Mplus VERSION 5.1 MUTHEN & MUTHEN 05/02/2008 11:38 AM INPUT INSTRUCTIONS title: math and reading montecarlo: names = y1-y10 x; nobs = 1000; nreps = 100; model population: [x@0]; x@1; f1 by y1-y5*.8 y6-y10*0 (*1); f2 by y1-y3*0 y4-y5*.25 y6-y10*.8(*1); y1-y10*.36; [y1-y10*0]; f1-f2@1; f1 with f2*.5; f1 on x*.5; f2 on x*1; analysis: rotation = geomin; model: f1 by y1-y5*.8 y6-y10@0; f2 by y1-y5@0 y6-y10*.8; y1-y10*.36; [y1-y10*0]; f1-f2@1; f1 with f2*.5; f1 on x*.5; f2 on x*1; output: tech9; INPUT READING TERMINATED NORMALLY math and reading SUMMARY OF ANALYSIS Number of groups 1 Number of observations 1000 Number of replications Requested 100 Completed 100 Value of seed 0 Number of dependent variables 10 Number of independent variables 1 Number of continuous latent variables 2 Observed dependent variables Continuous Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Observed independent variables X Continuous latent variables F1 F2 Estimator ML Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 SAMPLE STATISTICS FOR THE FIRST REPLICATION SAMPLE STATISTICS Means Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.017 0.033 0.024 -0.011 0.040 Means Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.018 0.006 -0.008 -0.009 -0.011 Means X ________ 1 0.000 Covariances Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 1.210 Y2 0.824 1.174 Y3 0.799 0.835 1.161 Y4 1.057 1.018 1.023 1.748 Y5 0.985 1.010 0.969 1.312 1.614 Y6 0.666 0.605 0.629 0.988 0.995 Y7 0.649 0.622 0.625 0.989 0.981 Y8 0.685 0.629 0.651 1.018 1.022 Y9 0.665 0.604 0.636 1.008 1.021 Y10 0.679 0.616 0.658 1.019 1.000 X 0.423 0.365 0.401 0.634 0.613 Covariances Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 1.569 Y7 1.238 1.616 Y8 1.261 1.244 1.664 Y9 1.242 1.259 1.315 1.664 Y10 1.213 1.244 1.263 1.289 1.633 X 0.750 0.731 0.764 0.796 0.791 Covariances X ________ X 0.989 Correlations Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 1.000 Y2 0.691 1.000 Y3 0.674 0.715 1.000 Y4 0.727 0.710 0.718 1.000 Y5 0.705 0.734 0.708 0.781 1.000 Y6 0.483 0.445 0.466 0.597 0.625 Y7 0.464 0.452 0.457 0.588 0.608 Y8 0.482 0.450 0.468 0.597 0.623 Y9 0.469 0.432 0.457 0.591 0.623 Y10 0.483 0.445 0.478 0.603 0.616 X 0.387 0.339 0.374 0.482 0.485 Correlations Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 1.000 Y7 0.778 1.000 Y8 0.780 0.758 1.000 Y9 0.768 0.768 0.790 1.000 Y10 0.758 0.766 0.766 0.782 1.000 X 0.602 0.578 0.595 0.620 0.623 Correlations X ________ X 1.000 TESTS OF MODEL FIT Number of Free Parameters 33 Chi-Square Test of Model Fit Degrees of freedom 42 Mean 196.284 Std Dev 29.537 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 23.650 130.954 0.980 1.000 25.383 133.741 0.950 1.000 28.144 142.021 0.900 1.000 30.765 158.087 0.800 1.000 34.157 168.205 0.700 1.000 36.755 179.580 0.500 1.000 41.335 195.200 0.300 1.000 46.282 210.981 0.200 1.000 49.456 219.379 0.100 1.000 54.090 238.077 0.050 1.000 58.124 244.861 0.020 1.000 62.892 252.216 0.010 1.000 66.206 264.579 