[R-sig-ME] variable-and person-centered approaches and multilevel models

[Elisabeth Schubach]

Dear all,
I am currently trying to figure out which parts of a multilevel model are
person-centered and which ones are variable-centered.
I have a three-level structure, with assessment points (Level 1) nested
in relationships (Level 2) nested in individuals (Level 3). And I model
closeness to relationship partner r of individual i at time t as a function
of PERSSONALITY-withinti 
(i.e., a time-varying covariate that was centered within individuals,
representing within-person deviations from an
individual's own mean level across time. To account for between-person
differences in the
respective PERSONALITY trait, I included personal mean (i.e., mean across
time points for
each specific individual, centered on the grand mean) as a time-invariant
covariate. I now wonder whether the within part is person-centered and
whether the between-part is variable-centered or whether 
the parameters β0 and β1 are variable-centered (because they represent
average associations) and the parameters b0i, b0ri, b1ri are person-centered
(because they are specific for each individual).
I would be very happy if you can tell me which specific parts in mlm are
person-centered and which ones variable-centered.
Best,
Elisabeth



CLOSENESS tri = (β0 + b0i + b0ri) 
	+ β1 (TIMEtri)
	+ (β1 + b1ri)  (PERSONALITY-withinti) 
	+ β2 (PERSONALITY-betweeni)
	+εtri

 with i = individual i
        r = relationship partner r 
        t = time t