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A Short Review on Structural Equation Modeling: Applications and Future Research
Directions
Article in Journal of Supply Chain Management Systems · July 2015
DOI: 10.21863/jscms/2015.4.3.014
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Surajit Bag
Université Internationale de Rabat
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A Short Review on Structural Equation Modeling:
Applications and Future Research Directions
Surajit Bag*
*Tega Industries Ltd., India. E-mail: surajit.bag@gmail.com
Abstract
The application of multivariate techniques is mainly to expand the researchers’ explanatory ability and statistical efficiency. The first generation analytical
techniques share a common limitation i.e. each technique can examine only a single relationship at a time. Structural Equation Modeling, an extension of
several multivariate techniques is the technique popularly used today can examine a series of dependence relationships simultaneously. The purpose of
this study is to provide a short review on Structural Equation Modeling (SEM) being used in social sciences research. A comprehensive literature review of
article appearing in top journals is conducted in order to identify how often SEM theory is used. Also the key SEM steps have been provided offering potential
researchers with a theoretical supported systematic approach that simplify the multiple options with performing SEM.
Keywords: Multivariate Data Analysis, SEM, Path Modeling
Introduction
Contemporary research in the area of social sciences
involves analysing datasets consisting of multiple
variables; the body of methodology dealing with this type
of datasets is called multivariate analysis. Additionally
more mathematics is required to derive multivariate
statistical techniques for making inference than in a
univariate setting.
SEM is a family of statistical models that seek to explain
the relationships among multiple variables. In this
process, it examines the structure of the interrelationships
expressed in a series of equations, similar to a series of
multiple regression equations. These equations depict the
relationships among constructs involved in the analysis.
Constructs are unobservable or latent factors represented
by multiple variables.
SEM is known by many names such as covariance structure
analysis, latent variable analysis and path modeling.
Although SEM models can be tested in many ways, all
SEM models are distinguished by three characteristics:
1. Estimation of multiple and interrelated dependence
relationships.
2. An ability to represent observable concepts in
these relationships and account for measurement
3. Defining a model to explain the entire set of
relationships.
The basic steps of SEM are 1) Model specification; 2)
Model identification; 3) Data preparation and screening;
4) Estimation of the model; and 5) Model Re-specification,
if necessary (Kline,2005).
Literature Review
Here researcher made an attempt to understand, what
work has been carried out in the past in the direction of
“Structural Equation Modeling”. In order to understand
the evolution of SEM, content analysis was performed on
papers published in reputed journals.
SEM has gained popularity over time but due to its
complexity, researchers often make mistakes in selecting
the right program.
SEM can be classified into covariance based SEM and
component based SEM. The first approach has been
developed around Karl Joreskog and second approach
around Herman Wold under the name Partial Least
Squares. Covariance based SEM is usually used with
an objective of model validation and requires a large
sample. Component based SEM is mainly used for score
computation and can be carried out on very small samples
(Tenenhaus, 2008).
SEM is a technique used to specify, estimate, and evaluate
models of linear models among a set of observed variables
in terms of an often smaller number of unobserved
A Short Review on Structural Equation Modeling: Applications and Future Research Directions
65
variables. SEM may be used to build or test theory. When
selecting the SEM, care should be taken to consider a
theory’s stage of development. Exploratory techniques
are well suited for establishing and whether it explains
a meaningful amount of variance in an endogenous
construct. Because of the components based approach
to estimating relationships, exploratory techniques such
as PLS are less prone to Type I error and better suited
for small, non-normal datasets often collected for initial
tests of relationships. Confirmatory techniques may be
used to build theory derived from well established set
of constructs. Regardless of whether the SEM technique
is exploratory or confirmatory, it possesses the ability to
integrate measurement and structural models (Roberts,
Thatcher and Grover, 2010).
Jayakumar and Sulthan (2013) used structural equation
modeling to throw light on different types of stress
factors, stress symptoms and their impact of stress on
college students.
