------------------------------------------------------------------------------ Module: HLM2 (6.02) beta Date: Apr 8, 2007 Time: 16:13:07 ------------------------------------------------------------------------------ SPECIFICATIONS FOR THIS HLM2 RUN Problem Title: HSB Test Run The data source for this run = hsb.mdm The command file for this run = hsb2.hlm Output file name = hsb2.out The maximum number of level-1 units = 7185 The maximum number of level-2 units = 160 The maximum number of iterations = 10000 Method of estimation: restricted maximum likelihood Weighting Specification ----------------------- Weight Variable Weighting? Name Normalized? Level 1 no Level 2 no Precision no The outcome variable is MATHACH The model specified for the fixed effects was: ---------------------------------------------------- Level-1 Level-2 Coefficients Predictors ---------------------- --------------- INTRCPT1, P0 INTRCPT2, B00 SIZE, B01 SECTOR, B02 PRACAD, B03 DISCLIM, B04 HIMINTY, B05 MEANSES, B06 MINORITY slope, P1 INTRCPT2, B10 MEANSES, B11 FEMALE slope, P2 INTRCPT2, B20 SES slope, P3 INTRCPT2, B30 The model specified for the covariance components was: --------------------------------------------------------- Sigma squared (constant across level-2 units) Tau dimensions INTRCPT1 MINORITY slope FEMALE slope SES slope Summary of the model specified (in equation format) --------------------------------------------------- Level-1 Model Y = P0 + P1*(MINORITY) + P2*(FEMALE) + P3*(SES) + E Level-2 Model P0 = B00 + B01*(SIZE) + B02*(SECTOR) + B03*(PRACAD) + B04*(DISCLIM) + B05*(HIMINTY) + B06*(MEANSES) + R0 P1 = B10 + B11*(MEANSES) + R1 P2 = B20 + R2 P3 = B30 + R3 Level-1 OLS regressions ----------------------- Level-2 Unit INTRCPT1 MINORITY slope FEMALE slope SES slope ------------------------------------------------------------------------------ 1224 12.88837 -8.72320 -3.00562 1.47322 1288 13.13595 -2.86801 0.88435 2.71298 1296 3.68352 5.55066 -1.69086 0.91791 1358 12.71682 -9.79049 -1.27271 3.29899 1374 14.61781 -9.02146 -4.15738 4.69677 1461 15.12214 -14.59908 -2.15309 5.02255 1477 14.47103 -2.04262 -0.70881 1.10533 1499 11.38238 -1.14141 -2.72635 3.28197 1637 11.38385 -5.72649 1.14472 1.42944 1906 15.86644 -6.55063 -0.14539 1.58082 1942 18.39507 3.93531 -0.76990 0.00718 1946 15.17617 0.83960 -4.60835 2.32094 2030 12.82329 -4.65172 -2.03053 1.26642 2336 16.29077 -2.34600 -1.07352 1.76492 2651 12.32996 -10.03662 -2.24700 4.56499 2655 18.16462 -1.62049 -1.78118 4.91515 2658 13.38279 -4.50024 -0.14349 2.27966 2768 12.36121 -0.67624 -2.57544 3.43239 2771 13.00544 -5.68321 0.84731 4.38749 2818 13.55908 -7.91136 0.32069 3.07492 2917 12.14963 -3.45691 -0.58637 0.75215 2995 10.12892 -2.59219 0.62552 1.24235 3013 13.79718 -3.24295 -2.67720 3.74017 3020 11.53764 4.60530 2.31981 1.82947 3088 11.09933 -4.15447 1.50350 0.66226 3152 16.01987 -8.14401 -4.37024 2.73188 3351 13.86428 -5.35666 -3.24809 1.36244 3377 16.36091 -8.51383 -0.96219 -1.68981 3498 17.33048 2.66100 -1.57425 -0.64891 3499 12.37106 -3.54362 3.24877 0.78556 3533 12.79854 3.61345 -6.15679 0.74443 3610 16.58700 -5.32759 -0.04092 3.06448 3657 14.27364 -8.77334 -4.58575 3.03900 3705 11.59262 -1.89983 -0.80432 0.51642 3716 16.85466 -6.45861 -3.02639 2.94512 3838 19.01786 -4.56115 -2.14001 -0.72970 3881 12.79013 -2.42405 -2.10043 2.48980 3992 14.74265 -2.00270 2.09161 -0.15627 3999 13.54926 -0.96520 -3.06988 3.37556 4173 11.40096 -4.94679 2.26871 3.56679 4223 16.46848 -5.64280 -2.88747 0.64848 4325 14.01049 -3.05302 -0.90354 2.79614 4350 10.93757 -3.31002 2.80923 4.02091 4383 11.87494 -6.41160 1.85825 5.27633 4410 12.92005 -9.39056 1.46549 2.55018 4458 8.73051 -4.58847 2.13116 0.50478 4642 13.41793 -3.56849 1.49576 3.38554 4868 13.05559 -1.31663 -1.51716 0.90358 4931 14.36383 -1.04703 -1.39688 1.02054 5192 9.00632 -4.16223 4.75153 1.59667 5650 17.32040 -0.34652 -3.89645 1.42390 5667 14.06678 -2.18997 -3.73188 3.20867 5762 3.20930 0.27142 -0.59594 -1.01489 5783 14.31243 -5.99058 -0.60481 3.68980 5815 10.74973 -5.52168 -1.39972 0.71449 5819 10.48287 4.32041 2.11336 2.34876 5838 14.71684 0.38488 -2.25714 1.73120 5937 15.78978 1.11355 0.25386 1.25426 6144 9.12493 -2.84884 2.37051 2.45701 6170 20.64922 -3.66727 -6.95095 5.37772 6291 11.54370 2.25090 -1.16181 4.43117 6366 16.93971 -6.44883 -1.02016 0.60245 6397 16.49556 -7.64551 -2.68666 0.73414 6415 13.05422 -1.18275 -0.94067 3.53766 6443 12.63114 -3.64933 -3.14245 -0.78597 6484 11.63579 2.07449 2.61320 1.81044 6600 12.37246 -1.08530 -0.74606 4.54761 6808 13.94602 -8.60601 -0.93080 0.24561 6897 15.47831 -4.33792 -0.91258 2.73547 7101 14.22990 -5.15046 -2.79721 0.93585 7172 10.94054 -1.66862 -2.08552 0.95269 7232 12.27518 2.15008 0.82336 5.05623 7276 15.86575 -4.87348 -3.69557 2.46480 7332 14.63723 -2.60102 -0.49457 2.34882 7341 12.59138 -3.23137 -3.03007 1.18889 7345 11.43293 -3.11582 1.21856 3.28354 7734 16.55851 -4.68646 -3.26943 4.58013 7890 10.29672 -7.00504 -2.83069 -0.12097 7919 13.68655 -5.58454 -1.42601 4.21916 8150 15.11294 0.06102 -0.32629 -0.19120 8175 11.23230 1.64290 -0.51640 1.91866 8188 13.22259 -8.58005 0.51702 4.09525 8202 15.58239 -5.25087 -5.48752 1.93566 8357 17.43193 -12.36157 -4.19796 2.42443 8367 6.30552 -7.35045 -1.39566 -0.18924 8477 16.46047 -4.96967 -4.05192 3.25521 8531 14.05027 -5.34267 -0.75967 2.32063 8627 11.96501 -5.83366 -0.33154 0.56723 8707 15.31459 -3.77534 -3.03113 2.52059 8775 11.29478 -2.76850 -1.93067 0.50142 8854 5.45731 -3.48431 1.38175 1.71559 8857 14.58393 -1.27697 2.22294 0.47696 8874 16.97175 -4.86043 -3.25148 3.71173 8946 10.61667 -2.83682 0.94746 1.71079 8983 12.95794 0.24637 -3.87840 1.01310 9021 13.48506 -0.98294 -0.40850 2.42748 9158 10.65990 -4.46631 0.67245 3.15646 9225 14.44196 -1.20139 -0.66526 2.88900 9397 10.47056 -1.83032 -0.37548 2.49213 9550 14.67396 -5.30508 -4.08475 3.56372 Note: OLS level-1 coefficients were computed for only 100 of 160 units that had sufficient data for estimation. The average OLS level-1 coefficient for INTRCPT1 = 13.33135 The average OLS level-1 coefficient for MINORITY = -3.54937 The average OLS level-1 coefficient for FEMALE = -1.13536 The average OLS level-1 coefficient for SES = 2.12135 Least Squares Estimates ----------------------- sigma_squared = 37.19769 The outcome variable is MATHACH Least-squares estimates of fixed effects ---------------------------------------------------------------------------- Standard Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 INTRCPT2, B00 11.397729 0.330313 34.506 7174 0.000 SIZE, B01 0.000745 0.000137 5.430 7174 0.000 SECTOR, B02 0.908063 0.240171 3.781 7174 0.000 PRACAD, B03 2.955812 0.508380 5.814 7174 0.000 DISCLIM, B04 -0.397820 0.115643 -3.440 7174 0.001 HIMINTY, B05 0.223078 0.213489 1.045 7174 0.297 MEANSES, B06 0.826200 0.332430 2.485 7174 0.013 For MINORITY slope, P1 INTRCPT2, B10 -2.998499 0.204010 -14.698 7174 0.000 MEANSES, B11 0.573145 0.385210 1.488 7174 0.137 For FEMALE slope, P2 INTRCPT2, B20 -1.380475 0.146621 -9.415 7174 0.000 For SES slope, P3 INTRCPT2, B30 1.896921 0.110324 17.194 7174 0.000 ---------------------------------------------------------------------------- The outcome variable is MATHACH Least-squares estimates of fixed effects (with robust standard errors) ---------------------------------------------------------------------------- Standard Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 INTRCPT2, B00 11.397729 0.497628 22.904 7174 0.000 SIZE, B01 0.000745 0.000207 3.608 7174 0.001 SECTOR, B02 0.908063 0.386897 2.347 7174 0.019 PRACAD, B03 2.955812 0.802595 3.683 7174 0.000 DISCLIM, B04 -0.397820 0.175445 -2.267 7174 0.023 HIMINTY, B05 0.223078 0.338110 0.660 7174 0.509 MEANSES, B06 0.826200 0.505788 1.633 7174 0.102 For MINORITY slope, P1 INTRCPT2, B10 -2.998499 0.259447 -11.557 7174 0.000 MEANSES, B11 0.573145 0.532360 1.077 7174 0.282 For FEMALE slope, P2 INTRCPT2, B20 -1.380475 0.184559 -7.480 7174 0.000 For SES slope, P3 INTRCPT2, B30 1.896921 0.119825 15.831 7174 0.000 ---------------------------------------------------------------------------- The least-squares likelihood value = -23197.286990 Deviance = 46394.57398 Number of estimated parameters = 1 STARTING VALUES --------------- sigma(0)_squared = 36.84749 Tau(0) INTRCPT1,P0 1.88855 -0.30386 -0.39837 0.72288 MINORITY,P1 -0.30386 0.05339 0.47160 -1.29283 FEMALE,P2 -0.39837 0.47160 0.28720 -0.24458 SES,P3 0.72288 -1.29283 -0.24458 0.12509 New Tau(0) INTRCPT1,P0 0.88904 0.00000 0.00000 0.00000 MINORITY,P1 0.00000 1.72247 0.00000 0.00000 FEMALE,P2 0.00000 0.00000 0.61890 0.00000 SES,P3 0.00000 0.00000 0.00000 0.31767 The outcome variable is MATHACH Estimation of fixed effects (Based on starting values of covariance components) ---------------------------------------------------------------------------- Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 INTRCPT2, B00 11.065970 0.500713 22.100 153 0.000 SIZE, B01 0.000834 0.000217 3.844 153 0.000 SECTOR, B02 0.709992 0.387666 1.831 153 0.069 PRACAD, B03 3.489798 0.816094 4.276 153 0.000 DISCLIM, B04 -0.314844 0.184513 -1.706 153 0.090 HIMINTY, B05 0.106282 0.327024 0.325 153 0.745 MEANSES, B06 0.930889 0.478509 1.945 153 0.053 For MINORITY slope, P1 INTRCPT2, B10 -3.022149 0.250536 -12.063 158 0.000 MEANSES, B11 0.564135 0.549972 1.026 158 0.307 For FEMALE slope, P2 INTRCPT2, B20 -1.272227 0.173960 -7.313 159 0.000 For SES slope, P3 INTRCPT2, B30 1.887756 0.120088 15.720 159 0.000 ---------------------------------------------------------------------------- The value of the likelihood function at iteration 1 = -2.314454E+04 The value of the likelihood function at iteration 2 = -2.314145E+04 The value of the likelihood function at iteration 3 = -2.314074E+04 The value of the likelihood function at iteration 4 = -2.314010E+04 The value of the likelihood function at iteration 5 = -2.313699E+04 . . . The value of the likelihood function at iteration 139 = -2.313453E+04 The value of the likelihood function at iteration 140 = -2.313453E+04 The value of the likelihood function at iteration 141 = -2.313452E+04 The value of the likelihood function at iteration 142 = -2.313452E+04 Iterations stopped due to small change in likelihood function ******* ITERATION 143 ******* Sigma_squared = 35.40322 Tau INTRCPT1,P0 2.00682 -0.33163 -0.90802 