> print("Descriptive Statistics in School-Level-2 Data")
[1] "Descriptive Statistics in School-Level-2 Data"
> Example4bMeans = unique(Example4b[, c("schoolID", "NperschoolID", 
+ "CM_math", "CM_PvD", "CM_RvF", "CM_Paid", "CM_Redu", "CM_Free")])
> univSummary(data = Example4bMeans, vars = c("NperschoolID", "CM_math", 
+ "CM_PvD", "CM_RvF", "CM_Paid", "CM_Redu", "CM_Free"))

 Variable      N    Mean      SD  Variance    Min     Max Median
 NperschoolID 94 139.170 138.202 19099.713 31.000 515.000 68.000
 CM_math      94  47.725   6.970    48.586 29.451  61.614 48.100
 CM_PvD       94   0.301   0.213     0.045  0.000   0.803  0.270
 CM_RvF       94   0.044   0.098     0.010 -0.330   0.310  0.040
 CM_Paid      94   0.699   0.213     0.045  0.197   1.000  0.730
 CM_Redu      94   0.107   0.127     0.016  0.000   0.727  0.087
 CM_Free      94   0.195   0.160     0.026  0.000   0.678  0.155

> Example4b$CM_PvD30 = Example4b$CM_PvD - 0.3
> Example4b$CM_RvF05 = Example4b$CM_RvF - 0.05
> Example4b$WC_PvD = Example4b$PvD - Example4b$CM_PvD
> Example4b$WC_RvF = Example4b$RvF - Example4b$CM_RvF
> Example4b$WC_math = Example4b$math - Example4b$CM_math
> print("Descriptive Statistics in Student-Level-1 Data")
[1] "Descriptive Statistics in Student-Level-1 Data"
> freqSummary(data = Example4b, var = "lunchF")

 Variable Level       N Proportion
 lunchF   0Paid    9059      0.692
 lunchF   1Reduced 1140      0.087
 lunchF   2Free    2883      0.220

> univSummary(data = Example4b, vars = c("PvD", "RvF", "WC_PvD", 
+ "WC_RvF"))

 Variable     N   Mean    SD Variance    Min   Max Median
 PvD      13082  0.308 0.461    0.213  0.000 1.000  0.000
 RvF      13082  0.067 0.269    0.072 -0.500 0.500  0.000
 WC_PvD   13082 -0.000 0.405    0.164 -0.803 0.989 -0.094
 WC_RvF   13082  0.000 0.254    0.065 -0.810 0.830 -0.027

> corrSummary(data = Example4b, vars = c("math", "PvD", "WC_math", 
+ "WC_PvD", "CM_math", "CM_PvD"), p.separate = TRUE)

Correlations:
 Variable   math    PvD WC_math WC_PvD CM_math CM_PvD
 math      1.000 -0.353   0.919 -0.215   0.395 -0.342
 PvD      -0.353  1.000  -0.205  0.877  -0.416  0.481
 WC_math   0.919 -0.205   1.000 -0.234  -0.000  0.000
 WC_PvD   -0.215  0.877  -0.234  1.000   0.000 -0.000
 CM_math   0.395 -0.416  -0.000  0.000   1.000 -0.865
 CM_PvD   -0.342  0.481   0.000 -0.000  -0.865  1.000

P-values:
 Variable  math   PvD WC_math WC_PvD CM_math CM_PvD
 math           <.001   <.001  <.001   <.001  <.001
 PvD      <.001         <.001  <.001   <.001  <.001
 WC_math  <.001 <.001          <.001   1.000  1.000
 WC_PvD   <.001 <.001   <.001          1.000  1.000
 CM_math  <.001 <.001   1.000  1.000          <.001
 CM_PvD   <.001 <.001   1.000  1.000   <.001       