Covariance based SEM is used when the sample size
is large, data is normally distributed and the model is
correctly specified. PLS SEM becomes a good alternative
to Covariance based SEM when the sample size is small,
researcher have little available theory, predictive accuracy
is paramount and correct model specification cannot be
ensured.
Zukuan et al., (2010) employed the SEM approach to
understand the relationship of TQM and organisational
performance.
Wong (2013) presented a technical note to the step wise
guide to the Smart PLS software for beginners. Different
software programs are used by researchers in performing
structural equation modeling. In Covariance based SEM
software packages AMOS, LISREL, EQS and MPlus are
commonly used.
In Partial Least Squares, which focuses on the analysis of
variance can be carried out using PLS-Graph, Visual PLS,
Smart PLS and WarpPLS.
The other approach is component based SEM known
as Generalized Structured Component analysis which
is implemented through Visual GSCA or a web based
application called GeSCA.
The advantages of SEM over traditional MANOVA/
MANCOVA analyses are: 1) estimating and removing
both random and correlated measurement errors; and 2)
examining the mediating process (Lee, 2011).
Structural Equation Modeling has been widely applied in
the area of social sciences.
Jayakumar and Sulthan (2014) used structural equation
modeling to bring out the employee perception on training
and development program in the industry.
Saxena and Khanna (2013) proposed a model for
measuring advertising value through structural equation
modeling.
Lee (2011) demonstrated a comprehensive statistical
analysis, SEM in the field of Educational Technology.
Explored how interventions affect learning and examine
the indirect effect of related psychological constructs.
Thomas and Bhasi (2011) used SEM in the area of
information technology for software project risk
management.
Singh et al., (2010) used SEM in the area of retail supply
chain.
Mohamad et al., (2011) used SEM to study empirically
and test a model to examine the relationships among
service recovery satisfaction and destination loyalty in
the hotel industry.
Silva et al., (2010) used SEM to identify determinants of
attitude towards ICT usage among rural administrators.
Biswas (2010) undertook multi-same studies to explore
the various Guna constructs of Indian philosophy. The
author has made a confirmatory assessment of the two
constructs using a SEM.
Grace and Bollen (2008) presented a framework for
discussing composites and demonstrate how the use of
partially reduced form models can help to overcome some
of the parameters estimation and evaluation problems
associated with models containing composites.
Yap and Khong (2006) used SEM to model the
relationships between critical success factors of business
process reengineering implementations, customer service
management and perceived business performance in
Malaysian banking institutions.
Tempelar et al., (2007) investigated the relationship
between attitudes and reasoning abilities by estimating a
full structural equation modeling.
Chen et al., (2011) conducted empirical study using
SEM on turnover intention by modeling job stress as a
mediating variable.
66
Journal of Supply Chain Management Systems
Hackl and Westlund (2000) used SEM for customer
satisfaction measurement.
Nachtigall et al., (2003) provide advantages and pitfalls
of structural equation modeling so that right application
can be performed by other researchers.
Bollen and Pearl (2013) have presented a technical report
which presents eight myths about causality and structural
equations models for better understanding of researchers.
Afthanorhan et al., (2015) intend to demonstrate a
parametric approach using z test to attain the probability
level with the help of SmartPls 2.0
Thomas and Bhasi (2011) and Pousette and Hanse (2002)
used multigroup SEM approach to test for multigroup
invariance in measurement models and structural models
between job characteristics, psychosocial intervening
variables, health outcomes and sickness absenteeism.
To tackle methods effect Pohl et al., (2008) presented a
new approach for modeling this kind of phenomenon,
consisting of a definition of method effects and a first
model, the method effect model, which can be used for
data analysis. This model may be applied to multi traitmulti method or to longitudinal data where the same
construct is measured with at least two methods at all
occasions.
