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Module: HLM2 (6.02) beta
Date: Apr 8, 2007
Time: 16:13:07
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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
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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
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Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
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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
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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
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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)
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Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
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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
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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:
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Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
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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
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Final estimation of variance components:
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Random Effect Standard Variance df Chi-square P-value
Deviation Component
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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
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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
