A Review of PLSSEM as Statistical Approach for
Business Research
Dr Sarvesh Kumar
Assistant Professor,
School of Commerce and Management
Studies,
Central University of Himachal Pradesh,
Dhauladhar campus— II, Dharamshala,
Himachal Pradesh
Email sarvesh_hcu@yahoo.co.in
Vikas Kumar Tyagi
Assistant Professor,
Department of Management Studies,
Panipat Institute of Engineering and
Technology,
Samalkha, Haryana
Email vktyagi@outlook.in
Dr. Yoginder Singh Kataria
Professor,
Faculty of Commerce and Management
SGT University, Gurugram, Haryana
Email yoginderkataria@gmail.com
Abstract:
Structural Equation Modeling (SEM), a
Second generation multivariate data analysis technique isin use for data
analysis, especially hypothesis testing from a long time. There are different
approaches to SEM used in research. The objective
of this research paper was to review different Structural Equation Modelling
techniques used in Business Research, with special reference to variance based
Partial Least Square Structural Equation Modeling (PLSSEM). PLSSEM is more
sensitive, simpler, and powerful statistical technique for data analysis. It is
mainly used in theory development for exploratory purposes and has less strict
assumptions. Severaltypes of research have been done in the past on this
subject; this paper compiles all the ideas by reviewing them and coveringthem
in the least complicated form. It would especially help the researchers and
practitioners in understanding the differences between different approaches to
SEM and its applications.
KEYWORDS: Structural Equation Modeling,
Partial Least Square, Covariance, Variance.
JEL CLASSIFICATION:
C14, C31, C88
Introduction:
Volatility, Uncertainty, Complexity, and
Ambiguity(VUCA) originated in the US Military (Whiteman, 1998) as cited by Bennett & Lemoine (2014). It has
become a synonym of constant change in dynamic business research scenario. Embedding
mathematical analysis simplifies decision making in a dynamic business
environment. PLSSEM has evolved as a handy tool for researchers. This tool
also helps researchers and decision makers to reach confident decisions concerning
their defined problems. Sewall Wright first developed Path analysis models in
the year 1921 (Wolfle, 1980). Structural Equation Modeling (SEM) is a second generation multivariatedata analysis technique (Elangovan & Rajendran,
2015). SEM has advantage of analyzing multiple layers of links between
independent (IV) and dependent variables (DV) simultaneously over first generation
regression models like Linear Regression, Analysis of variance (ANOVA), and Multivariate analysis of
variance (MANOVA); it can. Researchers use SEM extensively for hypothesis
testing (Bagozzi & Yi, 1988).
There are several, but the researchers
most commonly use two approaches to SEM. The first approach is the more widely
used and is older than PLSSEM; it is Covariancebased SEM (CBSEM), which is
more of confirmatory and conclusive. Covariance is the extent of how much two
variables change together or how well the variables are jointly related (Davis
& Pecar, 2013). The second approach, Variance based Partial Least Squares
SEM (PLSSEM) is more exploratory in nature and was less commonly used till recently.
Variance is the measure of the dispersion of the observations, to check how
dispersed the data values are about the mean values (Davis & Pecar, 2013). Hwang&
Takane, (2004) came up with the third approach, i.e. Generalized Structured
Component Analysis (GSCA), after these two methods. The researcherhas kept GSCA outside the purview of this
research.
In the quest
of statistical significance, during different time horizons, different types of
methods to interpret data have evolved, solving the problem of that time. Over
the years, the inherent gaps of existing methodology paved the path of newer
methodology whose structure has been built by refining current methods. Considering
one technique to be better than the other would not be right, both have their
advantages and disadvantages, discussed later in this paper.
There are several studies done on this
subject, giving their opinions and different aspects of the subject; this paper compiles all the ideas by reviewing them. This research paper would
help in understanding the differences between the concepts. This paperis an
essential guide reducing complexity, for learning it in more details researcher
suggests to go through researches such as Gaskin (2018); Hair Jr, Hult, Ringle,
& Sarstedt (2016) and Byrne, (2016).