0.17487 MINORITY,P1 -0.33163 1.67183 0.00448 -0.47877 FEMALE,P2 -0.90802 0.00448 0.77170 -0.05665 SES,P3 0.17487 -0.47877 -0.05665 0.25730 Tau (as correlations) INTRCPT1,P0 1.000 -0.181 -0.730 0.243 MINORITY,P1 -0.181 1.000 0.004 -0.730 FEMALE,P2 -0.730 0.004 1.000 -0.127 SES,P3 0.243 -0.730 -0.127 1.000 ---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, P0 0.424 MINORITY, P1 0.171 FEMALE, P2 0.174 SES, P3 0.115 ---------------------------------------------------- Note: The reliability estimates reported above are based on only 100 of 160 units that had sufficient data for computation. Fixed effects and variance components are based on all the data. The value of the likelihood function at iteration 143 = -2.313452E+04 The outcome variable is MATHACH Final estimation of fixed effects: ---------------------------------------------------------------------------- Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 INTRCPT2, B00 11.497138 0.515999 22.281 153 0.000 SIZE, B01 0.000717 0.000217 3.301 153 0.002 SECTOR, B02 0.768588 0.389205 1.975 153 0.050 PRACAD, B03 2.737844 0.823421 3.325 153 0.001 DISCLIM, B04 -0.416875 0.181134 -2.301 153 0.023 HIMINTY, B05 0.185546 0.320490 0.579 153 0.563 MEANSES, B06 1.181854 0.488146 2.421 153 0.017 For MINORITY slope, P1 INTRCPT2, B10 -3.062986 0.245144 -12.495 158 0.000 MEANSES, B11 0.549953 0.540388 1.018 158 0.311 For FEMALE slope, P2 INTRCPT2, B20 -1.277340 0.174893 -7.304 159 0.000 For SES slope, P3 INTRCPT2, B30 1.882698 0.116236 16.197 159 0.000 ---------------------------------------------------------------------------- The outcome variable is MATHACH Final estimation of fixed effects (with robust standard errors) ---------------------------------------------------------------------------- Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 INTRCPT2, B00 11.497138 0.567242 20.269 153 0.000 SIZE, B01 0.000717 0.000224 3.199 153 0.002 SECTOR, B02 0.768588 0.403215 1.906 153 0.058 PRACAD, B03 2.737844 0.863233 3.172 153 0.002 DISCLIM, B04 -0.416875 0.180677 -2.307 153 0.022 HIMINTY, B05 0.185546 0.327519 0.567 153 0.571 MEANSES, B06 1.181854 0.538289 2.196 153 0.029 For MINORITY slope, P1 INTRCPT2, B10 -3.062986 0.248605 -12.321 158 0.000 MEANSES, B11 0.549953 0.483768 1.137 158 0.258 For FEMALE slope, P2 INTRCPT2, B20 -1.277340 0.174062 -7.338 159 0.000 For SES slope, P3 INTRCPT2, B30 1.882698 0.119258 15.787 159 0.000 ---------------------------------------------------------------------------- Final estimation of variance components: ----------------------------------------------------------------------------- Random Effect Standard Variance df Chi-square P-value Deviation Component ----------------------------------------------------------------------------- INTRCPT1, R0 1.41662 2.00682 93 174.19371 0.000 MINORITY slope, R1 1.29299 1.67183 98 122.68809 0.046 FEMALE slope, R2 0.87847 0.77170 99 121.94876 0.059 SES slope, R3 0.50725 0.25730 99 113.40223 0.153 level-1, E 5.95006 35.40322 ----------------------------------------------------------------------------- Note: The chi-square statistics reported above are based on only 100 of 160 units that had sufficient data for computation. Fixed effects and variance components are based on all the data. Statistics for current covariance components model -------------------------------------------------- Deviance = 46269.048876 Number of estimated parameters = 11