> print("Correlations in School-Level-2 Data")
[1] "Correlations in School-Level-2 Data"
> corrSummary(data = Lecture3Means, p.separate = TRUE, vars = c("homework", 
+ "mixgrd", "CMverb", "CMlang"))

Correlations:
 Variable homework mixgrd CMverb CMlang
 homework    1.000 -0.142  0.103  0.088
 mixgrd     -0.142  1.000 -0.158 -0.227
 CMverb      0.103 -0.158  1.000  0.721
 CMlang      0.088 -0.227  0.721  1.000

P-values:
 Variable homework mixgrd CMverb CMlang
 homework           0.050  0.158  0.224
 mixgrd      0.050         0.029  0.002
 CMverb      0.158  0.029         <.001
 CMlang      0.224  0.002  <.001       

> print("Correlations in Student-Level-1 Data")
[1] "Correlations in Student-Level-1 Data"
> corrSummary(data = Lecture3, p.separate = TRUE, vars = c("verbal", 
+ "langpost", "WCverb", "WClang", "CMverb", "CMlang"))

Correlations:
 Variable verbal langpost WCverb WClang CMverb CMlang
 verbal    1.000    0.603  0.918  0.541  0.397  0.268
 langpost  0.603    1.000  0.513  0.870  0.333  0.493
 WCverb    0.918    0.513  1.000  0.589  0.000  0.000
 WClang    0.541    0.870  0.589  1.000  0.000 -0.000
 CMverb    0.397    0.333  0.000  0.000  1.000  0.675
 CMlang    0.268    0.493  0.000 -0.000  0.675  1.000

P-values:
 Variable verbal langpost WCverb WClang CMverb CMlang
 verbal             <.001  <.001  <.001  <.001  <.001
 langpost  <.001           <.001  <.001  <.001  <.001
 WCverb    <.001    <.001         <.001  1.000  1.000
 WClang    <.001    <.001  <.001         1.000  1.000
 CMverb    <.001    <.001  1.000  1.000         <.001
 CMlang    <.001    <.001  1.000  1.000  <.001       

> print("Two-Level Empty Means, Random Intercept for Language Outcome")
[1] "Two-Level Empty Means, Random Intercept for Language Outcome"
> Model2 = lmer(data = Lecture3, REML = TRUE, formula = langpost ~ 
+ 1 + (1 | schoolID))
> lmerSummary(Model2, ICC1 = TRUE)

Model Fit for Predicting langpost:
       AIC        BIC     logLik  -2*logLik 
 25196.953  25215.491 -12595.477  25190.953 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept   17.815   4.221
 Residual              62.229   7.889
Number of obs: 3566 , groups: schoolID, 191 

Fixed Effects:
 Term          Est    SE      DF t.value p.value
 Intercept  41.079 0.337 174.914 121.849   <.001

ICC1 intraclass correlation:
    Adjusted ICC: 0.223 
  Unadjusted ICC: 0.223 

> print("Two-Level Empty Means, Random Intercept for Verbal Predictor")
[1] "Two-Level Empty Means, Random Intercept for Verbal Predictor"
> EmptyVerb = lmer(data = Lecture3, REML = TRUE, formula = verbal ~ 
+ 1 + (1 | schoolID))
> lmerSummary(EmptyVerb, ICC1 = TRUE)

Model Fit for Predicting verbal:
      AIC       BIC    logLik -2*logLik 
15018.749 15037.287 -7506.375 15012.749 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept    0.504   0.710
 Residual               3.690   1.921
Number of obs: 3566 , groups: schoolID, 191 

Fixed Effects:
 Term         Est    SE      DF t.value p.value
 Intercept  9.989 0.062 163.010 161.720   <.001

ICC1 intraclass correlation:
    Adjusted ICC: 0.120 
  Unadjusted ICC: 0.120 

> print("Add L2-CM and Cluster-MC-L1 Student Verbal")
[1] "Add L2-CM and Cluster-MC-L1 Student Verbal"
> Model5 = lmer(data = Lecture3, REML = TRUE, formula = langpost ~ 
+ 1 + hw2 + mixgrd + CMverb10 + WCverb + (1 | schoolID))
> lmerSummary(Model5)

