10.3 Residualized Change

Before introducing the model behind each approach is is helpful to consider the data characteristics underlying each notion of change.

The first approach uses the measure at the second time point as a dependent variable regressed on the the measure at the first time point.

The term residualized change comes from the fact that an outcome, such as verbal scores at grade 6, is regressed on itself at a prior occasion, verbal scores at grade 1. Any variability in the outcome that is explained by the lagged regressor will be set aside and is threfore not explainable by a key predictor. Thus, the autoregressive effect residualizes the outcome leaving only variability that is unexplained by the lagged variable, which can be construed as the variability due to change.

In this way it is helpful to view the data as a scatter plot, like we would in a regression model.

library("ggplot2")
ggplot(data = wiscsub, aes(x = verb1, y = verb6)) +
  geom_point() + 
  xlab("Verbal Scores at Grade 1") + 
  ylab("Verbal Scores at Grade 6") + 
  theme_bw()