Repeated Measures for LET6 I have lots of reasons for living. (6) APPROACHING SIGNIFICANCE.

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#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 LET questions
library(reshape2); library(car)

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

data <- data.test4[,c("ID", "GROUP", "wave", "LET6")]
data <- dcast(data, ID + GROUP ~ wave, mean, value.var = "LET6")
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", "LET6", "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 LET 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 kurtosis
## BASELINE    1 86 4.44 0.85      5    4.60   0   2   5     3 -1.42     1.10
## LET6        2 59 4.52 0.78      5    4.66   0   2   5     3 -1.57     1.78
##            se
## BASELINE 0.09
## LET6     0.10
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed mad min max range  skew kurtosis
## BASELINE    1 88 4.39 0.78      5    4.53   0   2   5     3 -1.35     1.67
## LET6        2 54 4.70 0.74      5    4.89   0   1   5     4 -3.01    10.08
##            se
## BASELINE 0.08
## LET6     0.10

Create a plot that visualizes LET 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(LET6 ~ 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$residual <- NA
sel1 <- which(!is.na(data2$LET6)) 
sel2 <- which(!is.na(data2$BASELINE))
data2$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, LET6, 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(LET6 ~ WAVE + GROUP))

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

Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModel <- lme(LET6 ~ 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
##   163.2 182 -74.59
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept) Residual
## StdDev:      0.2456    0.419
## 
## Fixed effects: LET6 ~ GROUP * WAVE + BASELINE 
##               Value Std.Error DF t-value p-value
## (Intercept)  0.9822    0.3485 66   2.818  0.0064
## GROUP1       0.4760    0.2635 66   1.806  0.0754
## WAVE        -0.0236    0.1180 38  -0.200  0.8426
## BASELINE     0.7897    0.0674 66  11.725  0.0000
## GROUP1:WAVE -0.1887    0.1733 38  -1.089  0.2830
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.333                     
## WAVE        -0.449  0.623              
## BASELINE    -0.859 -0.016 -0.025       
## GROUP1:WAVE  0.290 -0.919 -0.682  0.036
## 
## Standardized Within-Group Residuals:
##     Min      Q1     Med      Q3     Max 
## -2.8653 -0.3783  0.1199  0.1762  2.0866 
## 
## Number of Observations: 109
## Number of Groups: 69

Table with P-values

	Value	Std.Error	DF	t-value	p-value
(Intercept)	0.9822	0.3485	66.0000	2.8184	0.0064
GROUP1	0.4760	0.2635	66.0000	1.8064	0.0754
WAVE	-0.0236	0.1180	38.0000	-0.1999	0.8426
BASELINE	0.7897	0.0674	66.0000	11.7253	0.0000
GROUP1:WAVE	-0.1887	0.1733	38.0000	-1.0890	0.2830

``` Table with confidence intervals

	est.	lower	upper
(Intercept)	0.9822	0.3025	1.6618
GROUP1	0.4760	-0.0379	0.9899
WAVE	-0.0236	-0.2570	0.2098
BASELINE	0.7897	0.6584	0.9211
GROUP1:WAVE	-0.1887	-0.5314	0.1540