Mplus VERSION 7.11 MUTHEN & MUTHEN 01/20/2014 10:47 AM INPUT INSTRUCTIONS TITLE: Kapitel 6, Abschnitt 6.5.4, Modell tau-äquivalenter Variablen für die sechs logarithmierten Reaktionszeitvariablen, Maximum-Likelihood-Schätzung !Einlesen der Daten DATA: FILE IS daten-kapitel-6.dat; VARIABLE: !Variablen im Datensatz NAMES ARE gender item1-item6; !Variablen in der Analyse USEVARIABLES ARE item1-item6; !Code für fehlende Werte MISSING ARE ALL (-999); ANALYSIS: !Maximum-Likelihood-Schätzung TYPE IS general; ESTIMATOR IS MLR; ITERATIONS = 1000; CONVERGENCE = 0.00005; Model: !Definition des Modells, erste Ladung durch Voreinstellung auf 1 fixiert; !weitere Ladungen auf 1 fixiert mit @1 eta by item1 item2@1 item3@1 item4@1 item5@1 item6@1; ! Fixierung der Leichtigkeitsparameter auf 0 [item1-item6@0]; ! Schätzung des Erwartungswertes von eta [eta]; !Anforderung der geschätzten Mittelwerte, Kovarianzen und Korrelationsn (sampstat), !der standardisierten Lösungen (stdyx) und der Konfidenzintervalle (cinterval) !und der vom Modell implizierten Kovarianzmatrix (residual) OUTPUT: sampstat stdyx cinterval residual; INPUT READING TERMINATED NORMALLY Kapitel 6, Abschnitt 6.5.4, Modell tau-äquivalenter Variablen für die sechs logarithmierten Reaktionszeitvariablen, Maximum-Likelihood-Schätzung SUMMARY OF ANALYSIS Number of groups 1 Number of observations 238 Number of dependent variables 6 Number of independent variables 0 Number of continuous latent variables 1 Observed dependent variables Continuous ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ITEM6 Continuous latent variables ETA Estimator MLR Information matrix OBSERVED 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 Input data file(s) daten-kapitel-6.dat Input data format FREE SUMMARY OF DATA Number of missing data patterns 1 COVARIANCE COVERAGE OF DATA Minimum covariance coverage value 0.100 PROPORTION OF DATA PRESENT Covariance Coverage ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 1.000 ITEM2 1.000 1.000 ITEM3 1.000 1.000 1.000 ITEM4 1.000 1.000 1.000 1.000 ITEM5 1.000 1.000 1.000 1.000 1.000 ITEM6 1.000 1.000 1.000 1.000 1.000 Covariance Coverage ITEM6 ________ ITEM6 1.000 SAMPLE STATISTICS ESTIMATED SAMPLE STATISTICS Means ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ 1 1.504 1.423 1.392 1.305 1.346 Means ITEM6 ________ 1 1.306 Covariances ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 0.128 ITEM2 0.063 0.135 ITEM3 0.064 0.067 0.153 ITEM4 0.067 0.070 0.081 0.165 ITEM5 0.045 0.065 0.066 0.072 0.141 ITEM6 0.057 0.056 0.065 0.075 0.054 Covariances ITEM6 ________ ITEM6 0.146 Correlations ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 1.000 ITEM2 0.481 1.000 ITEM3 0.453 0.463 1.000 ITEM4 0.457 0.465 0.510 1.000 ITEM5 0.331 0.473 0.446 0.471 1.000 ITEM6 0.413 0.400 0.433 0.485 0.379 Correlations ITEM6 ________ ITEM6 1.000 MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -427.396 THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 8 Loglikelihood H0 Value -477.454 H0 Scaling Correction Factor 1.1816 for MLR H1 Value -427.396 H1 Scaling Correction Factor 1.0867 for MLR Information Criteria Akaike (AIC) 970.908 Bayesian (BIC) 998.686 Sample-Size Adjusted BIC 973.329 (n* = (n + 2) / 24) Chi-Square Test of Model Fit Value 95.652* Degrees of Freedom 19 P-Value 0.0000 Scaling Correction Factor 1.0467 for MLR * 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 