VARIABLE LABELS
  studentID  "studentID: Student ID number"
schoolID  "schoolID: School ID number"
districtID "districtID: District ID number"
frlunch    "frlunch: 0=No, 1=Free/Reduced Lunch"
math       "math: Math Test Score".
* Selecting complete cases for analysis.
SELECT IF (NMISS(studentID, schoolID, frlunch, math)=0).
EXECUTE.

* Getting school means to use as level-2 predictors.
* SPSS 14+ can merge them back automatically.
SORT CASES BY schoolID studentID.
AGGREGATE
   /OUTFILE=* MODE=ADDVARIABLES
   /PRESORTED
   /BREAK = schoolID
   /SMfrlunch = MEAN(frlunch)
   /SMmath = MEAN(math)
    /SchoolN = N.

* Labeling new school mean variables.
VARIABLE LABELS
SMfrlunch "SMfrlunch: School Mean 0=No, 1=Free/Reduced Lunch"
  SMmath    "SMmath: School Mean Math"
SchoolN  "SchoolN: # Students Contributing Data".

* Selecting schools with data from at least 30 students.
SELECT IF (SchoolN GT 30).

* Descriptive statistics.
DESCRIPTIVES VARIABLES=math frlunch SMfrlunch SchoolN
  /STATISTICS=MEAN STDDEV MIN MAX.



Descriptives


Notes
Output Created 03-MAY-2013 12:51:03
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User defined missing values are treated as missing.
Cases Used All non-missing data are used.
Syntax DESCRIPTIVES VARIABLES=math frlunch SMfrlunch SchoolN
/STATISTICS=MEAN STDDEV MIN MAX.
Resources Processor Time 00:00:00.03
Elapsed Time 00:00:00.05


[DataSet1] 


Descriptive Statistics
  N Minimum Maximum Mean Std. Deviation
math: Math Test Score 13082 0 83 48.12 17.259
frlunch: 0=No, 1=Free/Reduced Lunch 13082 0 1 .31 .461
SMfrlunch: School Mean 0=No, 1=Free/Reduced Lunch 13082 .00 .80 .3075 .22209
SchoolN: # Students Contributing Data 13082 31 515 274.95 155.332
Valid N (listwise) 13082        


* Centering school mean predictors.
COMPUTE SMfrlunch30 = SMfrlunch - .30.
VARIABLE LABELS
 SMfrlunch30   "SMfrlunch30: 0=.30".
EXECUTE.

* Models for example.

TITLE "SPSS Model 0: 1-Level Empty Model for Math Outcome".


SPSS Model 0: 1-Level Empty Model for Math Outcome


MIXED math BY schoolID studentID
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV G
   /FIXED  = .



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:03
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID
/METHOD = ML
/PRINT = SOLUTION TESTCOV G
/FIXED = .
Resources Processor Time 00:00:00.86
Elapsed Time 00:00:00.88


[DataSet1] 


Warnings
A(n) FIXED subcommand has no specifications and will therefore be ignored.

Model Dimensiona
  Number of Levels Number of Parameters
Fixed Effects Intercept 1 1
Residual   1
Total 1 2
a. Dependent Variable: math: Math Test Score.

Information Criteriaa
-2 Log Likelihood 111647.984
Akaike's Information Criterion (AIC) 111651.984
Hurvich and Tsai's Criterion (AICC) 111651.984
Bozdogan's Criterion (CAIC) 111668.942
Schwarz's Bayesian Criterion (BIC) 111666.942
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 13082 101694.848 .000
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 48.118560 .150891 13082 318.896 .000 47.822792 48.414328
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 297.851943 3.682802 80.876 .000 290.720544 305.158275
a. Dependent Variable: math: Math Test Score.


TITLE "SPSS Model 1: 2-Level Empty Model for Math Outcome".


SPSS Model 1: 2-Level Empty Model for Math Outcome


MIXED math BY schoolID studentID
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV G
   /FIXED  =
   /RANDOM = INTERCEPT | SUBJECT(SchoolID) COVTYPE(UN) .



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:04
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID
/METHOD = ML
/PRINT = SOLUTION TESTCOV G
/FIXED =
/RANDOM = INTERCEPT | SUBJECT(SchoolID) COVTYPE(UN) .
Resources Processor Time 00:00:00.86
Elapsed Time 00:00:00.94


[DataSet1] 


Warnings
A(n) FIXED subcommand has no specifications and will therefore be ignored.
The covariance structure for random effect with only one level will be changed to Identity.