> print("Model 1: Empty Means, Random Intercept for Math")
[1] "Model 1: Empty Means, Random Intercept for Math"
> Model1 = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + (1 | schoolID))
> lmerSummary(Model1, ICC1 = TRUE, ICC2 = TRUE, Neff = TRUE, LRT = TRUE, 
+ randCI = TRUE)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
109795.717 109818.154 -54894.858 109789.717 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept   45.453   6.742
 Residual             253.176  15.912
Number of obs: 13082 , groups: schoolID, 94 

Fixed Effects:
 Term          Est    SE     DF t.value p.value
 Intercept  47.756 0.723 93.903  66.051   <.001

ICC1 intraclass correlation:
    Adjusted ICC: 0.152 
  Unadjusted ICC: 0.152 

Design Effect and Effective Sample Size:
  Design Effect (using mean n = 139.170 per cluster): 22.030 
  Effective N: 593.821 

LRT for random effect(s):
 Random Effect Dropped  Npar     LL   -2LL    AIC    BIC      LRT DF p.value p.mix
 <none>                    3 -54895 109790 109796 109818                          
 Intercept | schoolID      2 -55825 111650 111654 111669 1860.211  1   <.001 <.001

ICC2 reliability of the cluster means (using mean n = 139.170 per cluster):
0.962 

Random Effect 95% CIs (Fixed Effect +/- 1.96*SQRT(random effect variance)):
 Term                 FixedEffect Variance    SD  Lower  Upper
 Intercept | schoolID      47.756   45.453 6.742 34.542 60.970

> print("Empty Means, Random Intercept for Ordinal Lunch using ordinal package")
[1] "Empty Means, Random Intercept for Ordinal Lunch using ordinal package"
> EmptyLunch = ordinal::clmm(data = Example4b, link = "logit", 
+ formula = lunchF ~ 1 + (1 | schoolID))
> clmmSummary(EmptyLunch, ICC1 = TRUE, LRT = TRUE)

Model Fit for Predicting lunchF:
      AIC       BIC    logLik -2*logLik 
17967.429 17989.866 -8980.714 17961.429 

Model for the Variance:
 Groups    Name             Variance Std.Dev
 schoolID  Intercept           1.783   1.335
 Residual  (logit constant)  (3.290) (1.814)
Number of obs: 13082 , groups: schoolID, 94 

Intercepts predicting the logit of the probability
of being in the HIGHER category after | :
 Term                     Est    SE z.value p.value  Prob Prob.SE
 0Paid|1Reduced,2Free  -1.203 0.143  -8.428   <.001 0.231   0.025
 0Paid,1Reduced|2Free  -1.767 0.143 -12.336   <.001 0.146   0.018

Fixed Effects:
 Term    Est SE z.value p.value
 (none)                        

ICC1 intraclass correlation:
0.351 

LRT for random effect(s):
 Random Effect Dropped  Npar     LL  -2LL   AIC   BIC      LRT DF p.value p.mix
 <none>                    3  -8981 17961 17967 17990                          
 Intercept | schoolID      2 -10471 20942 20946 20961 2980.755  1   <.001 <.001

> print("Model 2: Add L1 Student Lunch")
[1] "Model 2: Add L1 Student Lunch"
> Model2 = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + (1 | schoolID))
> lmerSummary(Model2)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108962.804 109000.199 -54476.402 108952.804 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept   28.312   5.321
 Residual             238.161  15.432
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model  NumDF     DenDF F.value p.value
 Model2     2 13028.726 435.910   <.001

Fixed Effects:
 Term          Est    SE        DF t.value p.value
 Intercept  50.532 0.590    96.393  85.708   <.001
 PvD        -8.489 0.351 12944.113 -24.164   <.001
 RvF        -4.433 0.561 13075.382  -7.907   <.001

> PseudoR2(baseModel = Model1, altModel1 = Model2)

Pseudo-R2
 Term       Model  Variance Pseudo.R2
 Intercept  Model1   45.453          
 Intercept  Model2   28.312     0.377
 Residual   Model1  253.176          
 Residual   Model2  238.161     0.059