0.130 90 Percent C.I. 0.105 0.157 Probability RMSEA <= .05 0.000 CFI/TLI CFI 0.813 TLI 0.852 Chi-Square Test of Model Fit for the Baseline Model Value 424.389 Degrees of Freedom 15 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.163 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value ETA BY ITEM1 1.000 0.000 999.000 999.000 ITEM2 1.000 0.000 999.000 999.000 ITEM3 1.000 0.000 999.000 999.000 ITEM4 1.000 0.000 999.000 999.000 ITEM5 1.000 0.000 999.000 999.000 ITEM6 1.000 0.000 999.000 999.000 Means ETA 1.381 0.019 72.678 0.000 Intercepts ITEM1 0.000 0.000 999.000 999.000 ITEM2 0.000 0.000 999.000 999.000 ITEM3 0.000 0.000 999.000 999.000 ITEM4 0.000 0.000 999.000 999.000 ITEM5 0.000 0.000 999.000 999.000 ITEM6 0.000 0.000 999.000 999.000 Variances ETA 0.064 0.011 5.763 0.000 Residual Variances ITEM1 0.093 0.011 8.286 0.000 ITEM2 0.073 0.008 8.723 0.000 ITEM3 0.081 0.009 9.271 0.000 ITEM4 0.092 0.009 10.397 0.000 ITEM5 0.085 0.009 9.143 0.000 ITEM6 0.095 0.009 10.494 0.000 STANDARDIZED MODEL RESULTS STDYX Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value ETA BY ITEM1 0.637 0.039 16.314 0.000 ITEM2 0.683 0.038 17.820 0.000 ITEM3 0.663 0.040 16.659 0.000 ITEM4 0.639 0.039 16.464 0.000 ITEM5 0.655 0.039 16.979 0.000 ITEM6 0.634 0.038 16.523 0.000 Means ETA 5.471 0.513 10.666 0.000 Intercepts ITEM1 0.000 0.000 999.000 999.000 ITEM2 0.000 0.000 999.000 999.000 ITEM3 0.000 0.000 999.000 999.000 ITEM4 0.000 0.000 999.000 999.000 ITEM5 0.000 0.000 999.000 999.000 ITEM6 0.000 0.000 999.000 999.000 Variances ETA 1.000 0.000 999.000 999.000 Residual Variances ITEM1 0.594 0.050 11.952 0.000 ITEM2 0.534 0.052 10.198 0.000 ITEM3 0.560 0.053 10.599 0.000 ITEM4 0.592 0.050 11.925 0.000 ITEM5 0.571 0.051 11.285 0.000 ITEM6 0.598 0.049 12.268 0.000 R-SQUARE Observed Two-Tailed Variable Estimate S.E. Est./S.E. P-Value ITEM1 0.406 0.050 8.157 0.000 ITEM2 0.466 0.052 8.910 0.000 ITEM3 0.440 0.053 8.329 0.000 ITEM4 0.408 0.050 8.232 0.000 ITEM5 0.429 0.051 8.489 0.000 ITEM6 0.402 0.049 8.261 0.000 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.146E+00 (ratio of smallest to largest eigenvalue) CONFIDENCE INTERVALS OF MODEL RESULTS Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5% ETA BY ITEM1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 ITEM2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 ITEM3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 ITEM4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 ITEM5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 ITEM6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Means ETA 1.332 1.344 1.350 1.381 1.412 1.418 1.430 Intercepts ITEM1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Variances ETA 0.035 0.042 0.046 0.064 0.082 0.085 0.092 Residual Variances ITEM1 0.064 0.071 0.075 0.093 0.112 0.115 0.122 ITEM2 0.051 0.057 0.059 0.073 0.087 0.089 0.094 ITEM3 0.059 0.064 0.067 0.081 0.095 0.098 0.104 ITEM4 0.069 0.075 0.078 0.092 0.107 0.110 0.115 ITEM5 0.061 0.067 0.069 0.085 0.100 0.103 0.109 ITEM6 0.071 0.077 0.080 0.095 0.109 0.112 0.118 CONFIDENCE INTERVALS OF STANDARDIZED MODEL RESULTS STDYX Standardization Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5% ETA BY ITEM1 0.536 0.560 0.573 0.637 0.701 0.713 0.737 ITEM2 0.584 0.608 0.620 0.683 0.746 0.758 0.782 ITEM3 0.561 0.585 0.598 0.663 0.729 0.741 0.766 ITEM4 0.539 0.563 0.575 0.639 0.703 0.715 0.739 ITEM5 