extra two cents: many latent variable structural equation models are
estimable by instrumental variable methods. Unlike in economics, where
the instruments are usually pulled out of thin air, one can derive the
rigorous ways to pick model-implied instruments. IV methods are less
efficient that MLE (although I have not seen efficiency losses greater
than 30% in those applications), but they are more robust to model
misspecification. Moreover, one can test certain misspecifications
such as omitted paths or measurement error correlations with Hausman
test on instruments. Ken Bollen has been the main contributor to this
topic (Bollen, KA (1996) 'An Alternative Two Stage Least Squares
(2SLS) Estimator for Latent Variable Equations.' Psychometrika, 61:
109-121; Bollen, K A, and Bauer, D J (2004), Automating the Selection
of Model-Implied Instrumental Variables, Soc. Methods & Research, 32
(4), 425-452). Being his student, someday I should write a paper to
Stata Journal on how to do all that by -ivreg-...
--
Stas Kolenikov
http://stas.kolenikov.name
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