HLM Statistical Output File

------------------------------------------------------------------------------
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
------------------------------------------------------------------------------
       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