Model Dimensiona
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
Random Effects Intercept 1 Identity 1 schoolID
Residual     1  
Total 2   3  
a. Dependent Variable: math: Math Test Score.

Information Criteriaa
-2 Log Likelihood 109790.901
Akaike's Information Criterion (AIC) 109796.901
Hurvich and Tsai's Criterion (AICC) 109796.903
Bozdogan's Criterion (CAIC) 109822.338
Schwarz's Bayesian Criterion (BIC) 109819.338
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 94.919 4409.282 .000
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 47.756133 .719193 94.919 66.402 .000 46.328339 49.183926
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 253.175640 3.141541 80.590 .000 247.092603 259.408431
Intercept [subject = schoolID] Variance 44.936343 7.039958 6.383 .000 33.055530 61.087356
a. Dependent Variable: math: Math Test Score.

Random Effect Covariance Structure (G)a
  Intercept | schoolID
Intercept | schoolID 44.936343
Identity
a. Dependent Variable: math: Math Test Score.


TITLE "SPSS Model 2: Adding a Fixed Effect of Student Free/Reduced Lunch".

>Warning # 2003.  Command name: TITLE
>The title given exceeds 60 characters in length.  The first 60 characters will
>be used.


SPSS Model 2: Adding a Fixed Effect of Student Free/Reduced


MIXED math BY schoolID studentID WITH frlunch
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV G
   /FIXED  = frlunch
   /RANDOM = INTERCEPT | SUBJECT(SchoolID) COVTYPE(UN) .



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:05
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID WITH frlunch
/METHOD = ML
/PRINT = SOLUTION TESTCOV G
/FIXED = frlunch
/RANDOM = INTERCEPT | SUBJECT(SchoolID) COVTYPE(UN) .
Resources Processor Time 00:00:00.91
Elapsed Time 00:00:01.00


[DataSet1] 


Warnings
The covariance structure for random effect with only one level will be changed to Identity.

Model Dimensiona
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
frlunch 1   1  
Random Effects Intercept 1 Identity 1 schoolID
Residual     1  
Total 3   4  
a. Dependent Variable: math: Math Test Score.

Information Criteriaa
-2 Log Likelihood 109016.137
Akaike's Information Criterion (AIC) 109024.137
Hurvich and Tsai's Criterion (AICC) 109024.140
Bozdogan's Criterion (CAIC) 109058.053
Schwarz's Bayesian Criterion (BIC) 109054.053
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 97.956 7705.160 .000
frlunch 1 12946.758 808.170 .000
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 50.616115 .576631 97.956 87.779 .000 49.471803 51.760427
frlunch -9.431621 .331768 12946.758 -28.428 .000 -10.081936 -8.781307
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 239.328923 2.969964 80.583 .000 233.578120 245.221314
Intercept [subject = schoolID] Variance 26.889959 4.438975 6.058 .000 19.456935 37.162581
a. Dependent Variable: math: Math Test Score.

Random Effect Covariance Structure (G)a
  Intercept | schoolID
Intercept | schoolID 26.889959
Identity
a. Dependent Variable: math: Math Test Score.


TITLE "SPSS Model 3: Adding a Fixed Effect of School Proportion Free/Reduced Lunch".

>Warning # 2003.  Command name: TITLE
>The title given exceeds 60 characters in length.  The first 60 characters will
>be used.


SPSS Model 3: Adding a Fixed Effect of School Proportion Fre


MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV G
   /FIXED  = frlunch SMfrlunch30
   /SAVE = FIXPRED(lunchpred)
   /TEST = "FR Lunch Between-School Effect" frlunch 1 SMfrlunch30 1.



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:06
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
/METHOD = ML
/PRINT = SOLUTION TESTCOV G
/FIXED = frlunch SMfrlunch30
/SAVE = FIXPRED(lunchpred)
/TEST = "FR Lunch Between-School Effect" frlunch 1 SMfrlunch30 1.
Resources Processor Time 00:00:01.81
Elapsed Time 00:00:01.95
Variables Created lunchpred Fixed Predicted Values


[DataSet1] 


Model Dimensiona
  Number of Levels Number of Parameters
Fixed Effects Intercept 1 1
frlunch 1 1
SMfrlunch30 1 1
Residual   1
Total 3 4
a. Dependent Variable: math: Math Test Score.

