[R-sig-ME] Index-terms confusion

[Petar Milin]

On 24/12/10 01:37, John Maindonald wrote:
> A strict use of language would use the term "hierarchical multilevel model" when the error terms have a hierarchical structure, e.g. subplots within
> plots within blocks within sites.  One may also speak of a "hierarchical structure of variation".  In practice, "hierarchical multilevel model" is likely, in a context where multilevel models are in mind, to be abbreviated to "hierarchical model".
>
> In other contexts, there can be other hierarchies.  Where there is a sequence of models in which each model is nested in the next  (in the
> sense that its terms are a subset of those in the next models, one may speak of this as a hierarchy of models.
>
> You ask "How about statistics that should inform about changes in betas?"  I do not understand the intent of this question.
>    
Thanks for the clarification of the term (now officially) "hierarchical 
multilevel model".
As for the send question: there is considerable literature (c.f., Baron 
& Kenny, 1986; Robins & Greenland, 1992; Pearl, 2000; Muller, Judd, & 
Yzerbyt, 2005 etc.) of something which is also known as "mediation 
analysis". Sometimes, this group of techniques uses the term "multilevel 
modeling". To my understanding (and it is shallow, I confess, I only 
played with these techniques to get some general impression), index-term 
for this family of techniques could be "path analysis" or "causal 
analysis", and is related to SEM. This is exact point of confusion.
In the abovementioned techniques, changes of betas should inform 
researcher about "partial" or "complete" mediation of one variable that 
intervenes between the predictor and the criterion. In the toy-example I 
played with, structure was such that mother's iq-score was mediated by 
some score on achievement-motivation test, to some assessments of 
high-schoolers.

Best,
Petar