Mplus VERSION 7.11 MUTHEN & MUTHEN 01/22/2014 10:38 PM INPUT INSTRUCTIONS TITLE: Kapitel 7, Abschnitt 7.4 Beispiel zur Faktorenanalyse für ordinale Variablen DATA: FILE IS kapitel_7_beispiel_exploratorische_faktorenanalyse.dat; VARIABLE: NAMES ARE zufrieden gut munter wohl wach frisch; USEVARIABLES ARE zufrieden gut munter wohl wach frisch; MISSING ARE ALL (9); ! Auswahl der kategorialen Variablen mit geordneten Antwortkategorien CATEGORICAL ARE zufrieden gut munter wohl wach frisch; ANALYSIS: ! exploratorische Faktorenanalyse mit Auswahl von 1 bis 3 Faktoren wird durchgeführt TYPE IS EFA 1 3; ESTIMATOR IS WLSMV; ITERATIONS = 1000; CONVERGENCE = 0.00005; Rotation=oblimin; OUTPUT: SAMPSTAT; *** WARNING in VARIABLE command Note that only the first 8 characters of variable names are used in the output. Shorten variable names to avoid any confusion. 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS Kapitel 7, Abschnitt 7.4 Beispiel zur Faktorenanalyse für ordinale Variablen SUMMARY OF ANALYSIS Number of groups 1 Number of observations 482 Number of dependent variables 6 Number of independent variables 0 Number of continuous latent variables 0 Observed dependent variables Binary and ordered categorical (ordinal) ZUFRIEDE GUT MUNTER WOHL WACH FRISCH Estimator WLSMV Rotation OBLIMIN Row standardization CORRELATION Type of rotation OBLIQUE Gamma value 0.000D+00 Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Maximum number of iterations for H1 2000 Convergence criterion for H1 0.100D-03 Optimization Specifications for the Exploratory Factor Analysis Rotation Algorithm Number of random starts 30 Maximum number of iterations 10000 Derivative convergence criterion 0.100D-04 Input data file(s) kapitel_7_beispiel_exploratorische_faktorenanalyse.dat Input data format FREE SUMMARY OF DATA Number of missing data patterns 2 COVARIANCE COVERAGE OF DATA Minimum covariance coverage value 0.100 ! Anteil der verfügbaren Daten (ohne fehlende Werte) PROPORTION OF DATA PRESENT Covariance Coverage ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ ZUFRIEDE 1.000 GUT 0.998 0.998 MUNTER 1.000 0.998 1.000 WOHL 0.998 0.998 0.998 0.998 WACH 0.998 0.998 0.998 0.998 0.998 FRISCH 0.998 0.998 0.998 0.998 0.998 Covariance Coverage FRISCH ________ FRISCH 0.998 ! Univariate Häufigkeitsverteilungen UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES ZUFRIEDE Category 1 0.004 2.000 Category 2 0.077 37.000 Category 3 0.280 135.000 Category 4 0.488 235.000 Category 5 0.151 73.000 GUT Category 1 0.004 2.000 Category 2 0.037 18.000 Category 3 0.206 99.000 Category 4 0.593 285.000 Category 5 0.160 77.000 MUNTER Category 1 0.010 5.000 Category 2 0.108 52.000 Category 3 0.280 135.000 Category 4 0.454 219.000 Category 5 0.147 71.000 WOHL Category 1 0.006 3.000 Category 2 0.042 20.000 Category 3 0.227 109.000 Category 4 0.541 260.000 Category 5 0.185 89.000 WACH Category 1 0.006 3.000 Category 2 0.119 57.000 Category 3 0.370 178.000 Category 4 0.407 196.000 Category 5 0.098 47.000 FRISCH Category 1 0.015 7.000 Category 2 0.127 61.000 Category 3 0.374 180.000 Category 4 0.424 204.000 Category 5 0.060 29.000 SAMPLE