Repeated Measures for GRIT11 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", "GRIT11")]
data <- dcast(data, ID + GROUP ~ wave, mean, value.var = "GRIT11")
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", "GRIT11", "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 4.51 0.73      5    4.66   0   2   5     3 -1.47     1.69
## GRIT11      2 59 4.63 0.64      5    4.76   0   3   5     2 -1.44     0.80
##            se
## BASELINE 0.08
## GRIT11   0.08
## -------------------------------------------------------- 
## group: 1
##          vars  n mean   sd median trimmed  mad min max range  skew
## BASELINE    1 88 4.20 1.04      4    4.42 1.48   1   5     4 -1.62
## GRIT11      2 54 4.46 0.64      5    4.55 0.00   3   5     2 -0.73
##          kurtosis   se
## BASELINE     2.24 0.11
## GRIT11      -0.54 0.09

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(GRIT11 ~ 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$residual <- NA
sel1 <- which(!is.na(data2$GRIT11)) 
sel2 <- which(!is.na(data2$BASELINE))
data2$residual[intersect(sel1,sel2)] <- residual
qplot(GROUP, GRIT11, 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(GRIT11 ~ WAVE + GROUP))

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

Linear Mixed-Effects Model

Comparing Basline to Wave 2 and 3 by Group.

fullModel <- lme(GRIT11 ~ 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
##   170.1 189 -78.06
## 
## Random effects:
##  Formula: ~1 | ID
##         (Intercept) Residual
## StdDev:        0.36   0.3746
## 
## Fixed effects: GRIT11 ~ GROUP * WAVE + BASELINE 
##               Value Std.Error DF t-value p-value
## (Intercept)  2.3296    0.3581 66   6.505  0.0000
## GROUP1       0.1119    0.2520 66   0.444  0.6585
## WAVE         0.0978    0.1091 38   0.896  0.3759
## BASELINE     0.4728    0.0702 66   6.734  0.0000
## GROUP1:WAVE -0.1632    0.1598 38  -1.022  0.3134
##  Correlation: 
##             (Intr) GROUP1 WAVE   BASELI
## GROUP1      -0.418                     
## WAVE        -0.396  0.593              
## BASELINE    -0.880  0.111 -0.028       
## GROUP1:WAVE  0.330 -0.883 -0.681 -0.049
## 
## Standardized Within-Group Residuals:
##     Min      Q1     Med      Q3     Max 
## -2.4861 -0.3073  0.1871  0.3618  1.6018 
## 
## Number of Observations: 109
## Number of Groups: 69

Table with P-values

	Value	Std.Error	DF	t-value	p-value
(Intercept)	2.3296	0.3581	66.0000	6.5053	0.0000
GROUP1	0.1119	0.2520	66.0000	0.4439	0.6585
WAVE	0.0978	0.1091	38.0000	0.8960	0.3759
BASELINE	0.4728	0.0702	66.0000	6.7337	0.0000
GROUP1:WAVE	-0.1632	0.1598	38.0000	-1.0216	0.3134

``` Table with confidence intervals

	est.	lower	upper
(Intercept)	2.3296	1.6312	3.0280
GROUP1	0.1119	-0.3796	0.6034
WAVE	0.0978	-0.1180	0.3136
BASELINE	0.4728	0.3359	0.6097
GROUP1:WAVE	-0.1632	-0.4792	0.1527