load(file="/Users/dleibel1/Box Sync/R Data/DanThesisFinal.rdata")
library(lmerTest)
## Loading required package: Matrix
## Loading required package: lme4
## 
## Attaching package: 'lmerTest'
## The following object is masked from 'package:lme4':
## 
##     lmer
## The following object is masked from 'package:stats':
## 
##     step
library(zStat)
library(zUtil)

##Model 1: Main Effects
mm1 = lmer(PhyPerfSecsTandem ~Age + Sex + EF + Race + BMI + PovStat + WRATtotal + (1|HNDid), data=DanThesisFinal,REML=F)
summary(mm1)
## Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
##   approximations to degrees of freedom [lmerMod]
## Formula: 
## PhyPerfSecsTandem ~ Age + Sex + EF + Race + BMI + PovStat + WRATtotal +  
##     (1 | HNDid)
##    Data: DanThesisFinal
## 
##      AIC      BIC   logLik deviance df.resid 
##  11066.2  11123.1  -5523.1  11046.2     2184 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.8470  0.0492  0.1587  0.2557  1.3222 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  HNDid    (Intercept) 1.167    1.080   
##  Residual             7.884    2.808   
## Number of obs: 2194, groups:  HNDid, 1440
## 
## Fixed effects:
##                Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)   2.856e+01  5.553e-01  9.497e+02  51.426  < 2e-16 ***
## Age          -3.729e-02  7.290e-03  9.587e+02  -5.116 3.78e-07 ***
## SexMen        1.252e-01  1.386e-01  8.443e+02   0.903   0.3667    
## EF            3.177e-02  3.076e-02  1.414e+03   1.033   0.3018    
## RaceAfrAm     5.083e-01  1.430e-01  8.760e+02   3.554   0.0004 ***
## BMI          -1.100e-02  9.111e-03  1.005e+03  -1.207   0.2276    
## PovStatBelow -3.268e-01  1.446e-01  8.568e+02  -2.260   0.0241 *  
## WRATtotal     2.230e-02  1.023e-02  9.597e+02   2.181   0.0295 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Age    SexMen EF     RcAfrA BMI    PvSttB
## Age         -0.006                                          
## SexMen      -0.214 -0.001                                   
## EF           0.264  0.078 -0.019                            
## RaceAfrAm   -0.291  0.007 -0.010  0.115                     
## BMI         -0.502 -0.012  0.182  0.041 -0.015              
## PovStatBelw -0.262  0.099  0.042  0.071 -0.040  0.068       
## WRATtotal   -0.823 -0.006  0.025 -0.403  0.189 -0.017  0.169
##Model 2: Two-way Interactions
mm2 = lmer(PhyPerfSecsTandem ~(Age + Sex + EF + Race)^2 + BMI + PovStat + WRATtotal + (1|HNDid), data=DanThesisFinal,REML=F)
summary(mm2)
## Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
##   approximations to degrees of freedom [lmerMod]
## Formula: PhyPerfSecsTandem ~ (Age + Sex + EF + Race)^2 + BMI + PovStat +  
##     WRATtotal + (1 | HNDid)
##    Data: DanThesisFinal
## 
##      AIC      BIC   logLik deviance df.resid 
##  11065.0  11156.1  -5516.5  11033.0     2178 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.9349  0.0384  0.1366  0.2506  1.3678 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  HNDid    (Intercept) 1.047    1.023   
##  Residual             7.939    2.818   
## Number of obs: 2194, groups:  HNDid, 1440
## 
## Fixed effects:
##                    Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)       2.845e+01  5.588e-01  9.424e+02  50.909  < 2e-16 ***
## Age              -7.487e-02  1.338e-02  1.008e+03  -5.595 2.84e-08 ***
## SexMen            2.206e-01  2.185e-01  8.895e+02   1.010  0.31292    
## EF                3.125e-02  4.943e-02  1.303e+03   0.632  0.52738    
## RaceAfrAm         5.409e-01  1.860e-01  8.830e+02   2.908  0.00373 ** 
## BMI              -9.965e-03  9.166e-03  9.992e+02  -1.087  0.27718    
## PovStatBelow     -3.193e-01  1.439e-01  8.502e+02  -2.219  0.02677 *  
## WRATtotal         2.394e-02  1.021e-02  9.488e+02   2.344  0.01927 *  
## Age:SexMen        1.314e-02  1.479e-02  9.373e+02   0.889  0.37438    
## Age:EF            5.958e-03  2.910e-03  1.287e+03   2.048  0.04078 *  
## Age:RaceAfrAm     4.892e-02  1.532e-02  9.666e+02   3.193  0.00146 ** 
## SexMen:EF        -3.028e-02  5.630e-02  1.319e+03  -0.538  0.59083    
## SexMen:RaceAfrAm -1.392e-01  2.836e-01  8.747e+02  -0.491  0.62380    
## EF:RaceAfrAm      2.602e-02  5.579e-02  1.308e+03   0.466  0.64101    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation matrix not shown by default, as p = 14 > 12.
## Use print(x, correlation=TRUE)  or
##   vcov(x)     if you need it
##Model 3: Three-way Interactions
