Loading the dataset

data.test4 <- read.csv("/Volumes/TOSHIBA EXT/Dropbox/ADULT STUDY/adult_study011615.csv")
# Load the psych package
library(psych)
items <- grep("PWB[0-9]", names(data.test4), value=TRUE)
scaleKey <- c(-1,-1,-1,-1,-1,1,1,1,-1)
data.test4[,items] <- apply(data.test4[,items], 2, as.numeric)
data.test4$meanPWB <- scoreItems(scaleKey, items = data.test4[, items])$score
library(reshape2); library(car); library(Amelia);library(mitools);library(nlme);library(predictmeans)
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:psych':
## 
##     logit
## 
## Loading required package: Rcpp
## ## 
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.3, built: 2014-11-14)
## ## Copyright (C) 2005-2015 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ## 
## Loading required package: lme4
## Loading required package: Matrix
## 
## Attaching package: 'lme4'
## 
## The following object is masked from 'package:nlme':
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##     lmList
#Remove the meanPWB and ID Group and wave from data.test4 and create a new #dataset with only those variables.
data <- data.test4[,c("ID", "GROUP", "wave", "meanPWB")]
#Use dcast to cnage from long-format data to wide format data
data <- dcast(data, ID + GROUP ~ wave, mean, value.var = "meanPWB")
# Changing all NaNs to NA
data[,3:5] <- apply(data[,3:5],2,function(x) recode(x, "NaN = NA") )

Unsing the mapply function we create a new data set with ID Group baseline meanPWB and wave 2 and 3 of meanPWB. So we have a Baseline, which is Time 1 (placed in column 3 one on top of the other) to compare to both Time 2 and 3 (placed in column 4 one on top of the other). In the next line of code we then create a separate column called “wave” which calls the first 89 (which compares Time 2 to Baseline) “wave 1” and then the second 89 we call “wave 2” which compares Time 3 to Baseline. In the third line of code we add names to the new columns of the dataset.

data2 <- as.data.frame(mapply(c,data[,1:4], data[,c(1:3,5)]))
data2$wave <- rep(1:2, each=89)
names(data2) <- c("ID", "GROUP", "BASELINE", "meanPWB", "WAVE")

Intention to treat model (ITT) where we keep the cases who dropped out and did not complete the study (http://en.wikipedia.org/wiki/Intention-to-treat_analysis).

data2[which(data2$GROUP ==2), "GROUP"] <- 1

Make GROUP and ID a factor

data2$GROUP <-as.factor(data2$GROUP)
data2$ID <-as.factor(data2$ID)

Imputing missing data

MI <- amelia(data2, 50, idvars = c("ID"), ords = "GROUP")
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Creating new dataset with missing data imputed

data(MI$imputations)
## Warning in data(MI$imputations): data set 'MI$imputations' not found
allimplogreg<-lapply(MI$imputations,function(X) {lme(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = X, method = "ML", na.action = "na.omit")})
betas<-MIextract(allimplogreg, fun=fixef)
vars<-MIextract(allimplogreg, fun=vcov)
summary(MIcombine(betas,vars))
## Multiple imputation results:
##       MIcombine.default(betas, vars)
##               results         se     (lower    upper) missInfo
## (Intercept) 1.7154080 0.38739724  0.9509664 2.4798495     53 %
## GROUP1      0.1893165 0.29126243 -0.3831342 0.7617673     34 %
## WAVE        0.1362177 0.13495974 -0.1292768 0.4017121     39 %
## BASELINE    0.6035440 0.07480108  0.4555681 0.7515199     62 %
## GROUP1:WAVE 0.1252107 0.19066476 -0.2500052 0.5004267     41 %

