# Structural Equation Modeling

(Source: Wikipedia, May 2008)

Structural equation modeling (SEM)
is a statistical technique for testing and estimating causal
relationships using a combination of statistical data and qualitative
causal assumptions. This view of SEM was articulated by the geneticist
Sewall Wright (1921), the economists Trygve Haavelmo (1943) and Herbert
Simon (1953), and formally defined by Judea Pearl (2000) using a
calculus of counterfactuals.

SEM encourages confirmatory rather
than exploratory modeling; thus, it is suited to theory testing rather
than theory development. It usually starts with a hypothesis,
represents it as a model, operationalises the constructs of interest
with a measurement instrument, and tests the model. The causal
assumptions embedded in the model often have falsifiable implications
which can be tested against the data. With an accepted theory or
otherwise confirmed model, SEM can also be used inductively by
specifying the model and using data to estimate the values of free
parameters. Often the initial hypothesis requires adjustment in light
of model evidence, but SEM is rarely used purely for exploration.

Among its strengths is the ability
to model constructs as latent variables (variables which are not
measured directly, but are estimated in the model from measured
variables which are assumed to 'tap into' the latent variables). This
allows the modeler to explicitly capture the unreliability of
measurement in the model, which in theory allows the structural
relations between latent variables to be accurately estimated.

In SEM, the qualitative causal
assumptions are represented by the missing variables in each equation,
as well as vanishing covariances among some error terms. These
assumptions are testable in experimental studies and must be confirmed
judgmentally in observational studies.

An alternative technique for
specifying Structural Models using partial least squares has been
implemented in software such as LVPLS (Latent Variable Partial Least
Square), PLSGraph and SmartPLS (Ringle et al. 2005). Some feel this is
better suited to data exploration. More ambitiously, The TETRAD project
aims to develop a way to automate the search for possible causal models
from data.

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