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Stata Textbook Examples
Introduction to Multilevel Modeling by Kreft and de Leeuw
Chapter 4: Analyses

use http://www.ats.ucla.edu/stat/examples/imm/imm23, clear

describe
 
Contains data from imm23.dta
  obs:           519                          
 vars:            18                          19 Mar 2002 10:39
 size:        39,444 (99.8% of memory free)
-------------------------------------------------------------------------------
              storage  display     value
variable name   type   format      label      variable label
-------------------------------------------------------------------------------
schid           float  %9.0g                  School ID
stuid           float  %9.0g                  Student ID
ses             float  %9.0g                  Socioecnonomic Status
meanses         float  %9.0g                  Mean SES for the school
homework        float  %9.0g                  Time spent on math homework
                                                each week
white           float  %9.0g                  Race: 1=white, 0=non-white
parented        float  %9.0g                  Parents highest education level
public          float  %9.0g                  Public school: 1=public,
                                                0=non-public
ratio           float  %9.0g                  Student-Teacher ratio
percmin         float  %9.0g                  Percent minority in school
math            float  %9.0g                  Math score
sex             float  %9.0g                  Sex: 1=male, 2=female
race            float  %9.0g                  race of student, 1=asian,
                                                2=Hispanic, 3=Black, 4=White,
                                                5=Native American
sctype          float  %9.0g                  Type of school, 1=public,
                                                2=catholic, 3=Private other
                                                religious, 4=Private non-r
cstr            float  %9.0g                  
scsize          float  %9.0g                  
urban           float  %9.0g                  
region          float  %9.0g                  
-------------------------------------------------------------------------------
Sorted by:  schid  stuid
Page 64, 4.2.2, The Null Model, Model 0.
xtmixed math || schid:, variance

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1899.3393  
Iteration 1:   log restricted-likelihood = -1899.3393  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1899.3393          Prob > chi2        =         .

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   50.75885   1.151181    44.09   0.000     48.50258    53.01513
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Identity              |
                  var(_cons) |   26.12419   8.987209      13.31109    51.27103
-----------------------------+------------------------------------------------
               var(Residual) |   81.24387   5.153894      71.74516    92.00015
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =   134.06 Prob >= chibar2 = 0.0000

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1899.339      3     3804.679    3817.434
------------------------------------------------------------------------------
Page 65, 4.2.3 'Homework and 'MathAchievement', Model 1.
xtmixed math homework || schid:, variance

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1864.6598  
Iteration 1:   log restricted-likelihood = -1864.6598  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(1)       =     74.95
Log restricted-likelihood = -1864.6598          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   2.399867   .2771976     8.66   0.000     1.856569    2.943164
       _cons |   46.35575   1.162776    39.87   0.000     44.07676    48.63475
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Identity              |
                  var(_cons) |   21.34157   7.574593      10.64428    42.78943
-----------------------------+------------------------------------------------
               var(Residual) |   71.28374   4.530462      62.93498    80.74002
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =    96.43 Prob >= chibar2 = 0.0000

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .    -1864.66      4      3737.32    3754.327
------------------------------------------------------------------------------
Pages 66 and 67, 4.2.4 Random slope for 'Homework', model 2.
xtmixed math homework || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood =  -1817.781  
Iteration 1:   log restricted-likelihood =  -1817.781  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(1)       =      4.55
Log restricted-likelihood =  -1817.781          Prob > chi2        =    0.0329

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.980164   .9284474     2.13   0.033     .1604405    3.799888
       _cons |   46.32561   1.758932    26.34   0.000     42.87816    49.77305
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   17.72647   6.260262      8.871821    35.41863
                  var(_cons) |   62.42438   21.38146      31.90087    122.1535
         cov(homework,_cons) |  -27.59383   10.56622     -48.30324   -6.884415
-----------------------------+------------------------------------------------
               var(Residual) |   53.29463   3.465963      46.91659    60.53973
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   190.19   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1817.781      6     3647.562    3673.074
------------------------------------------------------------------------------
Page 69, 4.2.5 Adding 'ParentEducation', model 3.
xtmixed math homework parented || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1800.0217  
Iteration 1:   log restricted-likelihood = -1800.0217  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(2)       =     44.61
Log restricted-likelihood = -1800.0217          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.881702    .830247     2.27   0.023     .2544478    3.508956
    parented |   1.841414   .2959197     6.22   0.000     1.261422    2.421406
       _cons |   40.85465   1.790225    22.82   0.000     37.34588    44.36343
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |    13.8786   5.039229      6.812086    28.27557
                  var(_cons) |   47.86951   17.01638      23.84947    96.08136
         cov(homework,_cons) |  -21.95137   8.502263      -38.6155   -5.287237
-----------------------------+------------------------------------------------
               var(Residual) |   50.77825   3.311781      44.68502    57.70234
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   119.94   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1800.022      7     3614.043    3643.807
------------------------------------------------------------------------------
Page 70 and 71, 4.2.6 Traditional regression model.
xtmixed math homework parented , variance 