Check results with Imputations using Zelig

library("Zelig")
## Loading required package: boot
## 
## Attaching package: 'boot'
## 
## The following object is masked from 'package:car':
## 
##     logit
## 
## The following object is masked from 'package:psych':
## 
##     logit
## 
## Loading required package: MASS
## Loading required package: sandwich
## ZELIG (Versions 4.2-1, built: 2013-09-12)
## 
## +----------------------------------------------------------------+
## |  Please refer to http://gking.harvard.edu/zelig for full       |
## |  documentation or help.zelig() for help with commands and      |
## |  models support by Zelig.                                      |
## |                                                                |
## |  Zelig project citations:                                      |
## |    Kosuke Imai, Gary King, and Olivia Lau.  (2009).            |
## |    ``Zelig: Everyone's Statistical Software,''                 |
## |    http://gking.harvard.edu/zelig                              |
## |   and                                                          |
## |    Kosuke Imai, Gary King, and Olivia Lau. (2008).             |
## |    ``Toward A Common Framework for Statistical Analysis        |
## |    and Development,'' Journal of Computational and             |
## |    Graphical Statistics, Vol. 17, No. 4 (December)             |
## |    pp. 892-913.                                                |
## |                                                                |
## |   To cite individual Zelig models, please use the citation     |
## |   format printed with each model run and in the documentation. |
## +----------------------------------------------------------------+
## 
## 
## 
## Attaching package: 'Zelig'
## 
## The following objects are masked from 'package:psych':
## 
##     alpha, describe, sim
## 
## The following object is masked from 'package:utils':
## 
##     cite
zelig.fit <- zelig(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = MI$imputations,  model = "ls", cite = FALSE)
summary(zelig.fit)
## 
##   Model: ls
##   Number of multiply imputed data sets: 50 
## 
## Combined results:
## 
## Call:
## lm(formula = formula, weights = weights, model = F, data = data)
## 
## Coefficients:
##                 Value Std. Error    t-stat      p-value
## (Intercept) 1.7106748  0.3862160 4.4293217 1.620215e-05
## GROUP1      0.1895433  0.3092512 0.6129103 5.401869e-01
## WAVE        0.1362177  0.1446034 0.9420091 3.467133e-01
## BASELINE    0.6046133  0.0726183 8.3259086 1.517495e-13
## GROUP1:WAVE 0.1252191  0.2038988 0.6141240 5.394910e-01
## 
## For combined results from datasets i to j, use summary(x, subset = i:j).
## For separate results, use print(summary(x), subset = i:j).

Check assumptions with Random Computations

data1=MI$imputations[[1]]
library("Zelig")
zelig.fitdata1 <- zelig(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data1,  model = "ls", cite = FALSE)
summary(zelig.fitdata1)
## 
## Call:
## lm(formula = formula, weights = weights, model = F, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.84967 -0.28214 -0.00048  0.34253  1.29064 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.78739    0.26558   6.730 2.39e-10 ***
## GROUP1       0.34781    0.25641   1.356    0.177    
## WAVE         0.15664    0.11649   1.345    0.181    
## BASELINE     0.57885    0.04323  13.391  < 2e-16 ***
## GROUP1:WAVE  0.03926    0.16204   0.242    0.809    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5401 on 173 degrees of freedom
## Multiple R-squared:  0.532,  Adjusted R-squared:  0.5212 
## F-statistic: 49.16 on 4 and 173 DF,  p-value: < 2.2e-16

Describe the meanPWB variable by the GROUP variable

describeBy(data1[,3:4], group = data1$GROUP)
## group: 0
##          vars  n mean   sd median trimmed  mad  min max range  skew
## BASELINE    1 86 4.43 0.97   4.67    4.47 0.82 2.33   6  3.67 -0.43
## meanPWB     2 86 4.58 0.80   4.70    4.63 0.94 2.44   6  3.56 -0.52
##          kurtosis   se
## BASELINE    -0.75 0.10
## meanPWB     -0.23 0.09
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 92 4.21 0.91   4.06    4.25 0.99 1.00 5.82  4.82 -0.70
## meanPWB     2 92 4.87 0.74   4.91    4.90 0.63 2.74 6.41  3.67 -0.49
##          kurtosis   se
## BASELINE     1.35 0.10
## meanPWB      0.03 0.08

Create a plot that visualizes meanPWB variable by the GROUP variable

library(ggplot2)
## 
## Attaching package: 'ggplot2'
## 
## The following object is masked from 'package:psych':
## 
##     %+%
library(influence.ME)
## 
## Attaching package: 'influence.ME'
## 
## The following object is masked from 'package:stats':
## 
##     influence

Take a look at the residuals

residual <- lm(meanPWB ~ BASELINE, data=data1)$residual

Plot the residuals to see that they are random

plot(density(residual))# A density plot

qqnorm(residual) # A quantile normal plot to checking normality
qqline(residual)

Checking the different between intervention and control groups residuals. This allows us to control for individual unsystematic differences.

