Re: st: PCA or SEM for 2-indicator latent?

[William Buchanan <william@williambuchanan.net>]

Todd Little has a good book out regarding longitudinal SEM.  You have several issues to deal with and the SEM/PCA debate could be reconciled with your underlying theory.  The first issue with a two indicator latent variable is identification of the model; it can be done but requires you to constrain additional parameters.  Once you've been able to fit an identified measurement model, you would then want to test for factor invariance over time and that is likely where the sensitivity issues would come into play.  You may want to provide more specific details if you're hoping to get a more direct and/or helpful response from list members.

HTH,
Billy

Sent from my iPhone

> On Jan 8, 2014, at 20:40, "Lin, Tin-Chi" <TIN-CHI.LIN@libertymutual.com> wrote:
> 
> Dear Statalisters,
> 
> My data is longitudinal and I am facing a catch-22 in choosing a method to (1) construct the explanatory variable (let’s call it S), and (2) perform the regression modeling overall. SEM (structural equations modeling) and PCA (principal component analysis) are among the methods that I am considering.
> 
> The dilemma is that while SEM is generally preferred to PCA (see a short but good summary from http://www.stata.com/statalist/archive/2012-09/msg01050.html), there is only two indicators (S1, S2) available for S in each wave. From other website, I learned that where there is only two indicator for a single latent, the regression model will be very sensitive to model mis-specification (http://www.statmodel.com/discussion/messages/11/4965.html?1261084141), and I think the problem will get worse in a longitudinal setting.
> 
> Another question is, if I am going to use SEM and the primary explanatory variable is latent, is it possible to run a fixed-effect-like model to control for between-individual differences? I had this thought, because at the very beginning my plan was to ran PCA, get the prediction for S, and then use fixed-effects model to get rid of “contamination” from the unobserved differences. I know we can “translate” a fixed-effects model to SEM when all the x-variables are indicators, but I am not sure if we can still do so when an explanatory variable is latent.
> 
> Thanks very much
> 
> Tin-chi
> 
> 
> Tin-chi Lin
> Liberty Mutual Research Institute for Safety
> 
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