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

[Phillip Alday]

Following up on an unanswered (I think) old post:

I had not heard the term "person-centred approach" before, but after
searching a bit, it seems to refer to focus on clustering under a
specific grouping term instead of a specific co-variate. I think this
distinction is somewhat blurred in mixed-effects models. While the fixed
effects are more or less what is called "variable centered" (indeed, the
canonical examples in the psych literature are things like linear
regression and ANOVA), the random effects allow for variation to follow
the grouping variables, which is more like (although maybe not exactly
the same) as the "person-centred" approach. The covariance matrix / the
correlations between random effects is more difficult to comprehend, but
is actually the part that perhaps best captures "person centering", as
it shows the relationship between the by-person regression slopes.

As a side note, I'm not sure it makes sense to include the personal mean
as a separate covariate, as depending on the exact structure of your
data, it may already be captured in random intercept by participant.

Phillip

On 12/05/2016 11:20 AM, Elisabeth Schubach wrote:
> 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
> 
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