Mixed-effects REML regression                   Number of obs      =       519

                                                Wald chi2(2)       =    264.49
Log restricted-likelihood = -1859.9932          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   2.335361   .2683967     8.70   0.000     1.809313    2.861409
    parented |   3.003987   .2765059    10.86   0.000     2.462046    3.545929
       _cons |   37.23915   .9962789    37.38   0.000     35.28648    39.19182
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
               var(Residual) |   76.11628   4.725077      67.39652    85.96421
------------------------------------------------------------------------------

estat ic


------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1859.993      4     3727.986    3744.994
------------------------------------------------------------------------------

/* using the regress command */

regress math homework parented 

      Source |       SS       df       MS              Number of obs =     519
-------------+------------------------------           F(  2,   516) =  132.25
       Model |  20132.0446     2  10066.0223           Prob > F      =  0.0000
    Residual |  39276.0016   516  76.1162822           R-squared     =  0.3389
-------------+------------------------------           Adj R-squared =  0.3363
       Total |  59408.0462   518  114.687348           Root MSE      =  8.7245

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   2.335361   .2683967     8.70   0.000     1.808077    2.862646
    parented |   3.003987   .2765059    10.86   0.000     2.460771    3.547203
       _cons |   37.23915   .9962789    37.38   0.000     35.28189    39.19641
------------------------------------------------------------------------------
Page 73/74, 4.3.2 A model with 'SchoolSize' (Model 2).
xtmixed math homework scsize || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1817.1153  
Iteration 1:   log restricted-likelihood = -1817.1153  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(2)       =      5.02
Log restricted-likelihood = -1817.1153          Prob > chi2        =    0.0812

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.981179   .9298449     2.13   0.033     .1587166    3.803642
      scsize |   .4259322   .6409595     0.66   0.506    -.8303253     1.68219
       _cons |   44.97198   2.710876    16.59   0.000     39.65876     50.2852
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   17.78479   6.281797      8.900087    35.53883
                  var(_cons) |   66.42771   23.33067      33.37269    132.2231
         cov(homework,_cons) |  -28.75128   11.07166     -50.45133   -7.051229
-----------------------------+------------------------------------------------
               var(Residual) |    53.3058   3.467273      46.92541    60.55372
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   189.33   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1817.115      7     3648.231    3677.994
------------------------------------------------------------------------------
Page 74/75, 4.3.3 Changing 'SchoolSize' to 'Public' (Model 3).
xtmixed math homework public || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood =  -1814.194  
Iteration 1:   log restricted-likelihood =  -1814.194  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(2)       =      8.92
Log restricted-likelihood =  -1814.194          Prob > chi2        =    0.0116

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |    1.97527   .9184314     2.15   0.031     .1751778    3.775363
      public |  -4.060999   1.977904    -2.05   0.040     -7.93762   -.1843776
       _cons |   49.05035   2.184881    22.45   0.000     44.76807    53.33264
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   17.31097   6.113316      8.664078    34.58762
                  var(_cons) |   60.17005   20.89702      30.46202    118.8508
         cov(homework,_cons) |  -27.45916   10.38128      -47.8061   -7.112219
-----------------------------+------------------------------------------------
               var(Residual) |   53.34333   3.471559      46.95527    60.60046
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   157.64   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1814.194      7     3642.388    3672.151
------------------------------------------------------------------------------
Page 77, 4.3.4 Adding a cross level interaction with 'Public',  (Model 4).
generate homewrkXpublic = homework*public
 
xtmixed math homework public homewrkXpublic || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1812.5753  
Iteration 1:   log restricted-likelihood = -1812.5753  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(3)       =      8.72
Log restricted-likelihood = -1812.5753          Prob > chi2        =    0.0333

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   2.292791   1.591376     1.44   0.150    -.8262482    5.411831
      public |  -3.261944   3.714642    -0.88   0.380    -10.54251    4.018621
homewrkXpu~c |  -.4956655   1.972783    -0.25   0.802    -4.362249    3.370918
       _cons |   48.52887   3.016064    16.09   0.000      42.6175    54.44025
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   18.25189   6.551994      9.031228    36.88663
                  var(_cons) |   62.55576   22.05624       31.3434      124.85
         cov(homework,_cons) |  -28.95327   11.08199     -50.67357   -7.232962
-----------------------------+------------------------------------------------
               var(Residual) |   53.33265   3.470174      46.94705    60.58679
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   159.63   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1812.575      8     3641.151    3675.166
------------------------------------------------------------------------------
Page 80, 4.3.5 Model 4 will full NELS-88 data (we don't have these data, so this is omitted).