> print("Model 3: Add L2 Cluster Mean Student Lunch")
[1] "Model 3: Add L2 Cluster Mean Student Lunch"
> Model3 = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + CM_PvD30 + CM_RvF05 + (1 | schoolID))
> lmerSummary(Model3)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108904.022 108956.375 -54445.011 108890.022 

Model for the Variance:
 Groups    Name      Variance Std.Dev
 schoolID  Intercept   13.960   3.736
 Residual             238.225  15.435
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model  NumDF   DenDF F.value p.value
 Model3     4 169.182 247.890   <.001

Fixed Effects:
 Term           Est    SE        DF t.value p.value
 Intercept   50.554 0.440    90.056 114.855   <.001
 PvD         -8.209 0.354 12978.590 -23.179   <.001
 RvF         -4.568 0.563 12978.590  -8.112   <.001
 CM_PvD30   -18.246 2.108    86.917  -8.656   <.001
 CM_RvF05     8.162 4.611    90.183   1.770   0.080

> con1DTable(Model3, L = list(`L1 Within Paid v Redu Main Effect` = c(0, 
+ 1, -0.5, 0, 0), `L1 Within Paid v Free Main Effect` = c(0, 
+ 1, 0.5, 0, 0), `L1 Within Redu v Free Main Effect` = c(0, 
+ 0, 1, 0, 0), `L2 Contextual Paid v Redu Main Effect` = c(0, 
+ 0, 0, 1, -0.5), `L2 Contextual Paid v Free Main Effect` = c(0, 
+ 0, 0, 1, 0.5), `L2 Contextual Redu v Free Main Effect` = c(0, 
+ 0, 0, 0, 1)))

Requested Fixed Effects:
 Name                                      Est    SE        DF t.value p.value
 L1 Within Paid v Redu Main Effect      -5.925 0.521 12978.590 -11.368   <.001
 L1 Within Paid v Free Main Effect     -10.493 0.371 12978.590 -28.270   <.001
 L1 Within Redu v Free Main Effect      -4.568 0.563 12978.590  -8.112   <.001
 L2 Contextual Paid v Redu Main Effect -22.327 3.521    95.871  -6.341   <.001
 L2 Contextual Paid v Free Main Effect -14.165 2.669    77.942  -5.307   <.001
 L2 Contextual Redu v Free Main Effect   8.162 4.611    90.183   1.770   0.080

> PseudoR2(baseModel = Model1, altModel1 = Model2, altModel2 = Model3)

Pseudo-R2 and Change in Pseudo-R2
 Term       Model  Variance Pseudo.R2 Change.R2
 Intercept  Model1   45.453                    
 Intercept  Model2   28.312     0.377          
 Intercept  Model3   13.960     0.693     0.316
 Residual   Model1  253.176                    
 Residual   Model2  238.161     0.059          
 Residual   Model3  238.225     0.059    -0.000

> TotalR2(altModel1 = Model2, altModel2 = Model3)

Total-R2 and Change in Total-R2
 Model  Total.R2 Change.R2
 Model2    0.127          
 Model3    0.168     0.040

> print("Model 4a: Add Random Cluster-MC Student Lunch")
[1] "Model 4a: Add Random Cluster-MC Student Lunch"
> Model4a = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + CM_PvD30 + CM_RvF05 + (1 + WC_PvD + WC_RvF | 
+ 
+ schoolID))
> lmerSummary(Model4a, LRT = TRUE, LRTdrop = c("WC_PvD", "WC_RvF"), 
+ LRTdropGroup = "schoolID", randCI = TRUE, slopeRel = TRUE, 
+ randCIfixed = c("PvD", "RvF"), randCIrandom = c("WC_PvD", 
+ 
+ "WC_RvF"))

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108827.330 108917.078 -54401.665 108803.330 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr      
 schoolID  Intercept   13.908   3.729             
           WC_PvD      12.476   3.532 -0.508      
           WC_RvF       0.695   0.834 -0.885 0.851
 Residual             235.706  15.353             
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model4a     4 117.110 118.630   <.001