In VUCA times PLSSEM is gaining lot of prominence
in business research as popular choice of business research methods.
Internationally much work has been done by using the concept PLSSEM, such as
studies done in different fields such as by Aryanto, Fontana, & Afiff
(2015); Astrachan, Patel, & Wanzenried (2014); Hair, Sarstedt, Pieper,
& Ringle (2012); Okazaki, Mueller, &Taylor (2010); and Schwaiger,
Sarstedt, & Taylor (2010) in Marketing Research field. Peng & Lai (2012)
in the area of Operations Management. Chen, Preston, & Xia (2013) and
Hoffmann, Schiele, & Krabbendam (2013) in the field of Supply Chain
Management. Kallunki, Laitinen, & Silvola (2011) in Accounting Research. In
India Atulkar & Kesari (2018); Kesari, B., & Atulkar, S. (2016);
Kamath, Rodrigues, & Desai (2016); Shanmugapriya, & Subramanian (2015);
Venkatesh, Sykes, & Venkatraman (2014); Seetharaman, Bajaj, Raj, &
Saravanan (2013); did studies by using PLSSEM in the area of business
research.
In this paper, the introduction is
followed by the comparison between both PLSSEM and CBSEM and followed by the
advantages of one over another and situations when each one of them should be
selected. In the end, the conclusory remarks about the issue are mentioned.
Comparative Analysis between PLSSEM and CBSEM
Karl Joreskog developed CBSEM (Joreskog,
1970) in behavioural sciences, whereas PLSSEM was developed initially by Herman
Wold (1974) in social sciences. Sosik, Kahai, & Piovoso, (2009) considered
CBSEM as hard modelling for theory
testing whereas considered PLSSEM as
soft modelling approach for the theory
development. Tenenhaus (2008) called the
PLSSEM as component based SEM, just as the other one is called Covariancebased approach.
The most significant difference between
them lies in their respective objectives for which they are used. CBSEM helps
inevolvingtheoretical covariance matrix by estimating model parameters with an
objective of minimizing the differences between theoretical covariance matrix
and the estimated covariance matrix, without focusing on the explained
variance. Whereas, PLSSEM is used with an objective ofmaximizing the explained
variance of the dependent latent
construct in business research (Hair, Ringle, & Sarstedt, 2011). This is
the reason why majority of researchers do
not accept standard goodnessoffit statistic of PLSSEM.
CBSEM is the more popular technique as
it provides flexibility of using various software’s like Mplus, EQS, LISREL, andAMOS.
Whereas, PLSSEM is a less popular
technique despite being a more robust
estimator (Reinartz, Haenlein, & Henseler, 2009). The main reason for its lower popularity is also because the software on which it runs like: SmartPLS by
Ringle, Wende, and Will in 2005 and PLSGraph
by Chin in 2003 were developed much later. Other PLS Software’s such as
VisualPLS, WarpPLS, and ‘R’ statistical software package, can also be used to
run PLSSEM. Although VisualPLS and
PLSGraph have graphical interfaces they have not received any significant
updates since their release, and ‘R’ requires a bit advanced programming
language skills, making SmartPLS most used and popular software for PLS
applications. Its 2.0 version is available freely, making it the bestsuited software for the purpose (Wong,
2013).
Table
1: Studies comparing CBSEM vs PLSSEM, performed in different fields:
Author(s) 
Area
of Research 
Conclusions 
Richter,
Sinkovics, Ringle, & Schlaegel (2016) 
International
Business Research 
Out of 424 studies reviewed which used
SEM, 379 were using CB –SEM, and the rest 45 were using PLSSEM. They were
used due to their lower sample sizes and data measurement issues in place of
their objectives. Studies still don’t reap the benefits
of PLSSEM to its full Extent. 
Kaufmann
& Gaeckler (2015) 
Supply
Chain Management 
Use of PLSSEM has magnified in the
SCM recently, but most of them didn’t follow the standards of the technique. They found CBSEM to be better for the
subject if its assumptions are met. 
