# HLM Statistical Output File

```------------------------------------------------------------------------------
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
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
```