Information Criteriaa
-2 Log Likelihood 109318.955
Akaike's Information Criterion (AIC) 109326.955
Hurvich and Tsai's Criterion (AICC) 109326.958
Bozdogan's Criterion (CAIC) 109360.871
Schwarz's Bayesian Criterion (BIC) 109356.871
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 13082 88241.585 .000
frlunch 1 13082 722.567 .000
SMfrlunch30 1 13082 601.664 .000
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 51.070250 .171922 13082 297.055 .000 50.733258 51.407242
frlunch -9.172883 .341245 13082 -26.881 .000 -9.841774 -8.503992
SMfrlunch30 -17.393296 .709096 13082 -24.529 .000 -18.783227 -16.003365
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 249.276684 3.082191 80.876 .000 243.308311 255.391461
a. Dependent Variable: math: Math Test Score.


Custom Hypothesis Test  (FR Lunch Between-School Effect)


Contrast Estimatesa,b
Contrast Estimate Std. Error df Test Value t Sig. 95% Confidence Interval
Lower Bound Upper Bound
L1 -26.566179 .621585 13082 0 -42.739 .000 -27.784577 -25.347781
a. FR Lunch Between-School Effect
b. Dependent Variable: math: Math Test Score.

CORRELATIONS /VARIABLES = math lunchpred.



Correlations


Notes
Output Created 03-MAY-2013 12:51:09
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics for each pair of variables are based on all the cases with valid data for that pair.
Syntax CORRELATIONS /VARIABLES = math lunchpred.
Resources Processor Time 00:00:00.03
Elapsed Time 00:00:00.14


[DataSet1] 


Correlations
  math: Math Test Score Fixed Predicted Values
math: Math Test Score Pearson Correlation 1 .404
Sig. (2-tailed)   .000
N 13082 13082
Fixed Predicted Values Pearson Correlation .404 1
Sig. (2-tailed) .000  
N 13082 13082


TITLE "SPSS Model 4: Adding a Random Effect of Student Free/Reduced Lunch".

>Warning # 2003.  Command name: TITLE
>The title given exceeds 60 characters in length.  The first 60 characters will
>be used.


SPSS Model 4: Adding a Random Effect of Student Free/Reduced


MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV G
   /FIXED  = frlunch SMfrlunch30
   /RANDOM = INTERCEPT frlunch | SUBJECT(SchoolID) COVTYPE(UN) .



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:09
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
/METHOD = ML
/PRINT = SOLUTION TESTCOV G
/FIXED = frlunch SMfrlunch30
/RANDOM = INTERCEPT frlunch | SUBJECT(SchoolID) COVTYPE(UN) .
Resources Processor Time 00:00:00.92
Elapsed Time 00:00:01.66


[DataSet1] 


Model Dimensiona
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
frlunch 1   1  
SMfrlunch30 1   1  
Random Effects Intercept + frlunchb 2 Unstructured 3 schoolID
Residual     1  
Total 5   7  
a. Dependent Variable: math: Math Test Score.
b. As of version 11.5, the syntax rules for the RANDOM subcommand have changed. Your command syntax may yield results that differ from those produced by prior versions. If you are using version 11 syntax, please consult the current syntax reference guide for more information.

Information Criteriaa
-2 Log Likelihood 108877.387
Akaike's Information Criterion (AIC) 108891.387
Hurvich and Tsai's Criterion (AICC) 108891.396
Bozdogan's Criterion (CAIC) 108950.740
Schwarz's Bayesian Criterion (BIC) 108943.740
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 84.746 9539.311 .000
frlunch 1 98.593 226.718 .000
SMfrlunch30 1 77.012 79.379 .000
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 50.259303 .514586 84.746 97.669 .000 49.236124 51.282482
frlunch -8.449957 .561192 98.593 -15.057 .000 -9.563542 -7.336373
SMfrlunch30 -17.088213 1.917979 77.012 -8.909 .000 -20.907388 -13.269038
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 236.837224 2.946805 80.371 .000 231.131447 242.683856
Intercept + frlunch [subject = schoolID] UN (1,1) 19.930838 3.745502 5.321 .000 13.789977 28.806306
UN (2,1) -11.892772 3.164497 -3.758 .000 -18.095071 -5.690473
UN (2,2) 12.688191 3.311246 3.832 .000 7.607835 21.161105
a. Dependent Variable: math: Math Test Score.

Random Effect Covariance Structure (G)a
  Intercept | schoolID frlunch | schoolID
Intercept | schoolID 19.930838 -11.892772
frlunch | schoolID -11.892772 12.688191
Unstructured
a. Dependent Variable: math: Math Test Score.