STATISTICS ! geschätzte Schwellenparameter ESTIMATED SAMPLE STATISTICS MEANS/INTERCEPTS/THRESHOLDS ZUFRIEDE ZUFRIEDE ZUFRIEDE ZUFRIEDE GUT$1 ________ ________ ________ ________ ________ 1 -2.640 -1.399 -0.356 1.030 -2.639 MEANS/INTERCEPTS/THRESHOLDS GUT$2 GUT$3 GUT$4 MUNTER$1 MUNTER$2 ________ ________ ________ ________ ________ 1 -1.733 -0.683 0.994 -2.313 -1.184 MEANS/INTERCEPTS/THRESHOLDS MUNTER$3 MUNTER$4 WOHL$1 WOHL$2 WOHL$3 ________ ________ ________ ________ ________ 1 -0.258 1.048 -2.498 -1.666 -0.599 MEANS/INTERCEPTS/THRESHOLDS WOHL$4 WACH$1 WACH$2 WACH$3 WACH$4 ________ ________ ________ ________ ________ 1 0.896 -2.498 -1.152 -0.013 1.295 MEANS/INTERCEPTS/THRESHOLDS FRISCH$1 FRISCH$2 FRISCH$3 FRISCH$4 ________ ________ ________ ________ 1 -2.182 -1.074 0.039 1.552 ! Geschätzte polychorischen Korrelationen CORRELATION MATRIX (WITH VARIANCES ON THE DIAGONAL) ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ ZUFRIEDE GUT 0.709 MUNTER 0.430 0.496 WOHL 0.695 0.778 0.498 WACH 0.314 0.423 0.593 0.452 FRISCH 0.509 0.573 0.646 0.582 0.701 CORRELATION MATRIX (WITH VARIANCES ON THE DIAGONAL) FRISCH ________ ! modellgütekoeffizienten SUMMARY OF MODEL FIT INFORMATION Number of Degrees of Model Parameters Chi-Square Freedom P-Value ! Das Ein-Faktor-Modell muss verworfen werden 1-factor 6 266.937 9 0.0000 ! Das Zwei-Faktoren-Modell passt gut auf die daten 2-factor 11 4.480 4 0.3449 ! das Drei-Faktoren-Modell hat 0 Freiheitsgrade, es ist das saturierte Modell und ! passt perfekt auf die Daten, der p-Wert von 0 ist irreführend 3-factor 15 0.000 0 0.0000 ! Modell-Vergleiche Degrees of Models Compared Chi-Square Freedom P-Value ! Ein-Faktor-Modell passt signifikant schlechter als das Zwei-Faktoren-Modell 1-factor against 2-factor 203.888 5 0.0000 ! Zwei-Faktoren-Modell passt nicht signifikant schlechter als das Drei-Faktoren-Modell 2-factor against 3-factor 4.813 4 0.3070 ! Eigenwerte, Knick im Eigenwertverlauf zwischen dem zweiten und dritten Eigenwert ! legt das Zwei-Faktoren-Modell nahe RESULTS FOR EXPLORATORY FACTOR ANALYSIS EIGENVALUES FOR SAMPLE CORRELATION MATRIX 1 2 3 4 5 ________ ________ ________ ________ ________ 1 3.813 0.977 0.415 0.317 0.258 EIGENVALUES FOR SAMPLE CORRELATION MATRIX 6 ________ 1 0.221 ! Lösung für Ein-Faktor-Modell EXPLORATORY FACTOR ANALYSIS WITH 1 FACTOR(S): MODEL FIT INFORMATION Number of Free Parameters 6 Chi-Square Test of Model Fit Value 266.937* Degrees of Freedom 9 P-Value 0.0000 * The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-square difference testing in the regular way. MLM, MLR and WLSM chi-square difference testing is described on the Mplus website. MLMV, WLSMV, and ULSMV difference testing is done using the DIFFTEST option. RMSEA (Root Mean Square Error Of Approximation) Estimate 0.244 90 Percent C.I. 0.219 0.269 Probability RMSEA <= .05 0.000 CFI/TLI CFI 0.940 TLI 0.900 Chi-Square Test of Model Fit for the Baseline Model Value 4317.584 Degrees of Freedom 15 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.097 MINIMUM ROTATION FUNCTION VALUE 0.00000 OBLIMIN ROTATED LOADINGS (* significant at 5% level) 1 ________ ZUFRIEDE 0.747* GUT 0.843* MUNTER 0.690* WOHL 0.849* WACH 0.693* FRISCH 0.826* OBLIMIN FACTOR CORRELATIONS (* significant at 5% level) 1 ________ 1 1.000 ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 0.442 0.289 0.524 0.279 0.520 ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 0.317 S.E. OBLIMIN ROTATED LOADINGS 1 ________ ZUFRIEDE 0.020 GUT 0.016 MUNTER 0.025 WOHL 0.018 WACH 0.026 FRISCH 0.019 S.E. OBLIMIN FACTOR CORRELATIONS 1 ________ 1 0.000 S.E. ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 0.030 0.027 0.034 0.031 0.036 S.E. ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 0.031 Est./S.E. OBLIMIN ROTATED LOADINGS 1 ________ ZUFRIEDE 36.950 GUT 53.398 MUNTER 27.969 WOHL 46.312 WACH 26.411 FRISCH 43.937 Est./S.E. OBLIMIN FACTOR CORRELATIONS 1 ________ 1 0.000 Est./S.E. ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 14.639 10.849 15.398 8.961 14.292 Est./S.E. ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 10.218 ! Lösung für Ein-Faktor-Modell EXPLORATORY FACTOR ANALYSIS WITH 2 FACTOR(S): MODEL FIT INFORMATION Number of Free Parameters 11 ! Modellgütekoeffizienten zeigen an, dass das Modell passt Chi-Square Test of Model Fit Value 4.480* Degrees of Freedom 4 P-Value 0.3449 * The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-square difference testing in the regular way. MLM, MLR and WLSM chi-square difference testing is described on the Mplus website. MLMV, WLSMV, and ULSMV difference testing is done using the DIFFTEST option. RMSEA (Root Mean Square Error Of Approximation) Estimate 0.016 90 Percent C.I. 0.000 0.072 Probability RMSEA <= .05 0.788 CFI/TLI CFI 1.000 TLI 1.000 Chi-Square Test of Model Fit for the Baseline Model Value 4317.584 Degrees of Freedom 15 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.009 MINIMUM ROTATION FUNCTION VALUE 0.01843 ! Ladungen der oblimin rotierten Lösung OBLIMIN ROTATED LOADINGS (* significant at 5% level) 1 2 ________ ________ ZUFRIEDE 0.832* -0.048 GUT 0.879* 0.016 MUNTER 0.140* 0.643* WOHL 0.829* 0.065 WACH -0.114* 0.897* FRISCH 0.152* 0.767* ! Korrelation der Faktoren OBLIMIN FACTOR CORRELATIONS (* significant at 5% level) 1 2 ________ ________ 1 1.000 2 0.640* 1.000 ! Residualvarianzen ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 0.357 0.209 0.453 0.238 0.313 ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 0.240 ! Standardfehler S.E. OBLIMIN ROTATED LOADINGS 1 2 ________ ________ ZUFRIEDE 0.031 0.035 GUT 0.030 0.032 MUNTER 0.045 0.039 WOHL 0.041 0.039 WACH 0.011 0.026 FRISCH 0.061 0.053 S.E. OBLIMIN FACTOR CORRELATIONS 1 2 ________ ________ 1 0.000 2 0.039 0.000 S.E. ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 0.031 0.029 0.035 0.038 0.046 S.E. ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 0.033 Est./S.E. OBLIMIN ROTATED LOADINGS 1 2 ________ ________ ZUFRIEDE 26.691 -1.377 GUT 29.694 0.499 MUNTER 3.139 16.596 WOHL 20.180 1.665 WACH -10.251 34.133 FRISCH 2.514 14.526 Est./S.E. OBLIMIN FACTOR CORRELATIONS 1 2 ________ ________ 1 0.000 2 16.480 0.000 Est./S.E. ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 11.618 7.152 12.843 6.302 6.761 Est./S.E. ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 7.237 ! Korrelationen der Items mit den Faktoren FACTOR STRUCTURE 1 2 ________ ________ ZUFRIEDE 0.801 0.484 GUT 0.890 0.579 MUNTER 0.551 0.732 WOHL 0.871 0.596 WACH 0.460 0.824 FRISCH 0.643 0.864 ! Lösung für Drei-Faktor-Modell EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S): MODEL FIT INFORMATION Number of Free Parameters 15 Chi-Square Test of Model Fit Value 0.000* Degrees of Freedom 0 P-Value 0.0000 * The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-square difference testing in the regular way. MLM, MLR and WLSM chi-square difference testing is described on the Mplus website. MLMV, WLSMV, and ULSMV difference testing is done using the DIFFTEST option. RMSEA (Root Mean Square Error Of Approximation) Estimate 0.000 90 Percent C.I. 0.752 0.791 Probability RMSEA <= .05 0.000 CFI/TLI CFI 1.000 TLI 1.000 Chi-Square Test of Model Fit for the Baseline Model Value 4317.584 Degrees of Freedom 15 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.001 MINIMUM ROTATION FUNCTION VALUE 0.03523 OBLIMIN ROTATED LOADINGS (* significant at 5% level) 1 2 3 ________ ________ ________ ZUFRIEDE 0.734 0.006 0.207 GUT 0.868 0.021 -0.007 MUNTER 0.089 0.669* 0.079 WOHL 0.910 0.013 -0.103 WACH -0.058 0.879* -0.139 FRISCH 0.067 0.820* 0.128 OBLIMIN FACTOR CORRELATIONS (* significant at 5% level) 1 2 3 ________ ________ ________ 1 1.000 2 0.649* 1.000 3 0.344 -0.005 1.000 ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 0.308 0.226 0.456 0.211 0.263 ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 0.231 S.E. OBLIMIN ROTATED LOADINGS 1 2 3 ________ ________ ________ ZUFRIEDE 1.520 0.643 2.663 GUT 1.108 0.804 0.999 MUNTER 0.193 0.121 0.597 WOHL 0.981 0.392 0.785 WACH 0.406 0.080 1.247 FRISCH 0.110 0.234 1.134 S.E. OBLIMIN FACTOR CORRELATIONS 1 2 3 ________ ________ ________ 1 0.000 2 0.176 0.000 3 1.285 1.986 0.000 S.E. ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 1.001 0.439 0.089 0.690 1.150 S.E. ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 0.146 Est./S.E. OBLIMIN ROTATED LOADINGS 1 2 3 ________ ________ ________ ZUFRIEDE 0.483 0.010 0.078 GUT 0.783 0.026 -0.007 MUNTER 0.463 5.524 0.133 WOHL 0.927 0.033 -0.132 WACH -0.142 11.027 -0.111 FRISCH 0.605 3.511 0.113 Est./S.E. OBLIMIN FACTOR CORRELATIONS 1 2 3 ________ ________ ________ 1 0.000 2 3.683 0.000 3 0.267 -0.003 0.000 Est./S.E. ESTIMATED RESIDUAL VARIANCES ZUFRIEDE GUT MUNTER WOHL WACH ________ ________ ________ ________ ________ 1 0.307 0.515 5.096 0.305 0.229 Est./S.E. ESTIMATED RESIDUAL VARIANCES FRISCH ________ 1 1.582 FACTOR STRUCTURE 1 2 3 ________ ________ ________ ZUFRIEDE 0.809 0.482 0.459 GUT 0.879 0.585 0.291 MUNTER 0.551 0.727 0.107 WOHL 0.883 0.604 0.209 WACH 0.466 0.843 -0.163 FRISCH 0.643 0.863 0.146 DIAGRAM INFORMATION Mplus diagrams are currently not available for EFA. No diagram output was produced. Beginning Time: 22:38:25 Ending Time: 22:38:25 Elapsed Time: 00:00:00 MUTHEN & MUTHEN 3463 Stoner Ave. Los Angeles, CA 90066 Tel: (310) 391-9971 Fax: (310) 391-8971 Web: www.StatModel.com Support: Support@StatModel.com Copyright (c) 1998-2013 Muthen & Muthen