mm3 = lmer(PhyPerfSecsTandem~(Age + Sex + EF + Race)^3 + BMI + PovStat + WRATtotal + (1|HNDid), data=DanThesisFinal,REML=F)
summary(mm3)
## Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
##   approximations to degrees of freedom [lmerMod]
## Formula: PhyPerfSecsTandem ~ (Age + Sex + EF + Race)^3 + BMI + PovStat +  
##     WRATtotal + (1 | HNDid)
##    Data: DanThesisFinal
## 
##      AIC      BIC   logLik deviance df.resid 
##  11070.5  11184.3  -5515.2  11030.5     2174 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.9458  0.0408  0.1391  0.2486  1.3876 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  HNDid    (Intercept) 1.022    1.011   
##  Residual             7.952    2.820   
## Number of obs: 2194, groups:  HNDid, 1440
## 
## Fixed effects:
##                        Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)           2.847e+01  5.593e-01  9.380e+02  50.904  < 2e-16 ***
## Age                  -8.614e-02  1.612e-02  1.105e+03  -5.343 1.11e-07 ***
## SexMen                1.794e-01  2.255e-01  9.263e+02   0.795 0.426599    
## EF                    2.109e-02  5.557e-02  1.284e+03   0.379 0.704427    
## RaceAfrAm             5.255e-01  1.865e-01  8.827e+02   2.817 0.004950 ** 
## BMI                  -9.628e-03  9.158e-03  9.924e+02  -1.051 0.293417    
## PovStatBelow         -3.216e-01  1.438e-01  8.447e+02  -2.237 0.025554 *  
## WRATtotal             2.350e-02  1.020e-02  9.452e+02   2.304 0.021443 *  
## Age:SexMen            4.304e-02  2.491e-02  1.011e+03   1.727 0.084390 .  
## Age:EF                6.248e-03  5.143e-03  1.411e+03   1.215 0.224637    
## Age:RaceAfrAm         6.723e-02  2.009e-02  1.024e+03   3.347 0.000848 ***
## SexMen:EF             1.702e-03  8.364e-02  1.381e+03   0.020 0.983765    
## SexMen:RaceAfrAm     -9.546e-02  2.870e-01  8.857e+02  -0.333 0.739501    
## EF:RaceAfrAm          4.538e-02  7.347e-02  1.272e+03   0.618 0.536947    
## Age:SexMen:EF        -6.567e-04  5.904e-03  1.263e+03  -0.111 0.911439    
## Age:SexMen:RaceAfrAm -4.757e-02  3.130e-02  9.699e+02  -1.520 0.128846    
## Age:EF:RaceAfrAm      3.467e-04  5.898e-03  1.326e+03   0.059 0.953137    
## SexMen:EF:RaceAfrAm  -5.436e-02  1.125e-01  1.317e+03  -0.483 0.628999    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation matrix not shown by default, as p = 18 > 12.
## Use print(x, correlation=TRUE)  or
##   vcov(x)     if you need it
##Model 4: Four-way Interactions
mm4 = lmer(PhyPerfSecsTandem~(Age + Sex + EF + Race)^4 + BMI + PovStat + WRATtotal + (1|HNDid), data=DanThesisFinal,REML=F)
summary(mm4)
## Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
##   approximations to degrees of freedom [lmerMod]
## Formula: PhyPerfSecsTandem ~ (Age + Sex + EF + Race)^4 + BMI + PovStat +  
##     WRATtotal + (1 | HNDid)
##    Data: DanThesisFinal
## 
##      AIC      BIC   logLik deviance df.resid 
##  11072.3  11191.8  -5515.1  11030.3     2173 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.9438  0.0425  0.1379  0.2486  1.3854 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  HNDid    (Intercept) 1.026    1.013   
##  Residual             7.948    2.819   
## Number of obs: 2194, groups:  HNDid, 1440
## 
## Fixed effects:
##                           Estimate Std. Error         df t value Pr(>|t|)
## (Intercept)              2.847e+01  5.594e-01  9.394e+02  50.901  < 2e-16
## Age                     -8.454e-02  1.652e-02  1.157e+03  -5.116 3.64e-07
## SexMen                   1.856e-01  2.260e-01  9.221e+02   0.821  0.41167
## EF                       2.053e-02  5.559e-02  1.290e+03   0.369  0.71202
## RaceAfrAm                5.273e-01  1.866e-01  8.817e+02   2.826  0.00482
## BMI                     -9.675e-03  9.160e-03  9.941e+02  -1.056  0.29111
## PovStatBelow            -3.203e-01  1.438e-01  8.441e+02  -2.227  0.02619
## WRATtotal                2.345e-02  1.020e-02  9.462e+02   2.298  0.02178
## Age:SexMen               3.973e-02  2.602e-02  1.081e+03   1.527  0.12714
## Age:EF                   4.957e-03  5.918e-03  1.456e+03   0.838  