data2$residual <- NA
sel1 <- which(!is.na(data1$meanPWB)) 
sel2 <- which(!is.na(data1$BASELINE))
data1$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, meanPWB, data=data1, geom="boxplot")

Plot of the difference between intervention and control groups.

qplot(GROUP, residual, data=data1, geom="boxplot")

Two way repeated measures ======================================================== Graphing the Two-Way Interaction. Both meanPWB and the Residuals

# Load the nlme package
library(nlme)
with(data1, boxplot(meanPWB ~ WAVE + GROUP))

with(data1, boxplot(residual ~ WAVE + GROUP))
Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModeldata1 <- lme(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data1, method = "ML", na.action = "na.omit")

Cooks Distence

CookD(fullModeldata1)

Plot Cook’s distance:

plot(fullModeldata1, which="cook")
Check results on this random Imputation model
Results

Explanation of significance:

We asses the significance of our models by comparing them from the baseline model using the anova() function.
(Intercept): Where everything is 0
GROUP1: Is there a difference between group. If it is significant than there is a difference and the treatment had an effect.
WAVE: Asseses whether the effects gets bigger beteen time 2 and 3 (does not have to be significant)
BASELINE: Should not be significant. If it is then it shows that there is a difference between groups before the treatment.
GROUP1:WAVE: If this is significant then it means that the effect was either fleeting or it happened after the treatment i.e. between time 2 and 3.

summary(fullModeldata1)
## Linear mixed-effects model fit by maximum likelihood
##  Data: data1 
##        AIC     BIC    logLik
##   289.4385 311.711 -137.7193
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept)  Residual
## StdDev:   0.2619204 0.4636408
## 
## Fixed effects: meanPWB ~ GROUP * WAVE + BASELINE 
##                 Value  Std.Error DF   t-value p-value
## (Intercept) 1.7910791 0.26978398 87  6.638938  0.0000
## GROUP1      0.3476111 0.23036334 87  1.508969  0.1349
## WAVE        0.1566355 0.10142601 86  1.544332  0.1262
## BASELINE    0.5780153 0.04814989 86 12.004499  0.0000
## GROUP1:WAVE 0.0392716 0.14108229 86  0.278359  0.7814
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.480                     
## WAVE        -0.564  0.660              
## BASELINE    -0.790  0.050  0.000       
## GROUP1:WAVE  0.410 -0.919 -0.719 -0.006
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.09860914 -0.51390101  0.01253942  0.57410552  2.21424375 
## 
## Number of Observations: 178
## Number of Groups: 89

Another random imputation

data10=MI$imputations[[10]]
library("Zelig")
zelig.fitdata10 <- zelig(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data10,  model = "ls", cite = FALSE)
summary(zelig.fitdata10)
## 
## Call:
## lm(formula = formula, weights = weights, model = F, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.59946 -0.30742  0.01035  0.34814  1.54135 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.02986    0.26021   3.958  0.00011 ***
## GROUP1      -0.06887    0.25108  -0.274  0.78418    
## WAVE         0.19933    0.11410   1.747  0.08243 .  
## BASELINE     0.73558    0.04236  17.364  < 2e-16 ***
## GROUP1:WAVE  0.28444    0.15872   1.792  0.07486 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5291 on 173 degrees of freedom
## Multiple R-squared:  0.6554, Adjusted R-squared:  0.6474 
## F-statistic: 82.25 on 4 and 173 DF,  p-value: < 2.2e-16

Describe the meanPWB variable by the GROUP variable

describeBy(data10[,3:4], group = data10$GROUP)
## group: 0
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 86 4.43 0.97   4.67    4.47 0.82 2.33 6.00  3.67 -0.43
## meanPWB     2 86 4.58 0.91   4.78    4.63 0.83 2.16 6.56  4.40 -0.50
##          kurtosis  se
## BASELINE    -0.75 0.1
## meanPWB     -0.23 0.1
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 92 4.21 0.91   4.06    4.25 0.91 1.00 5.94  4.94 -0.68
## meanPWB     2 92 4.78 0.86   4.89    4.85 0.66 1.16 6.48  5.32 -1.07
##          kurtosis   se
## BASELINE     1.39 0.10
## meanPWB      2.20 0.09

Create a plot that visualizes meanPWB variable by the GROUP variable

library(ggplot2)
library(influence.ME)

