Reading focus
Syllabus: How Can We Study Change Within People?
Use the simulated examples to distinguish person means, temporal deviations and trends. Follow the correction notice when interpreting notation.
Why you’re reading it. Make the comparison represented by a longitudinal coefficient explicit.
A question to consider. Students are observed across different school years while workload rises. What would change if stress were compared with each student’s overall mean versus their expected level at that time?
Why this reading
An association across people can differ from the association observed as a person changes. Curran and Bauer show how a longitudinal model can separate these questions and why trends and observation schedules complicate that separation.
Before you read
A time-varying covariate is a predictor measured repeatedly. Person-mean centering subtracts each person’s observed mean; detrending instead compares observations with a fitted time trend. The resulting coefficient must be interpreted relative to that reference.
Read for
- Distinguish the components of a predictor from its associations with an outcome.
- Use the artificial examples to track what happens when predictors trend over time and people are observed at different ages.
Consider afterwards
- People are measured over different age windows while both stress and sleep change with age. What would a person’s average represent, and what question should the model answer?
Editorial context
The demonstrations use simulated data, not evidence about anxiety and alcohol use. The proposed methods have limitations, including uncertainty in estimated person-level quantities. Later work by Wang and Maxwell (2015) develops the centering and detrending issues further. A publisher erratum corrects subscripts and Equation 5; repository copies may retain errors. These distinctions do not make a within-person association causal.