10.7 Critique of Residualized Change

Some interpretational oddities arise from the autoregressive model that are worth considering.

Consider the following situation: We are studying a weight loss intervention where we measure weight prior to and after an intervention. The mean weight at time 1 is 250 pounds (\(\mu_{t1}=150\)) and the mean weight at time 2 is 230 pounds (\(\mu_{t1}=130\)). Now consider two people:

• Individual 1: Weight at time 1 was \(240lbs\) and weight at time 2 is \(240lbs\).
  • Relative standing has gone down so there is positive residualized change.
• Individual 2: Weight at time 1 was \(250lbs\) and weight at time 2 is \(230lbs\).
  • Relative standing is the same so there is no residualized change.