> Example4a$CMnon30 = Example4a$CMnon - 0.3
> Example4a$WCses = Example4a$ses - Example4a$CMses
> Example4a$WCnon = Example4a$nonwhite - Example4a$CMnon
> print("Model 4c: Fixed Cluster-Mean-Centered Level-1 Slopes Only")
[1] "Model 4c: Fixed Cluster-Mean-Centered Level-1 Slopes Only"
> Model4c = lmer(data = Example4a, REML = TRUE, formula = math ~ 
+ 1 + WCses + WCnon + CMses + CMnon30 + (1 | schoolID))
> lmerSummary(Model4c)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
 46404.554  46452.712 -23195.277  46390.554 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept    2.559   1.600
 Residual              36.136   6.011
Number of obs: 7185 , groups: schoolID, 160 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model4c     4 292.047 218.054   <.001

Fixed Effects:
 Term          Est    SE       DF t.value p.value
 Intercept  12.642 0.147  152.081  86.087   <.001
 WCses       1.952 0.109 7020.170  17.931   <.001
 WCnon      -2.896 0.220 7020.170 -13.152   <.001
 CMses       5.327 0.403  150.020  13.230   <.001
 CMnon30    -1.544 0.552  148.270  -2.798   0.006

> print("Model 5a: Add Random Slope for WCnon")
[1] "Model 5a: Add Random Slope for WCnon"
> Model5a = lmer(data = Example4a, REML = TRUE, formula = math ~ 
+ 1 + WCses + WCnon + CMses + CMnon30 + (1 + WCnon | schoolID))
> lmerSummary(Model5a, LRT = TRUE, randCI = TRUE, slopeRel = TRUE)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
 46396.177  46458.094 -23189.088  46378.177 

Model for the Variance:
 Groups    Name      Variance Std.Dev  Corr
 schoolID  Intercept    2.574   1.605      
           WCnon        2.427   1.558 0.367
 Residual              35.877   5.990      
Number of obs: 7185 , groups: schoolID, 160 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model5a     4 177.402 192.164   <.001

Fixed Effects:
 Term          Est    SE       DF t.value p.value
 Intercept  12.632 0.147  151.957  85.913   <.001
 WCses       1.923 0.109 6985.711  17.631   <.001
 WCnon      -2.897 0.267  107.144 -10.839   <.001
 CMses       5.214 0.398  150.227  13.103   <.001
 CMnon30    -1.746 0.547  149.953  -3.189   0.002

LRT for random effect(s):
 Random Effect Dropped  Npar     LL  -2LL   AIC   BIC    LRT DF p.value p.mix
 <none>                    9 -23189 46378 46396 46458                        
 WCnon | schoolID          7 -23195 46391 46405 46453 12.378  2   0.002 0.001

Random Slope Reliability (SR):
  SR = slope var / (slope var + res var / (mean L1n * var(X)))
 Term  SlopeVar ResVar Var.X    L1n    SR
 WCnon    2.427 35.877 0.107 44.906 0.245

Random Effect 95% CIs (Fixed Effect +/- 1.96*SQRT(random effect variance)):
 Term                 FixedEffect Variance    SD  Lower  Upper
 Intercept | schoolID      12.632    2.574 1.605  9.488 15.777
 WCnon | schoolID          -2.897    2.427 1.558 -5.951  0.156

> print("Model 5b: Add Cross-Level Interactions for WCnon")
[1] "Model 5b: Add Cross-Level Interactions for WCnon"
> Model5b = lmer(data = Example4a, REML = TRUE, formula = math ~ 
+ 1 + WCses + WCnon + CMses + CMnon30 + WCnon:CMses + WCnon:CMnon30 + 
+ 
+ (1 + WCnon | schoolID))
> lmerSummary(Model5b, LRT = TRUE)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
 46389.795  46465.473 -23183.898  46367.795 

Model for the Variance:
 Groups    Name      Variance Std.Dev  Corr
 schoolID  Intercept    2.572   1.604      
           WCnon        2.002   1.415 0.304
 Residual              35.874   5.989      
Number of obs: 7185 , groups: schoolID, 160 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model5b     6 169.905 131.352   <.001

Fixed Effects:
 Term              Est    SE       DF t.value p.value
 Intercept      12.639 0.147  152.076  85.984   <.001
 WCses           1.929 0.109 6972.044  17.698   <.001
 WCnon          -3.018 0.266  118.357 -11.365   <.001
 CMses           5.329 0.403  150.030  13.222   <.001
 CMnon30        -1.542 0.553  148.301  -2.791   0.006
 WCnon:CMses     1.113 0.663   84.701   1.679   0.097
 WCnon:CMnon30   2.932 1.103  127.512   2.659   0.009

LRT for random effect(s):
 Random Effect Dropped  Npar     LL  -2LL   AIC   BIC   LRT DF p.value p.mix
 <none>                   11 -23184 46368 46390 46465                       
 WCnon | schoolID          9 -23188 46376 46394 46456 8.178  2   0.017 0.010

> PseudoR2(baseModel = Model5a, altModel1 = Model5b)

Pseudo-R2
 Term       Model   Variance Pseudo.R2
 Intercept  Model5a    2.574          
 Intercept  Model5b    2.572     0.001
 WCnon      Model5a    2.427          
 WCnon      Model5b    2.002     0.175
 Residual   Model5a   35.877          
 Residual   Model5b   35.874     0.000

> TotalR2(altModel1 = Model4c, altModel2 = Model5a, altModel3 = Model5b)

Total-R2 and Change in Total-R2
 Model   Total.R2 Change.R2
 Model4c    0.184          
 Model5a    0.184    -0.000
 Model5b    0.186     0.001