Loglikelihood H0 Value Mean -12761.294 Std Dev 68.732 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.980 -12921.185 -12981.634 0.980 0.980 -12902.448 -12925.447 0.950 0.950 -12874.351 -12874.915 0.900 0.900 -12849.381 -12856.435 0.800 0.760 -12819.139 -12825.584 0.700 0.730 -12797.337 -12787.691 0.500 0.480 -12761.294 -12763.567 0.300 0.260 -12725.251 -12730.270 0.200 0.180 -12703.450 -12709.688 0.100 0.130 -12673.208 -12663.375 0.050 0.030 -12648.237 -12651.779 0.020 0.020 -12620.140 -12642.994 0.010 0.010 -12601.404 -12603.758 H1 Value Mean -12663.152 Std Dev 68.348 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 -12822.149 -12874.176 0.980 0.980 -12803.518 -12814.417 0.950 0.950 -12775.577 -12780.713 0.900 0.910 -12750.746 -12753.107 0.800 0.810 -12720.674 -12720.971 0.700 0.710 -12698.994 -12697.735 0.500 0.500 -12663.152 -12664.803 0.300 0.300 -12627.311 -12627.611 0.200 0.190 -12605.631 -12606.422 0.100 0.090 -12575.558 -12577.192 0.050 0.030 -12550.727 -12567.131 0.020 0.020 -12522.787 -12533.859 0.010 0.020 -12504.155 -12501.152 Information Criteria Akaike (AIC) Mean 25588.588 Std Dev 137.463 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 25268.807 25234.238 0.980 0.980 25306.280 25273.516 0.950 0.970 25362.475 25368.530 0.900 0.870 25412.415 25389.745 0.800 0.820 25472.899 25473.928 0.700 0.740 25516.502 25525.894 0.500 0.520 25588.588 25592.324 0.300 0.270 25660.674 25637.013 0.200 0.240 25704.277 25713.241 0.100 0.100 25764.761 25754.635 0.050 0.050 25814.702 25806.291 0.020 0.020 25870.897 25846.257 0.010 0.020 25908.369 25916.894 Bayesian (BIC) Mean 25750.544 Std Dev 137.463 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 25430.763 25396.194 0.980 0.980 25468.236 25435.472 0.950 0.970 25524.431 25530.485 0.900 0.870 25574.371 25551.701 0.800 0.820 25634.855 25635.884 0.700 0.740 25678.458 25687.850 0.500 0.520 25750.544 25754.280 0.300 0.270 25822.630 25798.969 0.200 0.240 25866.233 25875.197 0.100 0.100 25926.717 25916.591 0.050 0.050 25976.658 25968.247 0.020 0.020 26032.853 26008.213 0.010 0.020 26070.325 26078.850 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 25645.734 Std Dev 137.463 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 25325.953 25291.384 0.980 0.980 25363.426 25330.662 0.950 0.970 25419.621 25425.676 0.900 0.870 25469.561 25446.892 0.800 0.820 25530.045 25531.074 0.700 0.740 25573.648 25583.040 0.500 0.520 25645.734 25649.470 0.300 0.270 25717.820 25694.159 0.200 0.240 25761.423 25770.387 0.100 0.100 25821.907 25811.781 0.050 0.050 25871.848 25863.437 0.020 0.020 25928.043 25903.403 0.010 0.020 25965.515 25974.040 RMSEA (Root Mean Square Error Of Approximation) Mean 0.060 Std Dev 0.006 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.980 0.047 0.046 0.980 0.970 0.048 0.047 0.950 0.940 0.051 0.049 0.900 0.910 0.053 0.053 0.800 0.790 0.055 0.055 0.700 0.700 0.057 0.057 0.500 0.510 0.060 0.060 0.300 0.320 0.063 0.063 0.200 0.190 0.065 0.065 0.100 0.110 0.068 0.068 