Page 358 - Contributed Paper Session (CPS) - Volume 7

CPS2130 Abdul-Aziz A. Rahaman et al.
misspecification on parameter recovery across estimation methods
(Asparouhov & Muthén, 2010; Hwang, et al., 2010). The extent to which
estimates are impacted by the misspecification of the model depends on
design features and overall complexity of the model (Henseler, 2010). In the
context of SEM, latent variables can be modeled as the cause of those
observed values (Bollen & Lennox, 1991; Curtis & Jackson, 1962).
Until recent years, it was held that SEMs including measurement models
were inappropriate for traditional ML approaches altogether (Chin, 1998;
Hwang & Takane, 2004; Ringle et al., 2009). Several estimation methods and
variations of those methods have been developed and applied to SEMs,
including maximum likelihood (ML), and ML with robust standard errors
(Muthén & Muthén, 1998-2010), generalized least squares (GLS), and
weighted least squares (WLS). However, all of these methods are known to
perform poorly under some conditions. Specifically, ML and WLS typically fail
to produce accurate parameter estimates when applied to small samples (Hu
et al., 1992 & Olsson et al., 2000); the more precise estimates produced by
MLR are generally restricted to estimates of standard errors instead of path
coefficients. In response to the limitations of these, additional estimation
approaches have been applied to the estimation of SEMs (Wold, 1975; Hwang
& Takane, 2004; Kline, 2011). The most common estimation method used with
SEM is maximum likelihood (Hoyle, 2000). ML has been studied across myriad
contexts and data conditions, and its limitations are well documented. One
context in which ML does not perform well is in the presence of small samples
(Kline, 2011). As the field of methodology has advanced, alternative estimation
methods have developed and include generalized least squares, weighted
least squares, PLS, GSCA, and MCMC approaches (Henseler, 2012; Hwang et
al., 2010; Hwang Malhotra et al., 2010). Although estimation methods other
than those described here have been developed for use with SEMs when the
assumptions of ML are violated (robust ML, weighted least squares), it is not
feasible to compare and evaluate the performance of all such alternatives in a
single study. Thus, the present study will focus on the comparative
performance of regression method, Bartlett’s, Anderson-Rubin and EM
methods because they represent diverse and promising approaches for
addressing the problem of estimating residuals in SEM.

2. Methodology
In order to apply residual estimators in estimating the residuals of both
measurement and latent variables, a recursive model with a mediation
component was adopted from Hildreth (2013)

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