0.40234
## Age:RaceAfrAm            6.584e-02  2.034e-02  1.062e+03   3.237  0.00124
## SexMen:EF                3.836e-03  8.378e-02  1.402e+03   0.046  0.96348
## SexMen:RaceAfrAm        -1.052e-01  2.879e-01  8.798e+02  -0.365  0.71497
## EF:RaceAfrAm             4.669e-02  7.354e-02  1.283e+03   0.635  0.52555
## Age:SexMen:EF            2.413e-03  9.138e-03  1.480e+03   0.264  0.79175
## Age:SexMen:RaceAfrAm    -4.449e-02  3.207e-02  1.019e+03  -1.387  0.16573
## Age:EF:RaceAfrAm         2.531e-03  7.705e-03  1.340e+03   0.328  0.74263
## SexMen:EF:RaceAfrAm     -5.739e-02  1.127e-01  1.344e+03  -0.509  0.61072
## Age:SexMen:EF:RaceAfrAm -5.270e-03  1.198e-02  1.324e+03  -0.440  0.65997
##                            
## (Intercept)             ***
## Age                     ***
## SexMen                     
## EF                         
## RaceAfrAm               ** 
## BMI                        
## PovStatBelow            *  
## WRATtotal               *  
## Age:SexMen                 
## Age:EF                     
## Age:RaceAfrAm           ** 
## SexMen:EF                  
## SexMen:RaceAfrAm           
## EF:RaceAfrAm               
## Age:SexMen:EF              
## Age:SexMen:RaceAfrAm       
## Age:EF:RaceAfrAm           
## SexMen:EF:RaceAfrAm        
## Age:SexMen:EF:RaceAfrAm    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation matrix not shown by default, as p = 19 > 12.
## Use print(x, correlation=TRUE)  or
##   vcov(x)     if you need it
##Model 5: Significan Interactions Retained
mm5 = lmer(PhyPerfSecsTandem~Age + Sex + EF + Race + BMI + PovStat + WRATtotal + (1|HNDid) + Age*Race, data=DanThesisFinal,REML=F)
summary(mm5)
## Linear mixed model fit by maximum likelihood t-tests use Satterthwaite
##   approximations to degrees of freedom [lmerMod]
## Formula: 
## PhyPerfSecsTandem ~ Age + Sex + EF + Race + BMI + PovStat + WRATtotal +  
##     (1 | HNDid) + Age * Race
##    Data: DanThesisFinal
## 
##      AIC      BIC   logLik deviance df.resid 
##  11060.6  11123.2  -5519.3  11038.6     2183 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -8.8531  0.0497  0.1462  0.2496  1.3889 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  HNDid    (Intercept) 1.143    1.069   
##  Residual             7.875    2.806   
## Number of obs: 2194, groups:  HNDid, 1440
## 
## Fixed effects:
##                 Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)    2.850e+01  5.544e-01  9.462e+02  51.398  < 2e-16 ***
## Age           -6.260e-02  1.172e-02  9.758e+02  -5.342 1.14e-07 ***
## SexMen         1.293e-01  1.383e-01  8.430e+02   0.935 0.349877    
## EF             2.930e-02  3.071e-02  1.412e+03   0.954 0.340182    
## RaceAfrAm      4.897e-01  1.428e-01  8.697e+02   3.428 0.000636 ***
## BMI           -9.839e-03  9.099e-03  9.994e+02  -1.081 0.279818    
## PovStatBelow  -3.105e-01  1.444e-01  8.548e+02  -2.151 0.031781 *  
## WRATtotal      2.301e-02  1.021e-02  9.571e+02   2.254 0.024410 *  
## Age:RaceAfrAm  4.103e-02  1.489e-02  9.594e+02   2.756 0.005959 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Age    SexMen EF     RcAfrA BMI    PvSttB WRATtt
## Age          0.028                                                 
## SexMen      -0.214 -0.009                                          
## EF           0.265  0.072 -0.020                                   
## RaceAfrAm   -0.289  0.041 -0.011  0.117                            
## BMI         -0.503 -0.043  0.182  0.040 -0.017                     
## PovStatBelw -0.264  0.029  0.043  0.070 -0.042  0.070              
## WRATtotal   -0.824 -0.025  0.025 -0.404  0.188 -0.016  0.170       
## Age:RcAfrAm -0.041 -0.784  0.011 -0.030 -0.047  0.046  0.041  0.026
##Plot Age*Race interaction in Final Model
plotData = zHat(DanThesisFinal, mm5, xAxis='Age', factors=('Race'))
# plotData = aggregate(Hat~Age+Sex, data=plotData, FUN=mean)

lineTypes = c(1,2)

par(las=1, lwd=2)

plotData$AgeUn = plotData$Age + 50

with(plotData[plotData$Race=='White',], plot (AgeUn, Hat, lty=lineTypes[1], typ='l', ylim=c(26,31), ylab='Time to Complete 10 Stands (sec)', xlab='Age'))
with(plotData[plotData$Race=='AfrAm',], lines(AgeUn, Hat, lty=lineTypes[2]))

legend(30,28, c('White','AfrAm'), lty=lineTypes)