0.050 0.040 0.070 0.069 0.020 0.020 0.072 0.071 0.010 0.010 0.074 0.073 SRMR (Standardized Root Mean Square Residual) Mean 0.035 Std Dev 0.003 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 0.027 0.028 0.980 0.980 0.028 0.028 0.950 0.920 0.029 0.029 0.900 0.880 0.031 0.030 0.800 0.800 0.032 0.032 0.700 0.720 0.033 0.033 0.500 0.520 0.035 0.035 0.300 0.270 0.037 0.037 0.200 0.190 0.038 0.038 0.100 0.090 0.040 0.039 0.050 0.060 0.041 0.042 0.020 0.030 0.042 0.042 0.010 0.000 0.043 0.043 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff F1 BY Y1 0.800 0.7535 0.0246 0.0250 0.0028 0.540 1.000 Y2 0.800 0.7460 0.0221 0.0249 0.0034 0.480 1.000 Y3 0.800 0.7478 0.0258 0.0250 0.0034 0.480 1.000 Y4 0.800 0.9905 0.0281 0.0282 0.0371 0.000 1.000 Y5 0.800 0.9926 0.0260 0.0282 0.0378 0.000 1.000 Y6 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y7 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y8 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y9 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y10 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 F2 BY Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y5 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Y6 0.800 0.8019 0.0219 0.0236 0.0005 0.990 1.000 Y7 0.800 0.8006 0.0230 0.0235 0.0005 0.990 1.000 Y8 0.800 0.8020 0.0245 0.0235 0.0006 0.940 1.000 Y9 0.800 0.8004 0.0246 0.0235 0.0006 0.950 1.000 Y10 0.800 0.8019 0.0229 0.0236 0.0005 0.940 1.000 F1 ON X 0.500 0.6093 0.0334 0.0366 0.0131 0.130 1.000 F2 ON X 1.000 1.0004 0.0390 0.0417 0.0015 0.960 1.000 F1 WITH F2 0.500 0.6067 0.0263 0.0236 0.0121 0.010 1.000 Intercepts Y1 0.000 -0.0002 0.0306 0.0311 0.0009 0.960 0.040 Y2 0.000 -0.0010 0.0278 0.0309 0.0008 0.970 0.030 Y3 0.000 0.0017 0.0282 0.0310 0.0008 0.980 0.020 Y4 0.000 -0.0012 0.0299 0.0365 0.0009 0.990 0.010 Y5 0.000 0.0010 0.0314 0.0365 0.0010 0.990 0.010 Y6 0.000 0.0062 0.0329 0.0317 0.0011 0.940 0.060 Y7 0.000 0.0029 0.0310 0.0316 0.0010 0.990 0.010 Y8 0.000 0.0028 0.0328 0.0317 0.0011 0.920 0.080 Y9 0.000 0.0019 0.0305 0.0316 0.0009 0.940 0.060 Y10 0.000 0.0007 0.0265 0.0317 0.0007 0.970 0.030 Residual Variances Y1 0.360 0.3959 0.0229 0.0206 0.0018 0.540 1.000 Y2 0.360 0.3965 0.0193 0.0206 0.0017 0.640 1.000 Y3 0.360 0.4008 0.0208 0.0208 0.0021 0.560 1.000 Y4 0.360 0.3490 0.0214 0.0217 0.0006 0.910 1.000 Y5 0.360 0.3440 0.0190 0.0215 0.0006 0.900 1.000 Y6 0.360 0.3612 0.0205 0.0198 0.0004 0.960 1.000 Y7 0.360 0.3570 0.0201 0.0196 0.0004 0.940 1.000 Y8 0.360 0.3582 0.0184 0.0196 0.0003 0.980 1.000 Y9 0.360 0.3587 0.0189 0.0196 0.0004 0.960 1.000 Y10 0.360 0.3615 0.0191 0.0198 0.0004 0.960 1.000 F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 TECHNICAL OUTPUT PARAMETER SPECIFICATION NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 1 2 3 4 5 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 6 7 8 9 10 NU X ________ 1 0 LAMBDA F1 F2 X ________ ________ ________ Y1 11 0 0 Y2 12 0 0 Y3 13 0 0 Y4 14 0 0 Y5 15 0 0 Y6 0 16 0 Y7 0 17 0 Y8 0 