Repeated Measures for HAPPI + PERMA17

#Loading the dataset that has been reset into a long version
data.test4 <- read.csv("/Volumes/TOSHIBA EXT/Dropbox/ADULT STUDY/adult_study011615.csv")
#Creating a new variable that is the mean of all HAPPI questions
data.test4$HAPPIPERMA17 <- apply(data.test4[, c ("HAPPI1" ,"HAPPI2", "HAPPI3", "PERMA17")], 1, mean, na.rm = TRUE)
library(reshape2); library(car)

## Warning: package 'car' was built under R version 3.1.2

data <- data.test4[,c("ID", "GROUP", "wave", "HAPPIPERMA17")]
data <- dcast(data, ID + GROUP ~ wave, mean, value.var = "HAPPIPERMA17")
data[,3:5] <- apply(data[,3:5],2,function(x) recode(x, "NaN = NA") )

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", "HAPPIPERMA17", "WAVE")

Drop the cases where participants did not complete the intervention completely

#data2 <- data2[-c(which(data2$GROUP ==2)),]

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

For lme to work GROUP and ID need to be seen as factors

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

Load the psych package

library(psych)

## 
## Attaching package: 'psych'
## 
## The following object is masked from 'package:car':
## 
##     logit

Describe the HAPPI 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 5.48 1.38   5.75    5.62 1.11 2.25 7.75   5.5 -0.89
## HAPPIPERMA17    2 59 5.69 1.40   6.00    5.87 1.11 0.75 7.75   7.0 -1.48
##              kurtosis   se
## BASELINE         0.00 0.15
## HAPPIPERMA17     2.39 0.18
## -------------------------------------------------------- 
## group: 1
##              vars  n mean   sd median trimmed  mad  min  max range  skew
## BASELINE        1 88 5.30 1.39   5.38    5.35 1.48 1.75 7.75   6.0 -0.32
## HAPPIPERMA17    2 54 6.22 0.80   6.25    6.24 0.74 4.25 7.75   3.5 -0.26
##              kurtosis   se
## BASELINE        -0.23 0.15
## HAPPIPERMA17     0.10 0.11

Create a plot that visualizes HAPPI variable by the GROUP variable

library(ggplot2)

## 
## Attaching package: 'ggplot2'
## 
## The following object is masked from 'package:psych':
## 
##     %+%

Take a look at the residuals

residual <- lm(HAPPIPERMA17 ~ 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$residual <- NA
sel1 <- which(!is.na(data2$HAPPIPERMA17)) 
sel2 <- which(!is.na(data2$BASELINE))
data2$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, HAPPIPERMA17, 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).

# Load the nlme package
library(nlme)

Two way repeated measures Graphing the Two-Way Interaction.

with(data2, boxplot(HAPPIPERMA17 ~ WAVE + GROUP))

with(data2, boxplot(residual ~ WAVE + GROUP))

Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModel <- lme(HAPPIPERMA17 ~ GROUP * WAVE + BASELINE, random = ~1 | ID, data = data2, method = "ML", na.action = "na.omit")

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
##   267.6 286.4 -126.8
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept) Residual
## StdDev:      0.7308   0.4814
## 
## Fixed effects: HAPPIPERMA17 ~ GROUP * WAVE + BASELINE 
##               Value Std.Error DF t-value p-value
## (Intercept)  2.5294    0.4799 66   5.271  0.0000
## GROUP1       0.4676    0.3566 66   1.311  0.1944
## WAVE        -0.0954    0.1450 38  -0.658  0.5143
## BASELINE     0.5674    0.0752 66   7.548  0.0000
## GROUP1:WAVE  0.1537    0.2114 38   0.727  0.4716
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.344                     
## WAVE        -0.390  0.556              
## BASELINE    -0.864  0.002 -0.027       
## GROUP1:WAVE  0.270 -0.816 -0.686  0.015
## 
## Standardized Within-Group Residuals:
##      Min       Q1      Med       Q3      Max 
## -2.48680 -0.30248  0.07239  0.38320  1.98865 
## 
## Number of Observations: 109
## Number of Groups: 69

Table with P-values

	Value	Std.Error	DF	t-value	p-value
(Intercept)	2.5294	0.4799	66.0000	5.2707	0.0000
GROUP1	0.4676	0.3566	66.0000	1.3111	0.1944
WAVE	-0.0954	0.1450	38.0000	-0.6583	0.5143
BASELINE	0.5674	0.0752	66.0000	7.5479	0.0000
GROUP1:WAVE	0.1537	0.2114	38.0000	0.7272	0.4716

``` Table with confidence intervals

	est.	lower	upper
(Intercept)	2.5294	1.5935	3.4653
GROUP1	0.4676	-0.2279	1.1631
WAVE	-0.0954	-0.3821	0.1912
BASELINE	0.5674	0.4208	0.7140
GROUP1:WAVE	0.1537	-0.2642	0.5716