> conMDSummary(Model5b, terms = c("WCnon:CMses", "WCnon:CMnon30"))
Joint Test for:
WCnon:CMses, WCnon:CMnon30
 Model   NumDF   DenDF F.value p.value
 Model5b     2 110.165   3.889   0.023

> print("Model 6a: Add Random Slope for WCses")
[1] "Model 6a: Add Random Slope for WCses"
> Model6a = lmer(data = Example4a, REML = TRUE, formula = math ~ 
+ 1 + WCses + WCnon + CMses + CMnon30 + WCnon:CMses + WCnon:CMnon30 + 
+ 
+ (1 + WCnon + WCses | schoolID))
> lmerSummary(Model6a, LRT = TRUE, randCI = TRUE, slopeRel = TRUE)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
 46384.906  46481.223 -23178.453  46356.906 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr       
 schoolID  Intercept    2.574   1.604              
           WCnon        1.862   1.365  0.290       
           WCses        0.436   0.660 -0.411 -0.824
 Residual              35.665   5.972              
Number of obs: 7185 , groups: schoolID, 160 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model6a     6 138.358 111.332   <.001

Fixed Effects:
 Term              Est    SE      DF t.value p.value
 Intercept      12.626 0.147 151.359  85.942   <.001
 WCses           1.935 0.121 151.635  15.929   <.001
 WCnon          -3.003 0.264 116.935 -11.379   <.001
 CMses           5.259 0.398 148.987  13.206   <.001
 CMnon30        -1.954 0.545 146.397  -3.584   <.001
 WCnon:CMses     0.939 0.663  86.258   1.417   0.160
 WCnon:CMnon30   2.215 1.102 130.612   2.011   0.046

LRT for random effect(s):
 Random Effect Dropped  Npar     LL  -2LL   AIC   BIC    LRT DF p.value p.mix
 <none>                   14 -23178 46357 46385 46481                        
 WCnon | schoolID         11 -23183 46367 46389 46465 10.087  3   0.018 0.012
 WCses | schoolID         11 -23184 46368 46390 46465 10.889  3   0.012 0.008

Random Slope Reliability (SR):
  SR = slope var / (slope var + res var / (mean L1n * var(X)))
 Term  SlopeVar ResVar Var.X    L1n    SR
 WCnon    1.862 35.665 0.107 44.906 0.200
 WCses    0.436 35.665 0.436 44.906 0.193

Random Effect 95% CIs (Fixed Effect +/- 1.96*SQRT(random effect variance)):
 Term                 FixedEffect Variance    SD  Lower  Upper
 Intercept | schoolID      12.626    2.574 1.604  9.481 15.770
 WCnon | schoolID          -3.003    1.862 1.365 -5.677 -0.328
 WCses | schoolID           1.935    0.436 0.660  0.640  3.229

> print("Model 6b: Add Cross-Level Interactions for WCses")
[1] "Model 6b: Add Cross-Level Interactions for WCses"
> Model6b = lmer(data = Example4a, REML = TRUE, formula = math ~ 
+ 1 + WCses + WCnon + CMses + CMnon30 + WCnon:CMses + WCnon:CMnon30 + 
+ 
+ WCses:CMses + WCses:CMnon30 + (1 + WCnon + WCses | schoolID))
> lmerSummary(Model6b, LRT = TRUE)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
 46364.424  46474.500 -23166.212  46332.424 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr       
 schoolID  Intercept    2.565   1.602              
           WCnon        1.962   1.401  0.289       
           WCses        0.195   0.442 -0.528 -0.965
 Residual              35.627   5.969              
Number of obs: 7185 , groups: schoolID, 160 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model6b     8 195.702  91.584   <.001

Fixed Effects:
 Term              Est    SE      DF t.value p.value
 Intercept      12.637 0.147 152.205  86.128   <.001
 WCses           1.893 0.115 329.231  16.439   <.001
 WCnon          -3.022 0.265 127.826 -11.394   <.001
 CMses           5.332 0.402 150.166  13.252   <.001
 CMnon30        -1.543 0.552 148.443  -2.797   0.006
 WCnon:CMses     1.001 0.668  93.731   1.500   0.137
 WCnon:CMnon30   2.385 1.108 141.119   2.152   0.033
 WCses:CMses    -0.326 0.324 359.457  -1.007   0.314
 WCses:CMnon30  -2.079 0.423 285.383  -4.914   <.001

LRT for random effect(s):
 Random Effect Dropped  Npar     LL  -2LL   AIC   BIC    LRT DF p.value p.mix
 <none>                   16 -23166 46332 46364 46474                        
 WCnon | schoolID         13 -23172 46344 46370 46459 11.264  3   0.010 0.007
 WCses | schoolID         13 -23170 46339 46365 46455  7.036  3   0.071 0.050

> PseudoR2(baseModel = Model6a, altModel1 = Model6b)

Pseudo-R2
 Term       Model   Variance Pseudo.R2
 Intercept  Model6a    2.574          
 Intercept  Model6b    2.565     0.003
 WCnon      Model6a    1.862          
 WCnon      Model6b    1.962    -0.054
 WCses      Model6a    0.436          
 WCses      Model6b    0.195     0.553
 Residual   Model6a   35.665          
 Residual   Model6b   35.627     0.001

> TotalR2(altModel1 = Model4c, altModel2 = Model5b, altModel3 = Model6b)

Total-R2 and Change in Total-R2
 Model   Total.R2 Change.R2
 Model4c    0.184          
 Model5b    0.186     0.001
 Model6b    0.189     0.003

> conMDSummary(Model6b, terms = c("WCses:CMses", "WCses:CMnon30"))
Joint Test for:
WCses:CMses, WCses:CMnon30
 Model   NumDF   DenDF F.value p.value
 Model6b     2 320.444  13.128   <.001