Fixed Effects:
 Term           Est    SE      DF t.value p.value
 Intercept   50.362 0.510  81.893  98.656   <.001
 PvD         -7.688 0.572  88.311 -13.445   <.001
 RvF         -4.392 0.581 558.762  -7.561   <.001
 CM_PvD30   -17.359 2.094  97.982  -8.290   <.001
 CM_RvF05     6.708 4.438  91.263   1.511   0.134

LRT for random effect(s):
 Random Effect Dropped       Npar     LL   -2LL    AIC    BIC    LRT DF p.value p.mix
 <none>                        12 -54402 108803 108827 108917                        
 WC_PvD | schoolID              9 -54440 108879 108897 108964 75.836  3   <.001 <.001
 WC_RvF | schoolID              9 -54403 108805 108823 108890  1.775  3   0.620 0.516
 WC_PvD + WC_RvF | schoolID     7 -54445 108890 108904 108956 86.692  5   <.001      

Random Slope Reliability (SR):
  SR = slope var / (slope var + res var / (mean L1n * var(X)))
 Term   SlopeVar  ResVar Var.X     L1n    SR
 WC_PvD   12.476 235.706 0.164 139.170 0.547
 WC_RvF    0.695 235.706 0.065 139.170 0.026

Random Effect 95% CIs (Fixed Effect +/- 1.96*SQRT(random effect variance)):
 Term                           FixedEffect Variance    SD   Lower  Upper
 Intercept | schoolID                50.362   13.908 3.729  43.052 57.671
 WC_PvD | schoolID (fixed: PvD)      -7.688   12.476 3.532 -14.611 -0.765
 WC_RvF | schoolID (fixed: RvF)      -4.392    0.695 0.834  -6.027 -2.758

> print("Model 4b: Remove Random Cluster-MC RvF Student Lunch")
[1] "Model 4b: Remove Random Cluster-MC RvF Student Lunch"
> Model4b = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + CM_PvD30 + CM_RvF05 + (1 + WC_PvD | schoolID))
> lmerSummary(Model4b, LRT = TRUE, randCI = TRUE, slopeRel = TRUE, 
+ randCIfixed = c("PvD"), randCIrandom = c("WC_PvD"))

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108823.105 108890.416 -54402.553 108805.105 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr
 schoolID  Intercept   13.887   3.727       
           WC_PvD      13.436   3.666 -0.518
 Residual             235.736  15.354       
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model   NumDF   DenDF F.value p.value
 Model4b     4 146.601 122.780   <.001

Fixed Effects:
 Term           Est    SE        DF t.value p.value
 Intercept   50.366 0.510    82.430  98.820   <.001
 PvD         -7.688 0.584    93.895 -13.172   <.001
 RvF         -4.450 0.568 12481.252  -7.834   <.001
 CM_PvD30   -17.541 2.106    99.843  -8.330   <.001
 CM_RvF05     7.512 4.402    89.442   1.706   0.091

LRT for random effect(s):
 Random Effect Dropped  Npar     LL   -2LL    AIC    BIC    LRT DF p.value p.mix
 <none>                    9 -54403 108805 108823 108890                        
 WC_PvD | schoolID         7 -54445 108890 108904 108956 84.916  2   <.001 <.001

Random Slope Reliability (SR):
  SR = slope var / (slope var + res var / (mean L1n * var(X)))
 Term   SlopeVar  ResVar Var.X     L1n    SR
 WC_PvD   13.436 235.736 0.164 139.170 0.565

Random Effect 95% CIs (Fixed Effect +/- 1.96*SQRT(random effect variance)):
 Term                           FixedEffect Variance    SD   Lower  Upper
 Intercept | schoolID                50.366   13.887 3.727  43.062 57.670
 WC_PvD | schoolID (fixed: PvD)      -7.688   13.436 3.666 -14.872 -0.503

