Centering method for lagged variables

[PetrouEUR]

Dear MlwiN users,

Suppose we have weekly (or diary) data where a within-level X variable(s) predicts a within-level Y variable. Now I want to create lagged (previous-week) variables for both X and Y and add them as control variables. I have seen in a paper that while lagged Y was grandmean centered, lagged X was groupmean centered. Do you agree with that and is there any methodological reference to justify this?

Furthermore, when I experiment with different centering methods, I often run into some strange problems that I cannot interpret:
(1) When lagged Y is grandmean centered, variance at the between-level is 0. However, when lagged Y is groupmean centered, between-level variance is positive. What does this mean?
(2) While the effect of grandmean centered lagged Y is positive (which makes sense if we see this as "stability" effect), the effect becomes negative when lagged Y is groupmean centered. This looks like a strange artefact that does not agree with the correlation matrix. What does this mean?

Thank you!

Paris

[ChrisCharlton]

I asked around, but no-one I asked had enough experience with this to provide any direct advice. The feeling was that using a lagged Y as an X variable without taking the auto-regressive structure into account would be problematic. The following references were suggested:

Don’t Put Lagged Dependent Variables in Mixed Models: https://statisticalhorizons.com/lagged- ... -variables

Bell, Andrew, Kelvyn Jones, and Malcolm Fairbrother. 2017. “Understanding and Misunderstanding Group Mean Centering: A Commentary on Kelley et Al.’s Dangerous Practice.” Quality & Quantity

[PetrouEUR]

That really helps, thank you Chris!

Best,
Paris

[PetrouEUR]

And does anyone know if the same logic applies to a lagged X as predictor of Y? Is this allowed and if yes, what is the best centering method and why?

Thank you!
Paris

[Normanpo]

I asked around, but no-one I asked had enough experience with this to provide any direct advice. The feeling was that using a lagged Y as an X variable without taking the auto-regressive structure into account would be problematic. The following references were suggested:

Don’t Put Lagged Dependent Variables in Mixed Models: https://statisticalhorizons.com/lagged- ... -variables

Bell, Andrew, Kelvyn Jones, and Malcolm Fairbrother. 2017. “Understanding and Misunderstanding Group Mean Centering: A Commentary on Kelley et Al.’s Dangerous Practice.” Quality & Quantity

Thanks for the link.