Title: Estimation of Parameters in Latent Variable Models Using SIMEX as 
an Alternative to SEM

Author: Stella Bollmann, Andreas Hölzl, Helmut Küchenhoff

Affiliation: Ludwig Maximilians University Munich

Abstract: In psychometrics, regression is often based on latent variables
which are measured by a set of items.  In these cases, regression models
are problematic, because there is measurement error on the independent
latent variables and thus the parameter estimates are possibly biased.
This is one of the reasons why structural equation models (SEM) are used.
But in some cases the use of SEM is not possible, due to very complex
models, where parameter estimation does not converge.  For these cases, we
suggest a different kind of model for correcting the measurement error on
linear regression models, the simulation and extrapolation method (Cook &
Stefanski, 1994), which is implemented in R in (Lederer & Kuechenhof, 2006).
This kind of model was first proposed in the context of latent variables in
(Shang, 2012).  A first comparison of the estimations from SIMEX and SEM on
simulated data shows that estimations with SIMEX are accurate.  An
application on a real longitudinal data set on academic achievement
demonstrates the advantages of the new SIMEX method over SEM. The entire
model of the longitudinal study is computationally too complex for
estimation in SEM while with SIMEX estimation of parameters is possible.

References

Cook, J.R. and Stefanski, L.A. (1994) Simulation-extrapolation estimation
in parametric measurement error models.  Journal of American Statistical
Association, 89, 1314 - 1328

Lederer, W. and Kuechenhof, H. (2006) A short introduction to the SIMEX and
MCSIMEX. RNews, 6(4), 26 - 31

Shang Y., Measurement Error Adjustment Using the SIMEX Method: An
Application to Student Growth Percentiles (2012), Journal of Educational
Measurement Vol.  49, No.  4, pp.  446 - 465