Mplus VERSION 5.1 MUTHEN & MUTHEN 05/02/2008 11:33 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(.0001); model: 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; output: tech9; *** WARNING in MODEL command Values given in the MODEL command for EFA factors are used only as population values in computing coverage. EFA factors cannot be given starting values. 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS 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 EFA factors *1: F1 F2 Estimator ML Rotation GEOMIN Row standardization CORRELATION Type of rotation OBLIQUE Epsilon value Varies Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 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 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 41 Chi-Square Test of Model Fit Degrees of freedom 34 Mean 35.048 Std Dev 8.635 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.980 17.789 13.466 0.980 0.970 19.275 17.434 0.950 0.950 21.664 21.621 0.900 0.910 23.952 22.876 0.800 0.850 26.938 28.050 0.700 0.790 29.242 30.703 0.500 0.540 33.336 34.060 0.300 0.350 37.795 38.480 0.200 0.230 40.676 40.912 0.100 0.120 44.903 45.725 0.050 0.090 48.602 52.238 0.020 0.040 52.995 55.487 0.010 0.020 56.061 57.195 Loglikelihood H0 Value Mean -12680.676 Std Dev 68.341 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 -12839.659 -12892.723 0.980 0.980 -12821.029 -12829.533 0.950 0.940 -12793.091 -12800.380 0.900 0.920 -12768.263 -12767.370 0.800 0.810 -12738.192 -12740.357 0.700 0.700 -12716.515 -12718.175 0.500 0.490 -12680.676 -12682.012 0.300 0.310 -12644.838 -12643.173 0.200 0.210 -12623.160 -12621.844 0.100 0.090 -12593.090 -12598.127 0.050 0.030 -12568.262 -12583.833 0.020 0.020 -12540.324 -12554.220 0.010 0.020 -12521.694 -12516.704 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 25443.353 Std Dev 136.682 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.980 25125.388 25108.959 0.980 0.980 25162.648 25115.408 0.950 0.970 25218.524 25230.543 0.900 0.910 25268.181 25263.938 0.800 0.790 25328.321 25313.707 0.700 0.690 25371.677 25368.085 0.500 0.510 25443.353 25445.670 0.300 0.300 25515.029 25512.693 0.200 0.190 25558.385 25547.621 0.100 0.080 25618.525 25612.937 0.050 0.060 25668.182 25670.548 0.020 0.020 25724.058 25711.274 0.010 0.010 25761.317 25741.066 Bayesian (BIC) Mean 25644.571 Std Dev 136.682 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.980 25326.606 25310.177 0.980 0.980 25363.866 25316.626 0.950 0.970 25419.742 25431.761 0.900 0.910 25469.399 25465.156 0.800 0.790 25529.539 25514.925 0.700 0.690 25572.894 25569.303 0.500 0.510 25644.571 25646.888 0.300 0.300 25716.247 25713.911 0.200 0.190 25759.603 25748.839 0.100 0.080 25819.743 25814.155 0.050 0.060 25869.400 25871.765 0.020 0.020 25925.275 25912.492 0.010 0.010 25962.535 25942.284 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 25514.352 Std Dev 136.682 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.980 25196.388 25179.959 0.980 0.980 25233.648 25186.408 0.950 0.970 25289.523 25301.543 0.900 0.910 25339.180 25334.938 0.800 0.790 25399.321 25384.706 0.700 0.690 25442.676 25439.085 0.500 0.510 25514.352 25516.670 0.300 0.300 25586.029 25583.693 0.200 0.190 25629.384 25618.621 0.100 0.080 25689.525 25683.936 0.050 0.060 25739.181 25741.547 0.020 0.020 25795.057 25782.274 0.010 0.010 25832.317 25812.065 RMSEA (Root Mean Square Error Of Approximation) Mean 0.007 Std Dev 0.008 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 -0.012 0.000 0.980 1.000 -0.010 0.000 0.950 1.000 -0.006 0.000 0.900 1.000 -0.003 0.000 0.800 0.510 0.000 0.000 0.700 0.490 0.003 0.000 0.500 0.460 0.007 0.001 0.300 0.320 0.011 0.011 0.200 0.230 0.014 0.014 0.100 0.120 0.017 0.019 0.050 0.090 0.020 0.023 0.020 0.040 0.024 0.025 0.010 0.020 0.026 0.026 SRMR (Standardized Root Mean Square Residual) Mean 0.006 Std Dev 0.001 Number of successful computations 100 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 0.004 0.004 0.980 0.970 0.004 0.004 0.950 0.950 0.004 0.004 0.900 0.930 0.005 0.005 0.800 0.810 0.005 0.005 0.700 0.720 0.005 0.005 0.500 0.500 0.006 0.006 0.300 0.270 0.006 0.006 0.200 0.150 0.006 0.006 0.100 0.100 0.007 0.007 0.050 0.070 0.007 0.007 0.020 0.030 0.007 0.008 0.010 0.020 