Page 80/82, 4.3.6 Deleting 'HomePublic' and adding 'White' (Model 5).
xtmixed math homework public white || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1807.7266  
Iteration 1:   log restricted-likelihood = -1807.7266  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(3)       =     21.73
Log restricted-likelihood = -1807.7266          Prob > chi2        =    0.0001

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.899176   .9050575     2.10   0.036      .125296    3.673056
      public |  -3.882385   1.798686    -2.16   0.031    -7.407744   -.3570262
       white |   3.309409   .9698517     3.41   0.001     1.408534    5.210283
       _cons |   46.62829   2.192207    21.27   0.000     42.33164    50.92493
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   16.77652   5.931869      8.389431    33.54834
                  var(_cons) |   56.03024   19.63033      28.19694    111.3379
         cov(homework,_cons) |  -26.81495   10.00251     -46.41951   -7.210387
-----------------------------+------------------------------------------------
               var(Residual) |   52.72817   3.436984      46.40436    59.91377
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   133.03   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1807.727      8     3631.453    3665.468
------------------------------------------------------------------------------
Page 82/83, 4.3.7 Adding a random part for 'White' (Model 6).
xtmixed math homework public white || schid: homework white, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood =  -1805.255  
Iteration 1:   log restricted-likelihood = -1805.2505  
Iteration 2:   log restricted-likelihood = -1805.2505  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(3)       =     15.98
Log restricted-likelihood = -1805.2505          Prob > chi2        =    0.0011

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.940045   .9004501     2.15   0.031     .1751951    3.704894
      public |  -4.929207   1.650688    -2.99   0.003    -8.164497   -1.693917
       white |   2.598035   1.553804     1.67   0.095    -.4473641    5.643434
       _cons |   48.22768   2.340021    20.61   0.000     43.64132    52.81403
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   16.63131   5.874699      8.322529    33.23514
                  var(white) |   26.50044   22.54574      5.001239    140.4199
                  var(_cons) |   69.16463   31.24256      28.53549     167.642
         cov(homework,white) |   2.923541   7.944215     -12.64683    18.49392
         cov(homework,_cons) |  -28.54352   12.26504     -52.58255   -4.504491
            cov(white,_cons) |  -22.08364   20.96947     -63.18305    19.01577
-----------------------------+------------------------------------------------
               var(Residual) |   51.15698   3.384706       44.9352    58.24023
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(6) =   137.98   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1805.251     11     3632.501    3679.272
------------------------------------------------------------------------------
Page 85, 4.3.8 Making the coefficient of 'White' fixed and adding 'MeanSES' (Model 7).
xtmixed math homework public white meanses || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1803.2599  
Iteration 1:   log restricted-likelihood = -1803.2599  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(4)       =     31.50
Log restricted-likelihood = -1803.2599          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.924179   .8964219     2.15   0.032     .1672248    3.681134
      public |   .1604258   2.270945     0.07   0.944    -4.290545    4.611396
       white |   3.096913   .9630887     3.22   0.001     1.209294    4.984532
     meanses |   4.977274   1.950878     2.55   0.011     1.153624    8.800924
       _cons |   44.61584   2.235094    19.96   0.000     40.23513    48.99654
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   16.44364   5.821773       8.21552    32.91249
                  var(_cons) |   54.13689   19.09921      27.11402    108.0918
         cov(homework,_cons) |   -27.0358   9.902771     -46.44487   -7.626721
-----------------------------+------------------------------------------------
               var(Residual) |   52.79435   3.444721      46.45669    59.99659
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   109.59   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .    -1803.26      9      3624.52    3662.787
------------------------------------------------------------------------------
Page 86, 4.3.9 Deleting the school characteristic 'Public' (Model 8).
xtmixed math homework white meanses || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1804.9907  
Iteration 1:   log restricted-likelihood = -1804.9907  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(3)       =     32.52
Log restricted-likelihood = -1804.9907          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.925085   .8951596     2.15   0.032     .1706048    3.679566
       white |   3.114922   .9570099     3.25   0.001     1.239217    4.990627
     meanses |   4.892483   1.340592     3.65   0.000     2.264971    7.519995
       _cons |    44.7022   1.787226    25.01   0.000      41.1993     48.2051
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   16.39899   5.804124      8.195013     32.8159
                  var(_cons) |   53.57389   18.91041       26.8224    107.0061
         cov(homework,_cons) |  -26.99907   9.864397     -46.33293   -7.665203
-----------------------------+------------------------------------------------
               var(Residual) |   52.79042   3.444296      46.45353    59.99175
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   108.55   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1804.991      8     3625.981    3659.997
------------------------------------------------------------------------------
Page 87/88, 4.3.10 Adding an interaction between 'HomeWork' and 'MeanSES' (Model 9).
generate homewrkXmeanses = homework*meanses

