Helen,  I had exactly the same dilemma, and agree with Jeremy (in hindsight) - it just didn't get asked.  I found the following useful for arguing use of regression as adequate for my needs :
 
Gefen, D., Straub, D., & Boudreau, M.-C. (2000). Structural Equation Modeling and Regression: Guidelines for Research Practice. Communications of the Association for Information Systems, 4(7), from www.aisel.aisnet.org/cais/vol2014/iss2011/2017

Caroline Wilson

Institute of Energy and Sustainable Development
De Montfort University

Email: [log in to unmask] <mailto:[log in to unmask]> 
Web: www.iesd.dmu.ac.uk

Date:    Fri, 2 Sep 2011 15:34:18 +0000
From:    Helen Watts <[log in to unmask]>
Subject: SEM vs logistic regression

Hi all,

For my quantitative analysis in my PhD, I have used factor analysis to generate composite variables which I have then used in logistic regression analyses to predict a categorical outcome.

One of my supervisors has questioned why I didn't use SEM, and thinks I may get pulled up in my viva for this. I (wrongly) thought that SEM could only be used with continuous variables.

Does anyone have any thoughts/ advice over if SEM is superior to logistic regression when dealing with categorical outcomes? I have googled this topic, but information on this seems scarce.

Do I need to re-do all my analyses using SEM or is there a rationale I can use for choosing logistic regression?
Or do I just accept it as a limitation of my PhD?

All very stressful!!! Any help or advice would be much appreciated. Apparently it's sunny outside... all I can see is a grey cloud over my head.

Helen

Date:    Fri, 2 Sep 2011 09:05:23 -0700
From:    Jeremy Miles <[log in to unmask]>
Subject: Re: SEM vs logistic regression

Hi Helen

SEM can be used for this.

The advantage is that you specify the factor analysis and the logistic
regression in the same model.  This means that if something about the
logistic regression can 'break' the factor analysis model, you will
find out.  For example, you look at which items load on a factor in
the factor analysis stage.  Then you combine those items (you didn't
say how, doesn't really matter) and use them in a logistic regression.
 You are therefore assuming that all items in a factor have
(approximately) equal effects in the logistic regression.  If one item
has very different effects in the logistic regression from the other
items in the factor, you won't know if you do the two-step approach.
You will know if you do a SEM approach.  That's why you should do it.

HOWEVER:
There are pragmatic reasons not to.  You can't do this model in all
SEM software (AMOS, sem won't do it, it's hard in Mx).  Mplus is the
best, if you don't have it, it will cost you approaching 1000 pounds -
which is a lot to pay for one analysis.  It's a steep-ish learning
curve.  What happens if that model does fail?  Then you need to change
it - this is not a very easy task.

Your best argument is that SEM is used when you have a strong
theoretical conception of what to expect, so you know how to specify
the model.  The great thing about EFA is that you throw your data at
it, you'll get an answer.  The bad thing about EFA is that if you have
an expectation of what you might get, you might not get that, and if
you don't, you can't say that's because you were wrong about what you
thought you'd have.  In SEM, you specify what you think you should
have, and if you're wrong (or at least not close to right), you're
basically stuffed.  The best thing to do is just go back to EFA.

So your argument in a couple of sentences is "I don't think that the
theory in this field was sufficiently advanced to allow us to apply a
confirmatory approach such as SEM.  And I don't know how to do it."

Finally, don't worry about this.  SEM people will ALWAYS say that you
should do SEM.  I heard someone talking a couple of days ago about a
regression analysis. The outcome was height - they were seeing how
tall people were, and what predicted rate of growth.  Someone (else)
said they should have done SEM.  Height should be latent, with
multiple measures.  What??!!  I'm supposed to ask people how tall they
are.  And then ask them again??  WTF?  (This is what you do with
depression - you can ask people if they feel sad, and you can ask them
if they've lost their appetite - you can ask them if they are depresed
in lots of ways, but there's really only one way to ask them how tall
they are).    In addition, people worry a lot about their statistics
in their vivas - most examiners are not sophisticated at, or
interested in, statistical analysis (which is good - it keeps me in a
job).  They're not going to ask, they don't care.*

Jeremy

*Obviously if I'm your examiner, I am going to ask about little except
your statistics.  But I'm in the wrong country, so you're probably
safe.  (And I wouldn't ask about something as easy to answer as why
you didn't use SEM.  I'd