> print("Model 5: Add Cross-Level Interactions with Random PvD")
[1] "Model 5: Add Cross-Level Interactions with Random PvD"
> Model5 = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + CM_PvD30 + CM_RvF05 + PvD:CM_PvD30 + PvD:CM_RvF05 + 
+ 
+ (1 + WC_PvD | schoolID))
> lmerSummary(Model5)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108815.134 108897.402 -54396.567 108793.134 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr
 schoolID  Intercept   14.130   3.759       
           WC_PvD      12.412   3.523 -0.502
 Residual             235.737  15.354       
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model  NumDF   DenDF F.value p.value
 Model5     6 145.890  83.276   <.001

Fixed Effects:
 Term              Est    SE        DF t.value p.value
 Intercept      50.247 0.514    83.622  97.832   <.001
 PvD            -7.941 0.591   105.127 -13.442   <.001
 RvF            -4.429 0.574 12982.445  -7.718   <.001
 CM_PvD30      -20.430 2.771    94.826  -7.372   <.001
 CM_RvF05        9.941 6.961    92.240   1.428   0.157
 PvD:CM_PvD30    4.733 2.795   145.609   1.693   0.093
 PvD:CM_RvF05   -2.499 5.977   139.320  -0.418   0.676

> PseudoR2(baseModel = Model4b, altModel1 = Model5)

Pseudo-R2
 Term       Model   Variance Pseudo.R2
 Intercept  Model4b   13.887          
 Intercept  Model5    14.130    -0.018
 WC_PvD     Model4b   13.436          
 WC_PvD     Model5    12.412     0.076
 Residual   Model4b  235.736          
 Residual   Model5   235.737    -0.000

> print("Model 6: Add L2 Interactions with Random PvD")
[1] "Model 6: Add L2 Interactions with Random PvD"
> Model6 = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + CM_PvD30 + CM_RvF05 + PvD:CM_PvD30 + PvD:CM_RvF05 + 
+ 
+ CM_PvD30:CM_RvF05 + I(CM_PvD30^2) + (1 + WC_PvD | schoolID))
> lmerSummary(Model6)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108801.788 108899.015 -54387.894 108775.788 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr
 schoolID  Intercept   14.105   3.756       
           WC_PvD      12.206   3.494 -0.489
 Residual             235.738  15.354       
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model  NumDF   DenDF F.value p.value
 Model6     8 122.111  62.800   <.001

Fixed Effects:
 Term                   Est     SE        DF t.value p.value
 Intercept           50.722  0.660    95.864  76.864   <.001
 PvD                 -8.045  0.596   105.306 -13.489   <.001
 RvF                 -4.409  0.574 12972.668  -7.674   <.001
 CM_PvD30           -17.604  3.650   103.357  -4.823   <.001
 CM_RvF05            -1.179 13.448    98.248  -0.088   0.930
 I(CM_PvD30^2)      -15.324 10.569   104.263  -1.450   0.150
 PvD:CM_PvD30         6.166  2.997   114.940   2.057   0.042
 PvD:CM_RvF05        -3.398  6.054   130.541  -0.561   0.576
 CM_PvD30:CM_RvF05   27.627 32.223    92.259   0.857   0.393

> PseudoR2(baseModel = Model4b, altModel1 = Model5, altModel2 = Model6)

Pseudo-R2 and Change in Pseudo-R2
 Term       Model   Variance Pseudo.R2 Change.R2
 Intercept  Model4b   13.887                    
 Intercept  Model5    14.130    -0.018          
 Intercept  Model6    14.105    -0.016     0.002
 WC_PvD     Model4b   13.436                    
 WC_PvD     Model5    12.412     0.076          
 WC_PvD     Model6    12.206     0.092     0.015
 Residual   Model4b  235.736                    
 Residual   Model5   235.737    -0.000          
 Residual   Model6   235.738    -0.000    -0.000

