Repeated Measures for PERMA17 (Happiness)

#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 positive purpose HAPPI questions
library(reshape2); library(car)

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

data <- data.test4[,c("ID", "GROUP", "wave", "PERMA17")]
data <- dcast(data, ID + GROUP ~ wave, mean, value.var = "PERMA17")
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", "PERMA17", "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 6.81 1.83      7    6.97 1.48   2  10     8 -0.75
## PERMA17     2 59 7.05 2.08      8    7.35 1.48   0  10    10 -1.41
##          kurtosis   se
## BASELINE    -0.02 0.20
## PERMA17      1.96 0.27
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad min max range  skew
## BASELINE    1 88 6.70 2.02      7    6.92 1.48   2  10     8 -0.93
## PERMA17     2 54 7.72 1.50      8    7.93 1.48   3  10     7 -1.38
##          kurtosis   se
## BASELINE     0.13 0.22
## PERMA17      2.23 0.20

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(PERMA17 ~ 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$residual <- NA
sel1 <- which(!is.na(data2$PERMA17)) 
sel2 <- which(!is.na(data2$BASELINE))
data2$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, PERMA17, 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(PERMA17 ~ WAVE + GROUP))

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

Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModel <- lme(PERMA17 ~ 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: Assesses whether the effects gets bigger between 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
##   391.6 410.4 -188.8
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept) Residual
## StdDev:       1.179   0.9204
## 
## Fixed effects: PERMA17 ~ GROUP * WAVE + BASELINE 
##               Value Std.Error DF t-value p-value
## (Intercept)  2.8248    0.7709 66   3.664  0.0005
## GROUP1       0.9699    0.6521 66   1.487  0.1417
## WAVE         0.0371    0.2739 38   0.136  0.8929
## BASELINE     0.5751    0.0924 66   6.222  0.0000
## GROUP1:WAVE -0.0986    0.3998 38  -0.247  0.8065
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.373                     
## WAVE        -0.469  0.576              
## BASELINE    -0.819 -0.020 -0.022       
## GROUP1:WAVE  0.320 -0.846 -0.685  0.017
## 
## Standardized Within-Group Residuals:
##     Min      Q1     Med      Q3     Max 
## -2.8321 -0.3654  0.1024  0.4057  1.8754 
## 
## Number of Observations: 109
## Number of Groups: 69

Table with P-values

	Value	Std.Error	DF	t-value	p-value
(Intercept)	2.8248	0.7709	66.0000	3.6642	0.0005
GROUP1	0.9699	0.6521	66.0000	1.4873	0.1417
WAVE	0.0371	0.2739	38.0000	0.1355	0.8929
BASELINE	0.5751	0.0924	66.0000	6.2215	0.0000
GROUP1:WAVE	-0.0986	0.3998	38.0000	-0.2467	0.8065

``` Table with confidence intervals

	est.	lower	upper
(Intercept)	2.8248	1.3213	4.3282
GROUP1	0.9699	-0.3019	2.2417
WAVE	0.0371	-0.5045	0.5787
BASELINE	0.5751	0.3948	0.7554
GROUP1:WAVE	-0.0986	-0.8892	0.6920