[R-sig-ME] Index-terms confusion

Petar Milin pmilin at ff.uns.ac.rs
Sun Dec 26 18:00:38 CET 2010

Dear Steven,
This is very elaborated and precise explanation. Thank you very much!
Moreover, this is exactly what I learned about these terms. Recently, 
few of my students were confused with "multilevel models" term used in 
sense of "mediation analysis".

Thanks, again! Best,

On 26/12/10 16:51, Steven J. Pierce wrote:
> Petar,
> 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:
> 10.1146/annurev.psych.58.110405.085542
> 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
> 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

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