Take a look at the residuals

residual <- lm(meanPWB ~ BASELINE, data=data10)$residual

Plot the residuals to see that they are random

plot(density(residual))# A density plot

qqnorm(residual) # A quantile normal plot to checking normality
qqline(residual)

Checking the different between intervention and control groups residuals. This allows us to control for individual unsystematic differences.

data2$residual <- NA
sel1 <- which(!is.na(data10$meanPWB)) 
sel2 <- which(!is.na(data10$BASELINE))
data10$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, meanPWB, data=data10, geom="boxplot")

Plot of the difference between intervention and control groups.

qplot(GROUP, residual, data=data10, geom="boxplot")

Two way repeated measures ======================================================== Graphing the Two-Way Interaction. Both meanPWB and the Residuals

# Load the nlme package
library(nlme)
with(data10, boxplot(meanPWB ~ WAVE + GROUP))

with(data10, boxplot(residual ~ WAVE + GROUP))
Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModeldata10 <- lme(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data10, method = "ML", na.action = "na.omit")

Cooks Distence

CookD(fullModeldata10)

Plot Cook’s distance:

plot(fullModeldata10, which="cook")
Check results on this random Imputation model
Results

Explanation of significance:

We asses the significance of our models by comparing them from the baseline model using the anova() function.
(Intercept): Where everything is 0
GROUP1: Is there a difference between group. If it is significant than there is a difference and the treatment had an effect.
WAVE: Asseses whether the effects gets bigger beteen time 2 and 3 (does not have to be significant)
BASELINE: Should not be significant. If it is then it shows that there is a difference between groups before the treatment.
GROUP1:WAVE: If this is significant then it means that the effect was either fleeting or it happened after the treatment i.e. between time 2 and 3.

summary(fullModeldata10)
## Linear mixed-effects model fit by maximum likelihood
##  Data: data10 
##        AIC      BIC    logLik
##   287.3138 309.5863 -136.6569
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept) Residual
## StdDev:   0.1002689 0.511868
## 
## Fixed effects: meanPWB ~ GROUP * WAVE + BASELINE 
##                  Value  Std.Error DF   t-value p-value
## (Intercept)  1.0299358 0.26084385 87  3.948476  0.0002
## GROUP1      -0.0688757 0.24735461 87 -0.278449  0.7813
## WAVE         0.1993309 0.11197619 86  1.780119  0.0786
## BASELINE     0.7355584 0.04313362 86 17.053017  0.0000
## GROUP1:WAVE  0.2844421 0.15575658 86  1.826196  0.0713
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.514                     
## WAVE        -0.644  0.679              
## BASELINE    -0.732  0.034  0.000       
## GROUP1:WAVE  0.460 -0.944 -0.719  0.005
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -2.93140751 -0.55458270  0.02778605  0.65180129  2.92575242 
## 
## Number of Observations: 178
## Number of Groups: 89

Another random imputation

data15=MI$imputations[[15]]
library("Zelig")
zelig.fitdata15 <- zelig(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data15,  model = "ls", cite = FALSE)
summary(zelig.fitdata15)
## 
## Call:
## lm(formula = formula, weights = weights, model = F, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.63024 -0.28008 -0.01045  0.24735  1.30970 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.61659    0.24121   6.702 2.78e-10 ***
## GROUP1       0.05048    0.23185   0.218    0.828    
## WAVE         0.09096    0.10532   0.864    0.389    
## BASELINE     0.64017    0.03942  16.239  < 2e-16 ***
## GROUP1:WAVE  0.19399    0.14650   1.324    0.187    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4883 on 173 degrees of freedom
## Multiple R-squared:  0.6178, Adjusted R-squared:  0.609 
## F-statistic: 69.92 on 4 and 173 DF,  p-value: < 2.2e-16

Describe the meanPWB variable by the GROUP variable

describeBy(data15[,3:4], group = data15$GROUP)
## group: 0
##          vars  n mean   sd median trimmed  mad  min max range  skew
## BASELINE    1 86 4.43 0.97   4.67    4.47 0.82 2.33   6  3.67 -0.43
## meanPWB     2 86 4.59 0.82   4.75    4.63 0.86 2.44   6  3.56 -0.49
##          kurtosis   se
## BASELINE    -0.75 0.10
## meanPWB     -0.48 0.09
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 92 4.19 0.90   4.05    4.24 0.92 1.00 5.56  4.56 -0.73
## meanPWB     2 92 4.78 0.74   4.89    4.84 0.66 2.29 6.00  3.71 -0.92
##          kurtosis   se
## BASELINE      1.5 0.09
## meanPWB       0.7 0.08