18 0 Y9 0 19 0 Y10 0 20 0 X 0 0 0 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 21 Y2 0 22 Y3 0 0 23 Y4 0 0 0 24 Y5 0 0 0 0 25 Y6 0 0 0 0 0 Y7 0 0 0 0 0 Y8 0 0 0 0 0 Y9 0 0 0 0 0 Y10 0 0 0 0 0 X 0 0 0 0 0 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 26 Y7 0 27 Y8 0 0 28 Y9 0 0 0 29 Y10 0 0 0 0 30 X 0 0 0 0 0 THETA X ________ X 0 ALPHA F1 F2 X ________ ________ ________ 1 0 0 0 BETA F1 F2 X ________ ________ ________ F1 0 0 31 F2 0 0 32 X 0 0 0 PSI F1 F2 X ________ ________ ________ F1 0 F2 33 0 X 0 0 0 STARTING VALUES NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU X ________ 1 0.000 LAMBDA F1 F2 X ________ ________ ________ Y1 0.800 0.000 0.000 Y2 0.800 0.000 0.000 Y3 0.800 0.000 0.000 Y4 0.800 0.000 0.000 Y5 0.800 0.000 0.000 Y6 0.000 0.800 0.000 Y7 0.000 0.800 0.000 Y8 0.000 0.800 0.000 Y9 0.000 0.800 0.000 Y10 0.000 0.800 0.000 X 0.000 0.000 1.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.360 Y2 0.000 0.360 Y3 0.000 0.000 0.360 Y4 0.000 0.000 0.000 0.360 Y5 0.000 0.000 0.000 0.000 0.360 Y6 0.000 0.000 0.000 0.000 0.000 Y7 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 Y9 0.000 0.000 0.000 0.000 0.000 Y10 0.000 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 0.360 Y7 0.000 0.360 Y8 0.000 0.000 0.360 Y9 0.000 0.000 0.000 0.360 Y10 0.000 0.000 0.000 0.000 0.360 X 0.000 0.000 0.000 0.000 0.000 THETA X ________ X 0.000 ALPHA F1 F2 X ________ ________ ________ 1 0.000 0.000 0.000 BETA F1 F2 X ________ ________ ________ F1 0.000 0.000 0.500 F2 0.000 0.000 1.000 X 0.000 0.000 0.000 PSI F1 F2 X ________ ________ ________ F1 1.000 F2 0.500 1.000 X 0.000 0.000 0.989 POPULATION VALUES NU Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU X ________ 1 0.000 LAMBDA F1 F2 X ________ ________ ________ Y1 0.800 0.000 0.000 Y2 0.800 0.000 0.000 Y3 0.800 0.000 0.000 Y4 0.800 0.250 0.000 Y5 0.800 0.250 0.000 Y6 0.000 0.800 0.000 Y7 0.000 0.800 0.000 Y8 0.000 0.800 0.000 Y9 0.000 0.800 0.000 Y10 0.000 0.800 0.000 X 0.000 0.000 1.000 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 0.360 Y2 0.000 0.360 Y3 0.000 0.000 0.360 Y4 0.000 0.000 0.000 0.360 Y5 0.000 0.000 0.000 0.000 0.360 Y6 0.000 0.000 0.000 0.000 0.000 Y7 0.000 0.000 0.000 0.000 0.000 Y8 0.000 0.000 0.000 0.000 0.000 Y9 0.000 0.000 0.000 0.000 0.000 Y10 0.000 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 THETA Y6 Y7 Y8 Y9 Y10 ________ ________ ________ ________ ________ Y6 0.360 Y7 0.000 0.360 Y8 0.000 0.000 0.360 Y9 0.000 0.000 0.000 0.360 Y10 0.000 0.000 0.000 0.000 0.360 X 0.000 0.000 0.000 0.000 0.000 THETA X ________ X 0.000 ALPHA F1 F2 X ________ ________ ________ 1 0.000 0.000 0.000 BETA F1 F2 X ________ ________ ________ F1 0.000 0.000 0.500 F2 0.000 0.000 1.000 X 0.000 0.000 0.000 PSI F1 F2 X ________ ________ ________ F1 1.000 F2 0.500 1.000 X 0.000 0.000 1.000 TECHNICAL 9 OUTPUT Error messages for each replication (if any) Beginning Time: 11:38:51 Ending Time: 11:38:55 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