What I am studying. Whether people actually use the reference period an item states. If someone answers “past few hours” by reporting the last twenty minutes, the effective window is shorter than the nominal one, and it may differ between people.
Where I am stuck. The preprint shows that with separated lags the window widths cannot be recovered from the observed covariance structure; only differences between widths are identifiable, and only for one construct. What extra information would identify a person’s effective window: lags shorter than the window, a momentary item alongside the windowed one, or a separate behavioral task that measures how a person aggregates the recent past? I would like to design a study that estimates a person-specific window before trusting any model that assumes the nominal one.
Data situation. None yet; this is a design question. Simulation is possible for any proposed design.