xtmixed math homework white meanses homewrkXmeanses || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1803.5271  
Iteration 1:   log restricted-likelihood = -1803.5271  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(4)       =     32.31
Log restricted-likelihood = -1803.5271          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.974678   .9291318     2.13   0.034     .1536126    3.795742
       white |   3.115026   .9571186     3.25   0.001     1.239108    4.990944
     meanses |   3.977613   3.022684     1.32   0.188    -1.946739    9.901965
homewrkXme~s |   .5530935    1.64573     0.34   0.737    -2.672479    3.778666
       _cons |   44.61137   1.836096    24.30   0.000     41.01268    48.21005
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   17.23849   6.210693      8.508005    34.92775
                  var(_cons) |   55.88547   20.01922       27.6938    112.7756
         cov(homework,_cons) |  -28.38963   10.52383     -49.01596   -7.763291
-----------------------------+------------------------------------------------
               var(Residual) |   52.78088   3.443055       46.4462    59.97952
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   111.28   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1803.527      9     3625.054    3663.321
------------------------------------------------------------------------------
Page 88/89, 4.3.11 Adding another student-level variable (Model 10).
xtmixed math homework white meanses ses || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1796.3777  
Iteration 1:   log restricted-likelihood = -1796.3777  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(4)       =     50.25
Log restricted-likelihood = -1796.3777          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.825613   .8504767     2.15   0.032     .1587094    3.492517
       white |   2.170787   .9732755     2.23   0.026     .2632017    4.078372
     meanses |   2.945142   1.428078     2.06   0.039     .1461609    5.744123
         ses |   2.205733   .5356316     4.12   0.000     1.155914    3.255551
       _cons |   45.67481   1.752034    26.07   0.000     42.24089    49.10874
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   14.64975   5.247581      7.259843    29.56194
                  var(_cons) |   49.89752   17.73365      24.86341    100.1376
         cov(homework,_cons) |  -24.37951   9.046941     -42.11119   -6.647832
-----------------------------+------------------------------------------------
               var(Residual) |   51.29601   3.350503      45.13211    58.30175
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   103.65   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1796.378      9     3610.755    3649.023
------------------------------------------------------------------------------
Page 88/89, 4.3.12: Analyses with NELS-88 (we don't have these data, so these analyses are omitted).
Page 91, 4.4.1 'SES' as a student-level explanatory variable (Model 1).
xtmixed math ses || schid:, variance

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1873.0887  
Iteration 1:   log restricted-likelihood = -1873.0887  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(1)       =     58.53
Log restricted-likelihood = -1873.0887          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ses |   4.332311   .5662715     7.65   0.000     3.222439    5.442182
       _cons |   51.20085   .8507325    60.18   0.000     49.53345    52.86826
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Identity              |
                  var(_cons) |    12.6317   5.015357      5.800912      27.506
-----------------------------+------------------------------------------------
               var(Residual) |   75.32781    4.78723      66.50585    85.32001
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =    43.58 Prob >= chibar2 = 0.0000

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1873.089      4     3754.177    3771.185
------------------------------------------------------------------------------
Page 92, 4.4.2 Adding a random slope (Model 2). Model never converged.
set maxiter 100

xtmixed math ses || schid: ses, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1873.3707  
Iteration 1:   log restricted-likelihood = -1873.0375  

[output omitted]

Iteration 99:  log restricted-likelihood = -1872.9972  (not concave)
Iteration 100: log restricted-likelihood = -1872.9972  (not concave)
convergence not achieved

Computing standard errors:
standard error calculation failed

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(1)       =     58.02
Log restricted-likelihood = -1872.9972          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ses |    4.32386   .5676435     7.62   0.000     3.211299    5.436421
       _cons |   51.24839   .8562642    59.85   0.000     49.57015    52.92664
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
                    var(ses) |   .0962659          .             .           .
                  var(_cons) |   12.89715          .             .           .
              cov(ses,_cons) |  -1.114251          .             .           .
-----------------------------+------------------------------------------------
               var(Residual) |   75.19665          .             .           .
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =    43.77   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1872.997      2     3749.994    3758.498
------------------------------------------------------------------------------
Page 93, 4.4.3 Adding 'PercentMinorities' (Model 3), SAS Program.
xtmixed math ses percmin || schid:, variance

