There is a kind of collinearity that is good in SEM, and a kind that is
bad.
All else equal, collinearity is a good thing in SEM when you are
considering relationships among indicators of the same latent construct.
Theoretically, the latent variable is the underlying cause of
intercorrelation among indicators. The more intercorrelation, the more
reliably the latent factor is captured (presuming proper
conceptualization and specification).
Collinearity is a bad thing, particularly when it occurs among exogenous
latent variables. The same kinds of issues arise as one might see in
multiple regression (e.g., sign reversals, bad effects on standard
errors, suppression effects), often intensified in SEM because the
correlation among latent variables is disattenuated.
In the "bad" case of collinearity, it may be poor specification on the
part of the researcher - i.e., what the researcher has conceptualized as
two distinct constructs really are not two distinct constructs. If that
is true (e.g., a test of the correlation shows it not to be
significantly different from a value of 1.0), you may have a single
underlying factor, which could be indicated by all the indicators you
originally had indicating the two collinear constructs - or you could
select a subset of indicators from both former constructs and treat
those as the indicators of this new single latent construct.
Two other possibilities might be considered. First, you might specify a
second-order latent factor that explains the high correlation among the
two collinear lower-order factors. This can "solve" the problem by
capitalizing on the high correlation rather than being harmed by it.
However, there should be a good interpretive/theoretical basis for
considering the two collinear constructs to themselves be indicators of
whatever the second-order factor is.
Second, you might re-think the specification. One of the collinear
exogenous factors might actually be legitimately conceptualized as a
causal outcome of the other. In that case, one of the collinear
exogenous variables is re-specified as an endogenous latent variable
caused by the other originally collinear latent variable. Again you are
now capitalizing on what formerly was problematic, but again there must
be a sound conceptual/theoretical logic underlying such a decision.
Some theoretical constructs may well be highly correlated yet distinct.
That would then reflect some nomothetic reality. Other times, this
problem is due solely to the lack of clarity of specification (in
constructs, or in indicators, or in construct relationships) - a
researcher error rather than a statistical problem. For example, some
might take a previously unstructured set of measures, sub-optimally
employ exploratory factor work, forcing orthogonal rotation or more
factors than are called for, or refactoring a large factor on its own to
"break it up", then take some presumed discovered measurement structure
into an SEM model. That obviously is not best practice and can result
in problems like the one you describe. Higher levels of care in proper
conceptualization and specification of constructs, indicators, and
causal paths would likely eliminate many problems people run into when
estimating SEM models.
Doug Grisaffe
Department of Marketing
University of Texas at Arlington
________________________________
From: Structural Equation Modeling Discussion Group
[mailto:***@BAMA.UA.EDU] On Behalf Of P. Mallikarjun Rao
Sent: Wednesday, November 16, 2005 12:51 PM
To: ***@BAMA.UA.EDU
Subject: multicolliniearity
Dear all,
How to avoid multi-colliniearity in SEM models?.
Thanks in advance
Regards,
Mallik
________________________________
Yahoo! FareChase - Search multiple travel sites in one click.
<http://us.lrd.yahoo.com/_ylc=X3oDMTFqODRtdXQ4BF9TAzMyOTc1MDIEX3MDOTY2OD
gxNjkEcG9zAzEEc2VjA21haWwtZm9vdGVyBHNsawNmYw--/SIG=110oav78o/**http%3a/f
arechase.yahoo.com/>
-------------------------------------------------------------- To
unsubscribe from SEMNET, send email to ***@bama.ua.edu with the
body of the message as: SIGNOFF SEMNET Search the archives at
http://bama.ua.edu/archives/semnet.html
--------------------------------------------------------------
To unsubscribe from SEMNET, send email to ***@bama.ua.edu
with the body of the message as: SIGNOFF SEMNET
Search the archives at http://bama.ua.edu/archives/semnet.html