Model Fit for Predicting langpost:
       AIC        BIC     logLik  -2*logLik 
 23629.074  23672.328 -11807.537  23615.074 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept    8.396   2.898
 Residual              40.550   6.368
Number of obs: 3566 , groups: schoolID, 191 

Overall F-test for All Fixed Slopes:
 Model  NumDF   DenDF F.value p.value
 Model5     4 253.499 498.717   <.001

Fixed Effects:
 Term          Est    SE       DF t.value p.value
 Intercept  41.579 0.362  172.098 114.721   <.001
 hw2        -0.053 0.459  178.450  -0.115   0.909
 mixgrd     -1.121 0.516  197.041  -2.173   0.031
 CMverb10    3.660 0.271  207.383  13.508   <.001
 WCverb      2.423 0.057 3372.684  42.370   <.001

> con1DSummary(contest1D(Model5, L = c(0, 0, 0, 1, -1)), name = "L2 Contextual")

Fixed Effect: L2 Contextual
   Est    SE      DF t.value p.value
 1.237 0.277 226.180   4.468   <.001

> PseudoR2(baseModel = Model2, altModel1 = Model5)

Pseudo-R2
 Term       Model  Variance Pseudo.R2
 Intercept  Model2   17.815          
 Intercept  Model5    8.396     0.529
 Residual   Model2   62.229          
 Residual   Model5   40.550     0.348

> print("Add L2-CM and Constant-C-L1 Student Verbal")
[1] "Add L2-CM and Constant-C-L1 Student Verbal"
> Model6 = lmer(data = Lecture3, REML = TRUE, formula = langpost ~ 
+ 1 + hw2 + mixgrd + CMverb10 + verb10 + (1 | schoolID))
> lmerSummary(Model6)

Model Fit for Predicting langpost:
       AIC        BIC     logLik  -2*logLik 
 23629.074  23672.328 -11807.537  23615.074 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept    8.396   2.898
 Residual              40.550   6.368
Number of obs: 3566 , groups: schoolID, 191 

Overall F-test for All Fixed Slopes:
 Model  NumDF   DenDF F.value p.value
 Model6     4 261.076 498.717   <.001

Fixed Effects:
 Term          Est    SE       DF t.value p.value
 Intercept  41.579 0.362  172.098 114.721   <.001
 hw2        -0.053 0.459  178.450  -0.115   0.909
 mixgrd     -1.121 0.516  197.041  -2.173   0.031
 CMverb10    1.237 0.277  226.180   4.468   <.001
 verb10      2.423 0.057 3372.684  42.370   <.001

> con1DSummary(contest1D(Model6, L = c(0, 0, 0, 1, 1)), name = "L2 Between")

Fixed Effect: L2 Between
   Est    SE      DF t.value p.value
 3.660 0.271 207.383  13.508   <.001

> PseudoR2(baseModel = Model2, altModel1 = Model6)

Pseudo-R2
 Term       Model  Variance Pseudo.R2
 Intercept  Model2   17.815          
 Intercept  Model6    8.396     0.529
 Residual   Model2   62.229          
 Residual   Model6   40.550     0.348

> print("Add Smushed L1 Student Verbal")
[1] "Add Smushed L1 Student Verbal"
> Smush = lmer(data = Lecture3, REML = TRUE, formula = langpost ~ 
+ 1 + hw2 + mixgrd + verb10 + (1 | schoolID))
> lmerSummary(Smush)

Model Fit for Predicting langpost:
       AIC        BIC     logLik  -2*logLik 
 23645.600  23682.675 -11816.800  23633.600 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept    9.381   3.063
 Residual              40.574   6.370
Number of obs: 3566 , groups: schoolID, 191 

Overall F-test for All Fixed Slopes:
 Model NumDF   DenDF F.value p.value
 Smush     3 270.161 653.328   <.001

Fixed Effects:
 Term          Est    SE       DF t.value p.value
 Intercept  41.569 0.379  170.446 109.659   <.001
 hw2         0.130 0.477  176.056   0.273   0.785
 mixgrd     -1.398 0.534  195.227  -2.617   0.010
 verb10      2.472 0.056 3544.834  44.090   <.001