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1870.8054  
Iteration 1:   log restricted-likelihood = -1870.8054  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(2)       =     66.23
Log restricted-likelihood = -1870.8054          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ses |   4.298805   .5618229     7.65   0.000     3.197652    5.399958
     percmin |  -.8093957   .3647249    -2.22   0.026    -1.524243    -.094548
       _cons |   53.12666   1.178066    45.10   0.000     50.81769    55.43562
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Identity              |
                  var(_cons) |   10.69835   4.337275      4.833108    23.68137
-----------------------------+------------------------------------------------
               var(Residual) |   75.17249   4.769303      66.38266     85.1262
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =    40.65 Prob >= chibar2 = 0.0000

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1870.805      5     3751.611     3772.87
------------------------------------------------------------------------------
Page 95, 4.4.4 Adding 'MeanSES' (Model 4).
xtmixed math ses percmin meanses || schid:, variance

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1867.8075  
Iteration 1:   log restricted-likelihood = -1867.8075  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(3)       =     73.80
Log restricted-likelihood = -1867.8075          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ses |    3.88476   .6097731     6.37   0.000     2.689627    5.079894
     percmin |  -.6921886   .3456913    -2.00   0.045    -1.369731    -.014646
     meanses |   2.805075   1.479369     1.90   0.058    -.0944343    5.704584
       _cons |    53.0969   1.102666    48.15   0.000     50.93572    55.25809
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Identity              |
                  var(_cons) |   8.846737   3.936787      3.698277    21.16249
-----------------------------+------------------------------------------------
               var(Residual) |   75.24051   4.777618       66.4358     85.2121
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =    25.48 Prob >= chibar2 = 0.0000

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1867.808      6     3747.615    3773.126
------------------------------------------------------------------------------
Page 95, 4.4.5 Analyses with NELS-88, models 2 and 3 (we do not have these data, so these analyses are omitted).
Page 99, 4.5.1 Analysis with class size and a cross level interaction (Model 1).
xtmixed math homework ratio || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1818.3188  
Iteration 1:   log restricted-likelihood = -1818.3188  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(2)       =      4.74
Log restricted-likelihood = -1818.3188          Prob > chi2        =    0.0934

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   1.979276   .9288626     2.13   0.033     .1587383    3.799813
       ratio |  -.0944215   .2123894    -0.44   0.657     -.510697    .3218541
       _cons |    47.9616   4.083297    11.75   0.000     39.95848    55.96471
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   17.74195   6.268408      8.876944    35.46005
                  var(_cons) |   63.48001    21.7818      32.40153     124.368
         cov(homework,_cons) |  -27.70352   10.64132     -48.56012   -6.846919
-----------------------------+------------------------------------------------
               var(Residual) |   53.30429   3.467218      46.92401     60.5521
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   183.07   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1818.319      7     3650.638    3680.401
------------------------------------------------------------------------------
Page 100, 4.5.2 Interaction between 'Ratio' and 'HomeWork' (Model 2), SAS Program.
generate homewrkXratio = homework*ratio

xtmixed math homework homewrkXratio || schid: homework, variance covar(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -1818.9455  
Iteration 1:   log restricted-likelihood = -1818.9455  

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =       519
Group variable: schid                           Number of groups   =        23

                                                Obs per group: min =         5
                                                               avg =      22.6
                                                               max =        67

                                                Wald chi2(2)       =      4.66
Log restricted-likelihood = -1818.9455          Prob > chi2        =    0.0974

------------------------------------------------------------------------------
        math |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    homework |   2.884085   2.156817     1.34   0.181      -1.3432    7.111369
homewrkXra~o |  -.0525855   .1122818    -0.47   0.640    -.2726539    .1674828
       _cons |   46.33064   1.760591    26.32   0.000     42.87995    49.78134
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
schid: Unstructured          |
               var(homework) |   18.09523   6.390325      9.056545    36.15477
                  var(_cons) |   62.55502   21.42087      31.97298    122.3887
         cov(homework,_cons) |  -27.80043   10.65508     -48.68401   -6.916853
-----------------------------+------------------------------------------------
               var(Residual) |   53.29771    3.46642      46.91886     60.5438
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =   180.57   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
|    519           .   -1818.945      7     3651.891    3681.654
------------------------------------------------------------------------------
Page 100, 4.5.3 Reporting the modeling session with NELS-88  (we do not have these data, so these analyses are omitted).

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