0.556 0.580 0.592 0.655 0.719 0.731 0.755 ITEM6 0.535 0.559 0.571 0.634 0.698 0.710 0.733 Means ETA 4.150 4.466 4.627 5.471 6.315 6.477 6.793 Intercepts ITEM1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ITEM6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Variances ETA 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Residual Variances ITEM1 0.466 0.497 0.513 0.594 0.676 0.692 0.722 ITEM2 0.399 0.431 0.448 0.534 0.620 0.636 0.668 ITEM3 0.424 0.456 0.473 0.560 0.647 0.663 0.696 ITEM4 0.464 0.494 0.510 0.592 0.673 0.689 0.719 ITEM5 0.440 0.472 0.488 0.571 0.654 0.670 0.701 ITEM6 0.472 0.502 0.517 0.598 0.678 0.693 0.723 RESIDUAL OUTPUT ESTIMATED MODEL AND RESIDUALS (OBSERVED - ESTIMATED) Model Estimated Means/Intercepts/Thresholds ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ 1 1.381 1.381 1.381 1.381 1.381 Model Estimated Means/Intercepts/Thresholds ITEM6 ________ 1 1.381 Residuals for Means/Intercepts/Thresholds ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ 1 0.123 0.042 0.011 -0.076 -0.035 Residuals for Means/Intercepts/Thresholds ITEM6 ________ 1 -0.075 Standardized Residuals (z-scores) for Means/Intercepts/Thresholds ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ 1 9.212 2.907 0.665 -4.173 -2.266 Standardized Residuals (z-scores) for Means/Intercepts/Thresholds ITEM6 ________ 1 -4.725 Normalized Residuals for Means/Intercepts/Thresholds ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ 1 5.297 1.758 0.441 -2.893 -1.420 Normalized Residuals for Means/Intercepts/Thresholds ITEM6 ________ 1 -3.036 Model Estimated Covariances/Correlations/Residual Correlations ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 0.157 ITEM2 0.064 0.137 ITEM3 0.064 0.064 0.145 ITEM4 0.064 0.064 0.064 0.156 ITEM5 0.064 0.064 0.064 0.064 0.148 ITEM6 0.064 0.064 0.064 0.064 0.064 Model Estimated Covariances/Correlations/Residual Correlations ITEM6 ________ ITEM6 0.158 Residuals for Covariances/Correlations/Residual Correlations ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 -0.029 ITEM2 0.000 -0.001 ITEM3 0.000 0.003 0.008 ITEM4 0.003 0.006 0.017 0.009 ITEM5 -0.019 0.002 0.002 0.008 -0.007 ITEM6 -0.007 -0.007 0.001 0.012 -0.009 Residuals for Covariances/Correlations/Residual Correlations ITEM6 ________ ITEM6 -0.012 Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 999.000 ITEM2 -0.039 -0.204 ITEM3 -0.014 0.378 1.049 ITEM4 0.334 0.686 1.614 0.773 ITEM5 -3.161 0.330 0.259 0.946 -1.718 ITEM6 -1.424 -1.077 0.157 1.609 -1.912 Standardized Residuals (z-scores) for Covariances/Correlations/Residual Corr ITEM6 ________ ITEM6 -4.553 Normalized Residuals for Covariances/Correlations/Residual Correlations ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ________ ________ ________ ________ ________ ITEM1 -2.059 ITEM2 -0.020 -0.079 ITEM3 -0.008 0.217 0.545 ITEM4 0.209 0.424 1.130 0.517 ITEM5 -1.513 0.143 0.148 0.588 -0.465 ITEM6 -0.586 -0.566 0.085 0.888 -0.765 Normalized Residuals for Covariances/Correlations/Residual Correlations ITEM6 ________ ITEM6 -0.850 DIAGRAM INFORMATION Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram. If running Mplus from the Mplus Diagrammer, the diagram opens automatically. Diagram output c:\users\eid\documents\lehrbuch-testtheorie\kapitel\kapitel 6 - ktt\daten\lehrbuch\tau-äquivalen Beginning Time: 10:47:27 Ending Time: 10:47:27 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