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st: SEM: cannot correlate exogenous variable with endogenous variable


From   Jeremy Reynolds <jeremyr@uga.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: SEM: cannot correlate exogenous variable with endogenous variable
Date   Sat, 29 Jun 2013 18:00:40 -0400

Dear Statalist,

I am attempting to estimate an SEM model that contains reciprocal
effects and lagged predictors.  The model is based on the work of Paul
Allison see:

http://www.statisticalhorizons.com/wp-content/uploads/2012/01/Causal-Inference.pdf
(The model is also described on page 1247 of England et al. Social
Science Research 36: 2007 and in Allison's 2005 book, Fixed Effects
Regression Models Using SAS.)

My code is below.  The model I estimate contains measures of
victimization at 4 points in time (vic1-vic4) and offending at 3
points in time (off1-off3), as well as a latent variable that measures
time-invariant fixed effects.

The problem is that I am not able to specify a correlation between
off3 and vic2 as specified at the end of the cov option.  Stata
replies:

invalid specification of covariance between 'vic2' and 'off3';
  'vic2' is an observed dependent variable and
  'off3' is an observed independent variable

This correlation, however, is essential to the model.  Allison writes,
"the assumption of sequential exogeneity is modelled by allowing the
error term at each point in time to be correlated with future values
of the time-dependent covariates, but not past values (Wooldridge
2002)."

It appears that the intended model can be estimated in SAS and MPlus.
Is Stata not able to to estimate this model?  I am more inclined to
think that I have made a mistake in specifying the model, but I cannot
find it.

I would be grateful for any suggestions.

Jeremy


use "http://www.statisticalhorizons.com/wp-content/uploads/ousey.dta";, clear
rename off3 off4
rename off2 off3
rename off1 off2
rename off0 off1
rename vic3 vic4
rename vic2 vic3
rename vic1 vic2
rename vic0 vic1

#delimit ;
 sem
 (off1@off -> vic2)
 (off2@off -> vic3)
 (off3@off -> vic4)
 (vic1@vic -> vic2)
 (vic2@vic -> vic3)
 (vic3@vic -> vic4)
 (alpha@1 -> vic2 vic3 vic4),
 covstruct(_lexogenous,diagonal)
 cov(_lexogenous*_oexogenous@0)
 latent(alpha )
 cov(off1*alpha off2*alpha off3*alpha
 vic1*alpha
 off2*off3 off2*off1 off1*off3
 vic1*off1 vic1*off2 vic1*off3
 e.vic2@resid e.vic3@resid e.vic4@resid
off3*vic2)
 nocapslatent;
#delimit cr








--
********************
Dr. Jeremy Reynolds
Associate Professor
Undergraduate Coordinator
Department of Sociology
117 Baldwin Hall
University of Georgia
Athens, GA 30602-1611
Phone: (706) 583-8072
Web: http://uga.edu/soc/people/faculty/reynolds_jeremy.php
Fax: (706) 542-4320
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