0.008 0.008 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff F1 BY Y1 0.800 0.8108 0.0309 0.0298 0.0011 0.900 1.000 Y2 0.800 0.8045 0.0273 0.0298 0.0008 0.970 1.000 Y3 0.800 0.8069 0.0294 0.0303 0.0009 0.950 1.000 Y4 0.800 0.8074 0.0332 0.0324 0.0011 0.950 1.000 Y5 0.800 0.8133 0.0287 0.0324 0.0010 0.950 1.000 Y6 0.000 0.0011 0.0201 0.0231 0.0004 1.000 0.000 Y7 0.000 0.0033 0.0228 0.0232 0.0005 0.970 0.030 Y8 0.000 -0.0008 0.0195 0.0237 0.0004 1.000 0.000 Y9 0.000 0.0018 0.0219 0.0241 0.0005 1.000 0.000 Y10 0.000 0.0010 0.0220 0.0244 0.0005 0.970 0.030 F2 BY Y1 0.000 -0.0108 0.0157 0.0164 0.0004 0.950 0.050 Y2 0.000 -0.0122 0.0179 0.0167 0.0005 0.960 0.040 Y3 0.000 -0.0130 0.0146 0.0181 0.0004 0.970 0.030 Y4 0.250 0.2375 0.0259 0.0253 0.0008 0.910 1.000 Y5 0.250 0.2335 0.0230 0.0253 0.0008 0.890 1.000 Y6 0.800 0.8014 0.0243 0.0269 0.0006 0.980 1.000 Y7 0.800 0.7989 0.0271 0.0269 0.0007 0.970 1.000 Y8 0.800 0.8025 0.0261 0.0270 0.0007 0.960 1.000 Y9 0.800 0.7994 0.0257 0.0271 0.0007 0.990 1.000 Y10 0.800 0.8016 0.0259 0.0272 0.0007 0.970 1.000 F1 ON X 0.500 0.5169 0.0359 0.0374 0.0016 0.940 1.000 F2 ON X 1.000 1.0003 0.0387 0.0417 0.0015 0.970 1.000 F1 WITH F2 0.500 0.5131 0.0299 0.0299 0.0011 0.930 1.000 Intercepts Y1 0.000 0.0001 0.0307 0.0318 0.0009 0.960 0.040 Y2 0.000 -0.0007 0.0279 0.0316 0.0008 0.980 0.020 Y3 0.000 0.0019 0.0283 0.0317 0.0008 0.980 0.020 Y4 0.000 -0.0015 0.0297 0.0356 0.0009 0.990 0.010 Y5 0.000 0.0007 0.0313 0.0356 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 0.980 0.020 Residual Variances Y1 0.360 0.3583 0.0229 0.0203 0.0005 0.900 1.000 Y2 0.360 0.3589 0.0178 0.0202 0.0003 0.990 1.000 Y3 0.360 0.3631 0.0215 0.0204 0.0005 0.920 1.000 Y4 0.360 0.3602 0.0204 0.0204 0.0004 0.980 1.000 Y5 0.360 0.3565 0.0189 0.0203 0.0004 0.940 1.000 Y6 0.360 0.3610 0.0207 0.0199 0.0004 0.950 1.000 Y7 0.360 0.3568 0.0206 0.0197 0.0004 0.940 1.000 Y8 0.360 0.3575 0.0193 0.0198 0.0004 0.970 1.000 Y9 0.360 0.3586 0.0192 0.0198 0.0004 0.970 1.000 Y10 0.360 0.3607 0.0190 0.0199 0.0004 0.950 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 TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION 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 13 0 Y3 14 15 0 Y4 16 17 0 Y5 18 19 0 Y6 20 21 0 Y7 22 23 0 Y8 24 25 0 Y9 26 27 0 Y10 28 29 0 X 0 0 0 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 30 Y2 0 31 Y3 0 0 32 Y4 0 0 0 33 Y5 0 0 0 0 34 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 35 Y7 0 36 Y8 0 0 37 Y9 0 0 0 38 Y10 0 0 0 0 39 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 40 F2 0 0 41 X 0 0 0 PSI F1 F2 X ________ ________ ________ F1 0 F2 0 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 1.000 0.000 0.000 Y2 1.000 1.000 0.000 Y3 1.000 1.000 0.000 Y4 1.000 1.000 0.000 Y5 1.000 1.000 0.000 Y6 1.000 1.000 0.000 Y7 1.000 1.000 0.000 Y8 1.000 1.000 0.000 Y9 1.000 1.000 0.000 Y10 1.000 1.000 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 0.000 F2 0.000 0.000 0.000 X 0.000 0.000 0.000 PSI F1 F2 X ________ ________ ________ F1 1.000 F2 0.000 1.000 X 0.000 0.000 0.989 TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION 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 12 0 Y2 13 14 0 Y3 15 16 0 Y4 17 18 0 Y5 19 20 0 Y6 21 22 0 Y7 23 24 0 Y8 25 26 0 Y9 27 28 0 Y10 29 30 0 X 0 0 0 THETA Y1 Y2 Y3 Y4 Y5 ________ ________ ________ ________ ________ Y1 31 Y2 0 32 Y3 0 0 33 Y4 0 0 0 34 Y5 0 0 0 0 35 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 36 Y7 0 37 Y8 0 0 38 Y9 0 0 0 39 Y10 0 0 0 0 40 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 41 F2 0 0 42 X 0 0 0 PSI F1 F2 X ________ ________ ________ F1 0 F2 43 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 0.000 0.000 0.000 Y2 0.000 0.000 0.000 Y3 0.000 0.000 0.000 Y4 0.000 0.000 0.000 Y5 0.000 0.000 0.000 Y6 0.000 0.000 0.000 Y7 0.000 0.000 0.000 Y8 0.000 0.000 0.000 Y9 0.000 0.000 0.000 Y10 0.000 0.000 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 0.000 F2 0.000 0.000 0.000 X 0.000 0.000 0.000 PSI F1 F2 X ________ ________ ________ F1 1.000 F2 0.000 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: 11:33:03 Ending Time: 11:33:10 Elapsed Time: 00:00:07 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) 1998-2008 Muthen & Muthen