### Centering method for lagged variables

Posted:

**Wed Jun 13, 2018 2:10 pm**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

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