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 Anonymous posted on Sunday, October 13, 2002 - 10:27 pm
My apologies for posting a simple question, but I just purchased Mplus and I'm new to SEM. I believe that SEM'ing is appropriate for my problem because I have a construct (letís call it SATIS) in the theoretical model that I cannot directly measure, but I do have several variables that should serve as reasonable (although imperfect) proxies for this construct. The effect of SATIS, however, should only really be evident through an interaction with another variable. My question is the following:
My understanding is that if I run [logistic] regressions on the individual proxies, the results will be biased because each one only measures SATIS with error. However, by running a SEM that includes all 3 proxies for SATIS that bias can be substantially reduced. Is this true? And, if so, can anyone supply me with a reference for this? Thank you.
 bmuthen posted on Monday, October 14, 2002 - 8:53 am
Your understanding is correct. The Bollen SEM book in the Reference section on the Mplus web site provides a general reference to bias due to errors in predictors. I am not sure if the binary outcome case you describe is covered but it is analogous; you may also want to check
the book Carroll, Ruppert, Stefanski (1995), Measurement Error in Nonlinear Models (Chapman & Hall).

Regarding the interaction that you mention, the current Mplus can only handle interactions that involve a construct if the other variable is observed and categorical - this is done via multiple-group modeling.
 Anonymous posted on Friday, March 28, 2003 - 1:40 pm
I am also new to SEM and have questions surrounding the use of latent variables. What exactly are the advantages of SEM over path analysis using aggregate variables? ie, Given the interpretive ambiguity surrounding latent variable analysis, is there reason to prefer it? Opinion and references would be most welcome.
 bmuthen posted on Friday, March 28, 2003 - 5:07 pm
That's a big topic. One reference is Bollen's SEM book. See also other SEM references in the Reference section on the Mplus web site. Aggregate variables have the problem of containing measurement errors and using arbitrary weights (such as unti weights). If a correctly specified latent variable measurement model, such as a factor analysis model, can be formulated the resulting latent variable is free of measurement error and has been defined by variables where their weights (loadings) have been estimated at optimal values, not prespecified.
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