TITLE "SPSS Model 5: Adding Cross-Level Interaction of Student by School Free/Reduced Lunch".

>Warning # 2003.  Command name: TITLE
>The title given exceeds 60 characters in length.  The first 60 characters will
>be used.


SPSS Model 5: Adding Cross-Level Interaction of Student by S


MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV
   /FIXED  = frlunch SMfrlunch30 frlunch*SMfrlunch30
   /RANDOM = INTERCEPT frlunch | SUBJECT(schoolID) COVTYPE(UN).



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:11
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
/METHOD = ML
/PRINT = SOLUTION TESTCOV
/FIXED = frlunch SMfrlunch30 frlunch*SMfrlunch30
/RANDOM = INTERCEPT frlunch | SUBJECT(schoolID) COVTYPE(UN).
Resources Processor Time 00:00:00.94
Elapsed Time 00:00:01.06


[DataSet1] 


Model Dimensiona
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
frlunch 1   1  
SMfrlunch30 1   1  
frlunch * SMfrlunch30 1   1  
Random Effects Intercept + frlunchb 2 Unstructured 3 schoolID
Residual     1  
Total 6   8  
a. Dependent Variable: math: Math Test Score.
b. As of version 11.5, the syntax rules for the RANDOM subcommand have changed. Your command syntax may yield results that differ from those produced by prior versions. If you are using version 11 syntax, please consult the current syntax reference guide for more information.

Information Criteriaa
-2 Log Likelihood 108875.005
Akaike's Information Criterion (AIC) 108891.005
Hurvich and Tsai's Criterion (AICC) 108891.016
Bozdogan's Criterion (CAIC) 108958.837
Schwarz's Bayesian Criterion (BIC) 108950.837
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 86.471 9544.812 .000
frlunch 1 112.554 234.448 .000
SMfrlunch30 1 89.790 61.896 .000
frlunch * SMfrlunch30 1 104.061 2.471 .119
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 50.222826 .514064 86.471 97.698 .000 49.200980 51.244673
frlunch -8.688184 .567422 112.554 -15.312 .000 -9.812398 -7.563971
SMfrlunch30 -19.459319 2.473416 89.790 -7.867 .000 -24.373347 -14.545291
frlunch * SMfrlunch30 4.140637 2.633869 104.061 1.572 .119 -1.082388 9.363662
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 236.823249 2.946463 80.375 .000 231.118130 242.669198
Intercept + frlunch [subject = schoolID] UN (1,1) 19.825865 3.701117 5.357 .000 13.750827 28.584822
UN (2,1) -11.343115 3.087061 -3.674 .000 -17.393644 -5.292587
UN (2,2) 11.799118 3.165659 3.727 .000 6.973895 19.962902
a. Dependent Variable: math: Math Test Score.


TITLE "SPSS Model 6: Adding Level-2 Interaction of Quadratic School Free/Reduced Lunch".

>Warning # 2003.  Command name: TITLE
>The title given exceeds 60 characters in length.  The first 60 characters will
>be used.


SPSS Model 6: Adding Level-2 Interaction of Quadratic School


MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
  /METHOD = ML
   /PRINT  = SOLUTION TESTCOV
   /FIXED  = frlunch SMfrlunch30 frlunch*SMfrlunch30 SMfrlunch30*SMfrlunch30
   /RANDOM = INTERCEPT frlunch | SUBJECT(schoolID) COVTYPE(UN)
   /SAVE = FIXPRED(totalpred)
   /TEST = "FR Lunch Between-School Main Effect" frlunch 1 SMfrlunch30 1
   /TEST = "FR Lunch Between-School Interaction" frlunch*SMfrlunch30 1 SMfrlunch30*SMfrlunch30 1.



Mixed Model Analysis


Notes
Output Created 03-MAY-2013 12:51:12
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax MIXED math BY schoolID studentID WITH frlunch SMfrlunch30
/METHOD = ML
/PRINT = SOLUTION TESTCOV
/FIXED = frlunch SMfrlunch30 frlunch*SMfrlunch30 SMfrlunch30*SMfrlunch30
/RANDOM = INTERCEPT frlunch | SUBJECT(schoolID) COVTYPE(UN)
/SAVE = FIXPRED(totalpred)
/TEST = "FR Lunch Between-School Main Effect" frlunch 1 SMfrlunch30 1
/TEST = "FR Lunch Between-School Interaction" frlunch*SMfrlunch30 1 SMfrlunch30*SMfrlunch30 1.
Resources Processor Time 00:00:01.78
Elapsed Time 00:00:01.95
Variables Created totalpred Fixed Predicted Values