> print("Model 7: Remove Nonsignificant Unnecessary Interactions")
[1] "Model 7: Remove Nonsignificant Unnecessary Interactions"
> Model7 = lmer(data = Example4b, REML = TRUE, formula = math ~ 
+ 1 + PvD + RvF + CM_PvD30 + CM_RvF05 + I(CM_PvD30^2) + PvD:CM_PvD30 + 
+ 
+ (1 + WC_PvD | schoolID))
> lmerSummary(Model7)

Model Fit for Predicting math:
       AIC        BIC     logLik  -2*logLik 
108812.878 108895.147 -54395.439 108790.878 

Model for the Variance:
 Groups    Name      Variance Std.Dev   Corr
 schoolID  Intercept   13.934   3.733       
           WC_PvD      12.221   3.496 -0.477
 Residual             235.726  15.353       
Number of obs: 13082 , groups: schoolID, 94 

Overall F-test for All Fixed Slopes:
 Model  NumDF   DenDF F.value p.value
 Model7     6 126.573  83.586   <.001

Fixed Effects:
 Term               Est    SE        DF t.value p.value
 Intercept       50.759 0.656    96.907  77.401   <.001
 PvD             -8.066 0.596   106.814 -13.523   <.001
 RvF             -4.465 0.568 12452.849  -7.865   <.001
 CM_PvD30       -19.160 2.688    94.273  -7.128   <.001
 CM_RvF05         6.477 4.573    85.645   1.416   0.160
 I(CM_PvD30^2)  -11.814 9.646    97.918  -1.225   0.224
 PvD:CM_PvD30     5.675 2.821    92.824   2.011   0.047

> con1DTable(Model7, L = list(`L1 Within Paid v Redu Main Effect` = c(0, 
+ 1, -0.5, 0, 0, 0, 0), `L1 Within Paid v Free Main Effect` = c(0, 
+ 1, 0.5, 0, 0, 0, 0), `L1 Within Redu v Free Main Effect` = c(0, 
+ 0, 1, 0, 0, 0, 0), `L2 Contextual Paid v Redu Main Effect` = c(0, 
+ 0, 0, 1, -0.5, 0, 0), `L2 Contextual Paid v Free Main Effect` = c(0, 
+ 0, 0, 1, 0.5, 0, 0), `L2 Contextual Redu v Free Main Effect` = c(0, 
+ 0, 0, 0, 1, 0, 0)))

Requested Fixed Effects:
 Name                                      Est    SE        DF t.value p.value
 L1 Within Paid v Redu Main Effect      -5.834 0.701   208.425  -8.320   <.001
 L1 Within Paid v Free Main Effect     -10.299 0.617   116.981 -16.682   <.001
 L1 Within Redu v Free Main Effect      -4.465 0.568 12452.849  -7.865   <.001
 L2 Contextual Paid v Redu Main Effect -22.398 3.985   101.078  -5.621   <.001
 L2 Contextual Paid v Free Main Effect -15.921 3.004    91.435  -5.299   <.001
 L2 Contextual Redu v Free Main Effect   6.477 4.573    85.645   1.416   0.160

> PseudoR2(baseModel = Model4b, altModel1 = Model5, altModel2 = Model7)

Pseudo-R2 and Change in Pseudo-R2
 Term       Model   Variance Pseudo.R2 Change.R2
 Intercept  Model4b   13.887                    
 Intercept  Model5    14.130    -0.018          
 Intercept  Model7    13.934    -0.003     0.014
 WC_PvD     Model4b   13.436                    
 WC_PvD     Model5    12.412     0.076          
 WC_PvD     Model7    12.221     0.090     0.014
 Residual   Model4b  235.736                    
 Residual   Model5   235.737    -0.000          
 Residual   Model7   235.726     0.000     0.000

> TotalR2(altModel1 = Model3, altModel2 = Model7)

Total-R2 and Change in Total-R2
 Model  Total.R2 Change.R2
 Model3    0.168          
 Model7    0.169     0.001

