[R-sig-ME] Index-terms confusion

Steven J. Pierce pierces1 at msu.edu
Sun Dec 26 16:51:58 CET 2010


Mediation analysis is not necessarily tied to multilevel models. While you
can certainly test meditation hypotheses with multilevel models, you can
also test them in data that do not have the grouped or nested structure
associated with mixed effects models. 

Broadly speaking, mediation analyses are aimed at testing theories about
causal chains of variables so that you can better understand the process by
which one variable influences another. For example, if you believe that
variable A only has an indirect influence on variable C because of the way
it affects variable B, you can draw a path diagram  (A --> B --> C ), then
test the mediation hypotheses using various techniques described in
MacKinnon, Fairchild, & Fritz (2007)or MacKinnon (2008). The modern way to
test those hypotheses is via structural equation modeling (SEM), which can
also adjust for multilevel structure as well if you use software like Mplus.

It may help to remember that ultimately, multilevel models are a method for
correctly representing the non-independence of observations that may arise
because of how you did the sampling. They let you test all the sorts of
things you can test with simpler regression models, plus a few new
hypotheses about the variance structures.  Meanwhile, mediation analyses are
more narrow in scope and defined by the kind of hypothesis you are testing
than by the specific statistical model you are using to do so.

MacKinnon, D. P., Fairchild, A. J., & Fritz, M. S. (2007). Mediation
analysis. Annual Review of Psychology, 58, 593-614. doi:

MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. New
York, NY: Taylor & Francis Group, LLC.

Steven J. Pierce, Ph.D. 
Associate Director 
Center for Statistical Training & Consulting (CSTAT) 
Michigan State University 
178 Giltner Hall 
East Lansing, MI 48824 
E-mail: pierces1 at msu.edu 
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: Petar Milin [mailto:pmilin at ff.uns.ac.rs] 
Sent: Friday, December 24, 2010 4:21 AM
To: John Maindonald
Cc: r-sig-mixed-models at r-project.org Mixed
Subject: Re: [R-sig-ME] Index-terms confusion

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
> 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 


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