The main feature of SEM is to compare the model to
empirical data. This comparison leads to so called fit
statistics assessing the matching of model and data. If
the fit is acceptable, the assumed relationships between
latent and observed variables (measurement models) as
well as the assumed dependencies between the various
latent variables (structural model) are regarded as
being supported by the data. In some cases, only the fit
of a measurement model is of interest. In other cases,
parameters of the structural model may be of interest. Even
though researchers use the term effect, this does not mean
that a SEM is a causal model. Although under specific
circumstances, SEM can represent causal relationships,
a well fitting SEM does not necessarily have to contain
any information on causal dependencies at all. Hence the
testing the fit of a SEM is not tests of causality.
Singh (2009) has argued that in the social science
literature very few studies report the correct set of model
fit indices (FIs), with little justification. Effort was put to
reduce some of the confusion surrounding the appropriate
use of SEM model fit indices.
Volume 4 Issue 3 July 2015
Si� Sta�e� in Structura� E�uation
Mode�in�
Here the six stages in structural equation modeling are
presented.
Defining Individual Constructs
A good measurement theory is a necessary condition
to obtain useful results from SEM. Hypothesis tests
involving structural relationships among constructs
will be no more reliable or valid than the measurement
model, in explaining how these constructs are validated.
It entirely depends on how the researcher selects the items
to measure each construct which sets the foundation for
the entire remainder of the SEM analysis. The researcher
must invest significant time and effort early in the research
process to make sure the measurement quality will enable
valid conclusions to be drawn.
Developing the Overall Measurement Model
In this stage, each latent construct to be included in the
model is identified and the measured indicator variables are
assigned to latent constructs. Although this identification
and assignment can be represented by equations, it is
simpler to represent the process with a diagram. There are
three types of relationships: measurement relationships
between indicators/items and constructs; correlation
relationship among the constructs; and error terms for the
items.
Design a Study to Produce Empirical Results
After the basic model specified in term of constructs and
measured variables/indicators, the researcher must turn
attention to issues involved with research design and
estimation.
Research design includes decision making on the type of
data to be analyzed, either covariances or correlations;
the impact and remedies for missing data; the impact of
sample size.
The researcher must be careful to specify the type of data
(Metric or Non Metric) being used for each measured
variable so that appropriate measure of association can
be calculated. Also researcher must still choose between
correlation versus covariance based on interpretive and
statistical issues.
A Short Review on Structural Equation Modeling: Applications and Future Research Directions
Researcher must also make several important decisions
regarding the missing data.
Selecting the sample size in SEM is more critical
than other multivariate techniques because some of
the statistical algorithms used by SEM programs are
unreliable with small sample size. Five considerations
affecting the required sample size for SEM include:
multivariate normality of the data; model complexity; the
amount of missing data; the average error variance among
the reflective indicators.
Once the model is specified, researchers must choose
the estimation method, the mathematical algorithm
that will be used to identify estimates for each free
parameter. Several options are available such as Ordinary
Least Sqaures (OLS) regression. Maximum Likehood
estimation (MLE) is more efficient and unbiased when the
assumption of multivariate normality is met. The potential
sensitivity of MLE to non-normality however created
a need for alternative estimation techniques. Methods
such as weighted least squares (WLS), generalised least
squares (GLS), and asymptotically distribution free
(ADF) estimation became available. All of the alternative
estimation techniques have become widely available.
Various software programs are available today such as
AMOS, EQS and LISREL to test structural models.
Assessing the Measurement Model Validity
Measurement model validity depends on establishing
acceptable levels of goodness-of-fit for the measurement
model and finding specific evidence of construct validity.
Multiple fit indices should be used to assess a model’s
goodness of fit and should include:
 The Chi square value and the associated degree of
freedom
 One absolute fit index (i.e., GFI, RMSEA, or SRMR)
 One incremental fit index (i.e. CFI or TLI)
 One goodness of fit index (GFI, CFI, TLI etc.)
 One badness of fit index (RMSEA, SRMR, etc)
Thumb rules for use of model fit indices (FI): Regarding the overall fit, use the FIs cut-offs for continuous data as: RMSEA.95, CFI>.95,
SRMR.90) and the RMSEA (