Create a plot that visualizes meanPWB variable by the GROUP variable

library(ggplot2)
library(influence.ME)

Take a look at the residuals

residual <- lm(meanPWB ~ BASELINE, data=data15)$residual

Plot the residuals to see that they are random

plot(density(residual))# A density plot

qqnorm(residual) # A quantile normal plot to checking normality
qqline(residual)

Checking the different between intervention and control groups residuals. This allows us to control for individual unsystematic differences.

data2$residual <- NA
sel1 <- which(!is.na(data15$meanPWB)) 
sel2 <- which(!is.na(data15$BASELINE))
data15$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, meanPWB, data=data15, geom="boxplot")

Plot of the difference between intervention and control groups.

qplot(GROUP, residual, data=data15, geom="boxplot")

Two way repeated measures ======================================================== Graphing the Two-Way Interaction. Both meanPWB and the Residuals

# Load the nlme package
library(nlme)
with(data15, boxplot(meanPWB ~ WAVE + GROUP))

with(data15, boxplot(residual ~ WAVE + GROUP))
Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModeldata15 <- lme(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data15, method = "ML", na.action = "na.omit")

Cooks Distence

CookD(fullModeldata15)

Plot Cook’s distance:

plot(fullModeldata15, which="cook")
Check results on this random Imputation model
Results

Explanation of significance:

We asses the significance of our models by comparing them from the baseline model using the anova() function.
(Intercept): Where everything is 0
GROUP1: Is there a difference between group. If it is significant than there is a difference and the treatment had an effect.
WAVE: Asseses whether the effects gets bigger beteen time 2 and 3 (does not have to be significant)
BASELINE: Should not be significant. If it is then it shows that there is a difference between groups before the treatment.
GROUP1:WAVE: If this is significant then it means that the effect was either fleeting or it happened after the treatment i.e. between time 2 and 3.

summary(fullModeldata15)
## Linear mixed-effects model fit by maximum likelihood
##  Data: data15 
##        AIC      BIC    logLik
##   254.2403 276.5128 -120.1201
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept)  Residual
## StdDev:   0.2289384 0.4235173
## 
## Fixed effects: meanPWB ~ GROUP * WAVE + BASELINE 
##                 Value  Std.Error DF   t-value p-value
## (Intercept) 1.6199532 0.24501006 87  6.611783  0.0000
## GROUP1      0.0502845 0.20993818 87  0.239521  0.8113
## WAVE        0.0909639 0.09264861 86  0.981816  0.3289
## BASELINE    0.6394107 0.04364187 86 14.651313  0.0000
## GROUP1:WAVE 0.1940042 0.12887294 86  1.505391  0.1359
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.484                     
## WAVE        -0.567  0.662              
## BASELINE    -0.788  0.054  0.000       
## GROUP1:WAVE  0.412 -0.921 -0.719 -0.006
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -2.96771487 -0.52956887 -0.02611949  0.57234343  2.69211466 
## 
## Number of Observations: 178
## Number of Groups: 89

Another random imputation

data25=MI$imputations[[25]]

library("Zelig")
zelig.fitdata25 <- zelig(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data25,  model = "ls", cite = FALSE)
summary(zelig.fitdata25)
## 
## Call:
## lm(formula = formula, weights = weights, model = F, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.65965 -0.31483  0.00817  0.34480  1.25885 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.53793    0.27409   5.611 7.85e-08 ***
## GROUP1       0.22909    0.26514   0.864    0.389    
## WAVE         0.12096    0.12045   1.004    0.317    
## BASELINE     0.63884    0.04453  14.346  < 2e-16 ***
## GROUP1:WAVE  0.11874    0.16755   0.709    0.479    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5585 on 173 degrees of freedom
## Multiple R-squared:  0.562,  Adjusted R-squared:  0.5519 
## F-statistic: 55.49 on 4 and 173 DF,  p-value: < 2.2e-16

