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)
