v 1 -- v 5 0.826* ( 0.697 0.910) v 1 -- v 6 0.718* ( 0.458 0.828) v 1 -- v 7 0.638* ( 0.365 0.795) v 1 -- v 8 0.572* ( 0.359 0.725) v 2 -- v 3 0.671* ( 0.438 0.806) v 2 -- v 4 0.695* ( 0.469 0.819) v 2 -- v 5 0.858* ( 0.689 0.939) v 2 -- v 6 0.750* ( 0.443 0.856) v 2 -- v 7 0.677* ( 0.386 0.815) v 2 -- v 8 0.599* ( 0.358 0.753) v 3 -- v 4 0.955* ( 0.491 0.986) v 3 -- v 5 0.751* ( 0.598 0.865) v 3 -- v 6 0.791* ( 0.387 0.922) v 3 -- v 7 0.734* ( 0.567 0.875) v 3 -- v 8 0.539* ( 0.311 0.697) v 4 -- v 5 0.792* ( 0.653 0.895) v 4 -- v 6 0.791* ( 0.406 0.917) v 4 -- v 7 0.761* ( 0.596 0.905) v 4 -- v 8 0.578* ( 0.346 0.733) v 5 -- v 6 0.842* ( 0.646 0.944) v 5 -- v 7 0.746* ( 0.562 0.909) v 5 -- v 8 0.725* ( 0.536 0.830) v 6 -- v 7 0.934* ( 0.807 0.977) v 6 -- v 8 0.656* ( 0.360 0.790) v 7 -- v 8 0.615* ( 0.354 0.754) * Significantly different from zero at population -------------------------------------------------------------------------------- ADEQUACY OF THE POLYCHORIC CORRELATION MATRIX Determinant of the matrix < 0.000001 Bartlett's statistic = 1237.6 (df = 28; P = 0.000010) Kaiser-Meyer-Olkin (KMO) test = 0.78858 (fair) Bootstrap 95% confidence interval of KMO = ( 0.333 -nan(ind)) NORMED ITEM-MSA INDICES Items Quartile of Sum Relative difficulty Normed MSA Bootstrap 95% response scores index Confidence interval fam8 1 0.65816 **0.94555 ( 0.214 0.971) fam5 2 0.77934 **0.84364 ( 0.354 1.000) fam1 2 0.78061 **0.79146 ( 0.318 1.000) fam2 2 0.78827 **0.77656 ( 0.324 1.000) fam6 2 0.83291 **0.77784 ( 0.332 1.000) fam4 3 0.84311 **0.73580 ( 0.321 1.000) fam7 3 0.84566 **0.75751 ( 0.289 1.000) fam3 3 0.84821 **0.75513 ( 0.317 1.000) ** 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 6.16420 0.77053 0.77053 2 0.63551 0.07944 3 0.55218 0.06902 4 0.37298 0.04662 5 0.13653 0.01707 6 0.06410 0.00801 7 0.05232 0.00654 8 0.02217 0.00277 -------------------------------------------------------------------------------- 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 77.8890* 25.5758 30.0021 2 7.9000 21.1423 24.0265 3 6.6615 17.5248 19.9150 4 4.5317 14.0489 16.2683 5 1.7015 10.6460 12.9183 6 0.6926 7.2949 9.9702 7 0.6237 3.7674 6.4650 * 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 fam1 0.983 ( 0.859 1.000) 0.841 ( 0.627 0.976) 0.377 ( 0.132 0.573) fam2 0.975 ( 0.829 0.996) 0.814 ( 0.597 0.915) 0.425 ( 0.300 0.591) fam3 0.994 ( 0.926 1.000) 0.898 ( 0.711 0.999) 0.295 ( 0.020 0.520) fam4 0.996 ( 0.948 1.000) 0.920 ( 0.749 0.999) 0.267 ( 0.025 0.484) fam5 1.000 ( 0.994 1.000) 0.972 ( 0.901 1.000) 0.159 ( 0.013 0.302) fam6 0.999 ( 0.966 1.000) 0.968 ( 0.788 1.000) 0.168 ( 0.010 0.448) fam7 0.996 ( 0.680 1.000) 0.918 ( 0.481 0.997) 0.260 ( 0.050 0.577) fam8 1.000 ( 1.000 1.000) 0.997 ( 0.974 1.000) 0.040 ( 0.000 0.120) OVERALL ASSESSMENT UniCo = 0.993 BC BOOTSTRAP 95% CONFIDENCE INTERVALS = ( 0.983 0.998) ECV = 0.910 BC BOOTSTRAP 95% CONFIDENCE INTERVALS = ( 0.859 0.949) MIREAL = 0.249 BC BOOTSTRAP 95% CONFIDENCE INTERVALS = ( 0.185 0.336) 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) = 0.109; BC Bootstrap 95% confidence interval = ( 0.0276 0.1813) (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 = 17.487 (P = 0.629741) Robust Mean and Variance-Adjusted Chi Square with 20 degrees of freedom = 46.285 (P = 0.000822) Chi-Square for independence model with 28 degrees of freedom = 1713.356 Non-Normed Fit Index (NNFI; Tucker & Lewis) = 0.978; BC Bootstrap 95% confidence interval = ( 0.927 0.998) Comparative Fit Index (CFI) = 0.984; BC Bootstrap 95% confidence interval = ( 0.948 0.999) (between 0.950 and 0.990 : close) Schwarz’s Bayesian Information Criterion (BIC) = 121.781; BC Bootstrap 95% confidence interval = ( 96.060 168.471) Goodness of Fit Index (GFI) = 0.992; BC Bootstrap 95% confidence interval = ( 0.979 0.997) Adjusted Goodness of Fit Index (AGFI) = 0.989; BC Bootstrap 95% confidence interval = ( 0.971 0.996) Goodness of Fit Index without diagonal values (GFI) = 0.990; BC Bootstrap 95% confidence interval = ( 0.973 0.997) Adjusted Goodness of Fit Index without diagonal values(AGFI) = 0.986; BC Bootstrap 95% confidence interval = ( 0.962 0.996) EIGENVALUES OF THE REDUCED CORRELATION MATRIX Variable Eigenvalue 1 5.918811853 2 0.385154698 3 0.216049228 4 0.052624675 5 -0.085699477 6 -0.152698906 7 -0.194606067 8 -0.220823574 -------------------------------------------------------------------------------- UNROTATED LOADING MATRIX Variable F 1 Communality fam1 0.850 0.723 fam2 0.866 0.750 fam3 0.855 0.732 fam4 0.888 0.788 fam5 0.932 0.868 fam6 0.922 0.851 fam7 0.850 0.722 fam8 0.696 0.484 EXPLAINED VARIANCE AND RELIABILITY OF EAP SCORES Ferrando & Lorenzo-Seva (2016) Factor Variance EAP Reliability Factor Determinacy Index 1 5.919 0.902 0.950 -------------------------------------------------------------------------------- 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 0.965 ( 0.933 0.977) 0.828 ( 0.738 0.886) The H index evaluates how well a set of items represents a common factor. 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) 0.950 EAP marginal reliability 0.902 Sensitivity ratio (SR) 3.037 Expected percentage of true differences (EPTD) 98.9% 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 fam1 0.850 ( 0.689 0.908) fam2 0.866 ( 0.467 0.924) fam3 0.855 ( 0.713 0.922) fam4 0.888 ( 0.778 0.956) fam5 0.932 ( 0.840 0.969) fam6 0.922 ( 0.756 0.986) fam7 0.850 ( 0.661 0.938) fam8 0.696 ( 0.522 0.808) -------------------------------------------------------------------------------- CONDITIONAL EAP/ORION RELIABILITIES DISTRIBUTION Ferrando, Navarro-Gonzalez, & Lorenzo-Seva (2019) FACTOR: 1 Factor Conditional score reliability | -3.25 0.000 | * · -3.01 0.000 | * · -2.77 0.838 | ·* -2.52 0.000 | * · -2.28 0.000 | * · -2.04 0.981 | · * -1.80 0.990 | · * -1.56 0.993 | · * -1.32 0.966 | · * -1.08 0.996 | · * -0.84 0.958 | · * -0.60 0.997 | · * -0.36 0.964 | · * -0.12 0.997 | · * 0.12 0.994 | · * 0.36 0.955 | · * 0.60 0.982 | · * 0.84 0.947 | · * 1.08 0.956 | · * 1.32 0.907 | · * 1.56 0.844 | ·* 1.81 0.582 | * · 2.05 0.320 | * · 2.29 0.672 | * · 2.53 0.000 | * · 2.77 0.000 | * · 3.01 0.000 | * · 3.25 0.000 | * · 3.49 0.000 | * · 3.73 0.000 | * · +-----------+---------+---------+-----------+ 0 0.2 0.5 0.7 1.0 Conditional reliabilities function reports the statistical information corresponding to each score level of the latent trait. It is interpreted as the test information function in IRT context. The graphic shows (1) the conditional reliabilities against the factor score estimates as '*' marks, and (2) the cut-off value of 0.80 as a vertical dotted line. -------------------------------------------------------------------------------- DISTRIBUTION OF RESIDUALS Number of Residuals = 28 Summary Statistics for Fitted Residuals Smallest Fitted Residual = -0.0850 Median Fitted Residual = -0.0272 Largest Fitted Residual = 0.2085 Mean Fitted Residual = -0.0001 Variance Fitted Residual = 0.0056 Root Mean Square of Residuals (RMSR) = 0.0750 BC Bootstrap 95% confidence interval of RMSR = ( 0.043 0.111) 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) = 0.1079 (values under 1.0 have been recommended to represent good fit; Yu & Muthen, 2002) BC Bootstrap 95% confidence interval of WRMR = ( 0.063 0.163) Histogram for fitted residuals Value Freq | -0.0850 4 | ************* -0.0361 12 | **************************************** 0.0128 7 | *********************** 0.0617 2 | ****** 0.1106 0 | 0.1596 1 | *** 0.2085 2 | ****** +-----------+---------+---------+-----------+ 0 3.0 6.0 9.0 12.0 Summary Statistics for Standardized Residuals Smallest Standardized Residual = -0.90 Median Standardized Residual = -0.29 Largest Standardized Residual = 2.20 Mean Standardized Residual = -0.00 Stemleaf Plot for Standardized Residuals -0 | 9877665555443322 0 | 001112458 1 | 6 2 | 12 -------------------------------------------------------------------------------- DETECTING CORRELATED RESIDUALS ASSESSMENT BASED ON MORGANA METHOD (Minimum expected