[DataSet1] 


Model Dimensiona
  Number of Levels Covariance Structure Number of Parameters Subject Variables
Fixed Effects Intercept 1   1  
frlunch 1   1  
SMfrlunch30 1   1  
frlunch * SMfrlunch30 1   1  
SMfrlunch30 * SMfrlunch30 1   1  
Random Effects Intercept + frlunchb 2 Unstructured 3 schoolID
Residual     1  
Total 7   9  
a. Dependent Variable: math: Math Test Score.
b. As of version 11.5, the syntax rules for the RANDOM subcommand have changed. Your command syntax may yield results that differ from those produced by prior versions. If you are using version 11 syntax, please consult the current syntax reference guide for more information.

Information Criteriaa
-2 Log Likelihood 108872.484
Akaike's Information Criterion (AIC) 108890.484
Hurvich and Tsai's Criterion (AICC) 108890.498
Bozdogan's Criterion (CAIC) 108966.795
Schwarz's Bayesian Criterion (BIC) 108957.795
The information criteria are displayed in smaller-is-better forms.
a. Dependent Variable: math: Math Test Score.


Fixed Effects


Type III Tests of Fixed Effectsa
Source Numerator df Denominator df F Sig.
Intercept 1 103.931 6318.554 .000
frlunch 1 114.517 234.552 .000
SMfrlunch30 1 88.159 48.017 .000
frlunch * SMfrlunch30 1 107.832 3.854 .052
SMfrlunch30 * SMfrlunch30 1 87.979 2.595 .111
a. Dependent Variable: math: Math Test Score.

Estimates of Fixed Effectsa
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 50.859458 .639827 103.931 79.489 .000 49.590647 52.128270
frlunch -8.835695 .576927 114.517 -15.315 .000 -9.978528 -7.692862
SMfrlunch30 -17.984780 2.595432 88.159 -6.929 .000 -23.142525 -12.827035
frlunch * SMfrlunch30 5.428155 2.764984 107.832 1.963 .052 -.052620 10.908930
SMfrlunch30 * SMfrlunch30 -14.202363 8.815805 87.979 -1.611 .111 -31.721981 3.317254
a. Dependent Variable: math: Math Test Score.


Covariance Parameters


Estimates of Covariance Parametersa
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Residual 236.818504 2.946413 80.375 .000 231.113481 242.664354
Intercept + frlunch [subject = schoolID] UN (1,1) 18.949302 3.572306 5.305 .000 13.095601 27.419592
UN (2,1) -10.922133 3.032685 -3.601 .000 -16.866086 -4.978180
UN (2,2) 11.819499 3.178753 3.718 .000 6.977113 20.022690
a. Dependent Variable: math: Math Test Score.


Custom Hypothesis Test 1 (FR Lunch Between-School Main Effect)


Contrast Estimatesa,b
Contrast Estimate Std. Error df Test Value t Sig. 95% Confidence Interval
Lower Bound Upper Bound
L1 -26.820475 2.603224 90.622 0 -10.303 .000 -31.991750 -21.649200
a. FR Lunch Between-School Main Effect
b. Dependent Variable: math: Math Test Score.


Custom Hypothesis Test 2 (FR Lunch Between-School Interaction)


Contrast Estimatesa,b
Contrast Estimate Std. Error df Test Value t Sig. 95% Confidence Interval
Lower Bound Upper Bound
L1 -8.774208 8.417363 75.813 0 -1.042 .301 -25.539507 7.991090
a. FR Lunch Between-School Interaction
b. Dependent Variable: math: Math Test Score.

CORRELATIONS /VARIABLES = math totalpred.



Correlations


Notes
Output Created 03-MAY-2013 12:51:14
Comments  
Input Active Dataset DataSet1
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 13082
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics for each pair of variables are based on all the cases with valid data for that pair.
Syntax CORRELATIONS /VARIABLES = math totalpred.
Resources Processor Time 00:00:00.02
Elapsed Time 00:00:00.16


[DataSet1] 


Correlations
  math: Math Test Score Fixed Predicted Values
math: Math Test Score Pearson Correlation 1 .405
Sig. (2-tailed)   .000
N 13082 13082
Fixed Predicted Values Pearson Correlation .405 1
Sig. (2-tailed) .000  
N 13082 13082