10.4 Raw Change

The second approach involves computing a change score by subtracting the measure at time 1 from the measure at time 2 (e.g. \(y_{t}-y_{t-1}\))

This raw change score is then typically used as the dependent variable in a regression equation.

Here we are speaking in terms of difference scores and raw change. We can plot intraindividual change, by putting time along the x-axis. This requires reshaping the data from wide format to long format.

To recap, our wide data looks like this:

head(round(wiscsub,2))

##   id verb1 verb2 verb4 verb6 perfo1 perfo2 perfo4 perfo6 momed grad
## 1  1 24.42 26.98 39.61 55.64  19.84  22.97  43.90  44.19   9.5    0
## 2  2 12.44 14.38 21.92 37.81   5.90  13.44  18.29  40.38   5.5    0
## 3  3 32.43 33.51 34.30 50.18  27.64  45.02  46.99  77.72  14.0    1
## 4  4 22.69 28.39 42.16 44.72  33.16  29.68  45.97  61.66  14.0    1
## 5  5 28.23 37.81 41.06 70.95  27.64  44.42  65.48  64.22  11.5    0
## 6  6 16.06 20.12 38.02 39.94   8.45  15.78  26.99  39.08  14.0    1

We can reshape our data to a long format using the reshape() function as follows

wiscsublong <- reshape(
  data = wiscsub[c("id","verb1","verb6")], 
  varying = c("verb1","verb6"), 
  timevar = "grade", 
  idvar = "id", 
  direction = "long", 
  sep = ""
)

wiscsublong <- wiscsublong[order(wiscsublong$id,wiscsublong$grade),]

head(round(wiscsublong,2))

##     id grade  verb
## 1.1  1     1 24.42
## 1.6  1     6 55.64
## 2.1  2     1 12.44
## 2.6  2     6 37.81
## 3.1  3     1 32.43
## 3.6  3     6 50.18

Now, the long data is structured in a manner amenable to plotting.

Notice here that each line indicates how an individual’s Grade 6 score differs from their Grade 1 score: intraindividual change.

library("ggplot2")
ggplot(data = wiscsublong, aes(x = grade, y = verb, group = id)) +
  geom_point() + 
  geom_line() +
  xlab("Grade") + 
  ylab("WISC Verbal Score") + ylim(0,100) +
  scale_x_continuous(breaks=seq(1,6,by=1)) + 
  theme_bw()