bias Of Residual and loadinG vAlues iN sAmple estimates method) INDEX COMPUTED: ROBUST EREC (Expected REsidual correlation direct Change index) Ferrando, Hernandez-Dorado & Lorenzo-Seva (2021) Pairs EREC Doublet according to Mean as threshold 3 - 4 0.80380 YES 1 - 2 0.74138 YES 6 - 7 0.73778 NO 5 - 8 0.30787 NO 2 - 5 0.30447 NO 1 - 7 0.30312 NO * Number of doublets detected: 2 The EREC (Expected REsidual correlation direct Change) index assesses the residual correlation between a pair of items once the influence of the common factors has been partialled out. EREC is an estimate of the residual correlation (in absolute value) between a pair of items once the influence of the prescribed common factors has been partialled out. However, EREC is obtained by using a sectioning procedure and is expected to provide a less biased estimate of this correlation than that provided by alternative indices. Being an absolute correlation, EREC values range from 0 to 1, and substantial values above the cut-off criteria suggests that the pair shares specific variance beyond that can be explained by the common factors, and so that is a possible doublet. Simulation studies suggests that EREC is the best index for detecting doublets and is implemented as a default in FACTOR. -------------------------------------------------------------------------------- DESCRIPTIVES RELATED TO MISSING DATA Missing value code : 999 No missing data was observed in your data -------------------------------------------------------------------------------- DIRECT ITEM ADDITION OF NON AHEAD PROPOSED SETS (DIANA) Ferrando & Lorenzo-Seva (2021) Model to estime factor scores: graded model with 20 nodes VARIABLES TO BE ADDED TO COMPUTE SUM SCORES Variable F 1 fam1 fam2 fam3 + fam4 + fam5 fam6 + fam7 + fam8 +: variables to be added in the corresponding factor -: variables to be reversed before to be added in the corresponding factor Ordinal Coefficient of Fidelity (O-COF) F 1 0.856 DIANA is a procedure that helps to select the optimal set of items that must be added in order to compute individuals' scores as unit-weight sum scores. The procedure aims to maximize fidelity and correlational accuracy in the context of multiple factor solutions intended for ordered-categorical responses. Ordinal Coefficient of Fidelity (O-COF) is a direct index for assessing the extent to which the raw addition of participants' responses is a good proxy for measuring the factor structure. When the factor model holds, the accuracy of the raw addition as a proxy for the true latent scores increases with the number of items and the the signal/noise ratio (i.e.increase in loadings and decrease in the residual variances). An O-COF value equal or larger than .90 would suggest an acceptable accuracy. A minimum sample of N=200 is needed in order to compute crossvlidation studies. -------------------------------------------------------------------------------- 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., Hernandez-Dorado, A., & Lorenzo-Seva, U. (2021). Detecting correlated residuals in exploratory factor analysis: new proposals and a comparison of procedures. Technical report. Universitat Rovira i Virgili, Tarragona. 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 Ferrando, P. J., & Lorenzo-Seva, U. (2021). The Appropriateness of Sum Scores as Estimates of Factor Scores in the Multiple Factor Analysis of Ordered-Categorical Responses. Educational and Psychological Measurement, 81, 205-228. doi:10.1177/0013164420938108 Ferrando, P. J., Navarro-Gonzalez, & Lorenzo-Seva U. (2019). Assessing the quality and effectiveness of the factor score estimates in psychometric factor-analytic applications. Methodology, 15, 119-127. doi:10.1027/1614-2241/a000170 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 : 324.08 minutes. Matrices generated : 1292055079 Our last advice: Distrust 5% of statistics, and 95% of statisticians. (Cal desconfiar un 5% de l'estadistica, i un 95% de l'estadistic.)