Describe the meanPWB variable by the GROUP variable

describeBy(data25[,3:4], group = data25$GROUP)
## group: 0
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 86 4.43 0.97   4.67    4.47 0.82 2.33 6.00  3.67 -0.43
## meanPWB     2 86 4.55 0.87   4.56    4.61 0.82 1.70 6.21  4.51 -0.64
##          kurtosis   se
## BASELINE    -0.75 0.10
## meanPWB      0.42 0.09
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 92 4.21 0.92   4.06    4.25 0.91 1.00 6.22  5.22 -0.64
## meanPWB     2 92 4.82 0.78   4.89    4.86 0.58 2.25 6.69  4.44 -0.66
##          kurtosis   se
## BASELINE     1.37 0.10
## meanPWB      1.05 0.08

Create a plot that visualizes meanPWB variable by the GROUP variable

library(ggplot2)
library(influence.ME)

Take a look at the residuals

residual <- lm(meanPWB ~ BASELINE, data=data25)$residual

Plot the residuals to see that they are random

plot(density(residual))# A density plot

qqnorm(residual) # A quantile normal plot to checking normality
qqline(residual)

Checking the different between intervention and control groups residuals. This allows us to control for individual unsystematic differences.

data2$residual <- NA
sel1 <- which(!is.na(data25$meanPWB)) 
sel2 <- which(!is.na(data25$BASELINE))
data25$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, meanPWB, data=data25, geom="boxplot")

Plot of the difference between intervention and control groups.

qplot(GROUP, residual, data=data25, geom="boxplot")

Two way repeated measures ======================================================== Graphing the Two-Way Interaction. Both meanPWB and the Residuals

# Load the nlme package
library(nlme)
with(data25, boxplot(meanPWB ~ WAVE + GROUP))

with(data25, boxplot(residual ~ WAVE + GROUP))
Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModeldata25 <- lme(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data25, method = "ML", na.action = "na.omit")

Cooks Distence

CookD(fullModeldata25)

Plot Cook’s distance:

plot(fullModeldata25, which="cook")
Check results on this random Imputation model
Results

Explanation of significance:

We asses the significance of our models by comparing them from the baseline model using the anova() function.
(Intercept): Where everything is 0
GROUP1: Is there a difference between group. If it is significant than there is a difference and the treatment had an effect.
WAVE: Asseses whether the effects gets bigger beteen time 2 and 3 (does not have to be significant)
BASELINE: Should not be significant. If it is then it shows that there is a difference between groups before the treatment.
GROUP1:WAVE: If this is significant then it means that the effect was either fleeting or it happened after the treatment i.e. between time 2 and 3.

summary(fullModeldata25)
## Linear mixed-effects model fit by maximum likelihood
##  Data: data25 
##        AIC      BIC    logLik
##   305.8344 328.1069 -145.9172
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept)  Residual
## StdDev:   0.1732411 0.5226527
## 
## Fixed effects: meanPWB ~ GROUP * WAVE + BASELINE 
##                 Value  Std.Error DF   t-value p-value
## (Intercept) 1.5405111 0.27580973 87  5.585412  0.0000
## GROUP1      0.2289453 0.25446177 87  0.899724  0.3708
## WAVE        0.1209606 0.11433546 86  1.057944  0.2930
## BASELINE    0.6382604 0.04666829 86 13.676531  0.0000
## GROUP1:WAVE 0.1187501 0.15903943 86  0.746671  0.4573
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.509                     
## WAVE        -0.622  0.674              
## BASELINE    -0.749  0.045  0.000       
## GROUP1:WAVE  0.452 -0.938 -0.719 -0.006
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.05664893 -0.52421392  0.01444234  0.61537119  2.22010279 
## 
## Number of Observations: 178
## Number of Groups: 89

Check assumptions on model without any imputations

Describe the meanPWB variable by the GROUP variable

describeBy(data2[,3:4], group = data2$GROUP)
## group: 0
##          vars  n mean   sd median trimmed  mad  min max range  skew
## BASELINE    1 86 4.43 0.97   4.67    4.47 0.82 2.33   6  3.67 -0.43
## meanPWB     2 59 4.69 0.82   4.78    4.75 0.82 2.44   6  3.56 -0.70
##          kurtosis   se
## BASELINE    -0.75 0.10
## meanPWB      0.03 0.11
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE    1 88 4.17 0.91   4.00    4.21 0.99 1.00 5.56  4.56 -0.69
## meanPWB     2 54 4.88 0.64   4.94    4.93 0.49 2.89 6.00  3.11 -0.83
##          kurtosis   se
## BASELINE     1.41 0.10
## meanPWB      0.69 0.09

Create a plot that visualizes meanPWB variable by the GROUP variable

library(ggplot2)
library(influence.ME)

Take a look at the residuals

residual <- lm(meanPWB ~ BASELINE, data=data2)$residual

Plot the residuals to see that they are random

plot(density(residual))# A density plot

qqnorm(residual) # A quantile normal plot to checking normality
qqline(residual)

Checking the different between intervention and control groups residuals. This allows us to control for individual unsystematic differences.

data2$residual <- NA
sel1 <- which(!is.na(data2$meanPWB)) 
sel2 <- which(!is.na(data2$BASELINE))
data2$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, meanPWB, data=data2, geom="boxplot")
## Warning: Removed 65 rows containing non-finite values (stat_boxplot).

Plot of the difference between intervention and control groups.

qplot(GROUP, residual, data=data2, geom="boxplot")
## Warning: Removed 69 rows containing non-finite values (stat_boxplot).

Two way repeated measures ======================================================== Graphing the Two-Way Interaction. Both meanPWB and the Residuals

# Load the nlme package
library(nlme)
with(data2, boxplot(meanPWB ~ WAVE + GROUP))

with(data2, boxplot(residual ~ WAVE + GROUP))
Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModel <- lme(meanPWB ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data2, method = "ML", na.action = "na.omit")

Cooks Distence

CookD(fullModel)

Plot Cook’s distance:

plot(fullModel, which="cook")
Results on Model with data that contains no imputations
Results

Explanation of significance:

We asses the significance of our models by comparing them from the baseline model using the anova() function.
(Intercept): Where everything is 0
GROUP1: Is there a difference between group. If it is significant than there is a difference and the treatment had an effect.
WAVE: Asseses whether the effects gets bigger beteen time 2 and 3 (does not have to be significant)
BASELINE: Should not be significant. If it is then it shows that there is a difference between groups before the treatment.
GROUP1:WAVE: If this is significant then it means that the effect was either fleeting or it happened after the treatment i.e. between time 2 and 3.

summary(fullModel)
## Linear mixed-effects model fit by maximum likelihood
##  Data: data2 
##        AIC     BIC    logLik
##   176.3976 195.237 -81.19878
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept)  Residual
## StdDev:   0.4091197 0.3619596
## 
## Fixed effects: meanPWB ~ GROUP * WAVE + BASELINE 
##                 Value Std.Error DF  t-value p-value
## (Intercept) 1.8931604 0.3810992 66 4.967632  0.0000
## GROUP1      0.0601033 0.2504277 66 0.240003  0.8111
## WAVE        0.0681424 0.1066892 38 0.638700  0.5268
## BASELINE    0.5790232 0.0749272 66 7.727815  0.0000
## GROUP1:WAVE 0.2198848 0.1559119 38 1.410314  0.1666
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.380                     
## WAVE        -0.383  0.585              
## BASELINE    -0.896  0.090 -0.002       
## GROUP1:WAVE  0.258 -0.860 -0.684  0.007
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -2.29290462 -0.47354223  0.08279482  0.52335417  1.88597819 
## 
## Number of Observations: 109
## Number of Groups: 69
Table with P-value

|             |      Value|  Std.Error|  DF|    t-value|    p-value|
|:------------|----------:|----------:|---:|----------:|----------:|
|(Intercept)  |  1.8931604|  0.3810992|  66|  4.9676319|  0.0000051|
|GROUP1       |  0.0601033|  0.2504277|  66|  0.2400027|  0.8110720|
|WAVE         |  0.0681424|  0.1066892|  38|  0.6387000|  0.5268493|
|BASELINE     |  0.5790232|  0.0749272|  66|  7.7278147|  0.0000000|
|GROUP1:WAVE  |  0.2198848|  0.1559119|  38|  1.4103142|  0.1665805|

Table with confidence intervals

est. lower upper
(Intercept) 1.8931604 1.1499278 2.6363930
GROUP1 0.0601033 -0.4282893 0.5484960
WAVE 0.0681424 -0.1428268 0.2791116
BASELINE 0.5790232 0.4328977 0.7251487
GROUP1:WAVE 0.2198848 -0.0884182 0.5281878