Astrachan,
Patel, & Wanzenried (2014) 
Family
Firms Research 
Found PLSSEM better than CBSEM for
the studies in their area of research. PLSSEM enables the extension of more
indicator variables, whereas, CBSEM explains variance better, but in the
case of Nonnormal data, CBSEM gives inflated R^{2}. 
Hair,
Sarstedt, Ringle, & Mena (2012) 
Marketing
Research 
PLSSEM has become more widely used in
Marketing Research. However, this has been misunderstood as it lacks in the
standard textbooks. It is a robust technique but should not be applied to
ditch the assumptions of CBSEM. 
Peng
& Lai (2012) 
Operation
Management Research 
PLSSEM is most widely used in the
field of the information system, and not as widely in the area of Operation
Management field, where still CBSEM is used. They found CBSEM to be superior, but
only if its assumptions are met otherwise, PLSSEM should be opted. 
Gefen,
Rigdon, & Straub (2011) 
Administrative
and Social Science Research 
Found that it would not be right to
mention one of them to be better than another. However, they should be opted
as per their objectives. PLSSEM should be used in exploratory studies,
whereas CBSEM in confirmatory studies. 
Lee,
Petter, Fayard, & Robinson (2011) 
Accounting
Research 
PLSSEM is commonly used in Social
Sciences but not in Accounting discipline where traditional regression is
used. Studies in this field are yet to avail its benefits to its full extent.

Fornell
& Bookstein (1982) 
Marketing
Applications 
Found PLSSEM to be a more feasible
option. Although CBSEM was found to give statistically precise results but
need to follow strict assumptions and require a larger sample size for
accurate results. Whereas, PLSSEM have prediction accuracy even with smaller
sample sizes and can also deal with larger models with many variables. 
Source: Literature Review
Advantages of one over another
According to Hair, Ringle, & Sarsted
(2011) PLSSEM has a higher level of
statistical power as compared to CBSEM; generates better path coefficients and
significance level and is more sensitive in detecting relationships (Sosik,
Kahai, & Piovoso, 2009); is simpler in nature (Tenenhaus, 2008), yet can
deal with high model complexity (Hair, Ringle, & Sarstedt, 2011). PLS
techniques can work even when there are just one or two items per construct,
unlike CBSEM. It can deal with both formative and reflective measurements
models more easily than CBSEM can, which requires relatively more complex
rules (Hair, Ringle, & Sarstedt, 2011 and Sosik, Kahai, & Piovoso,
2009).
PLS methods are nonparametric
techniques (Nagarajan, Savitskie, Ranganathan, Sen, & Alexandrov, 2013), unlikeCovariance based methods, which are parametric.
Therefore, unlike CB Techniques, researchers do not have to satisfy any sets of
assumptions before the application of PLS techniques. Model specifications or
data in PLSSEM do not use any limiting assumptions. While,multivariate
normality of data can work well on nonnormal data; PLS algorithm adjusts a
nonnormal data according to the central limit theory (Cassel, Hackl, &
Westlund, 1999); minimum sample size as it can work with a small and much wider range of sample sizes
(Diamantopoulos & Siguaw, 2013 and Ringle, Sarstedt, & Straub, 2012).
Observational independence and interval scaled data as PLSSEM can be applied
even when the data is nonindependent or
is in Ordinal or Nominal scale (Sosik, Kahai, & Piovoso, 2009). According
to Wong (2013), it is challenging to find the data that meet all these
assumptions. Moreover, as commented by
Wold (1982) as cited in Hair, Ringle, & Sarstedt (2011), the informational
and distributional requirements or assumptions for CBSEM are unrealistic. They
are making PLS Techniques more realistic.
PLSSEM is more suitable on the smaller
sample sizes compared to CBSEM (Wong, 2013); (Sosik, Kahai, & Piovoso,
(2009); (Tenenhaus, 2008) and (Marcoulides & Saunders, 2006). Ringle, Sarstedt, & Straub (2012) reviewed/metaanalyzed
204 of studies which were done using PLSSEM, they found that the average
sample size in those studies was 238.12, and the median was 198. In addition to
that, it was evident through the study
that 33.8 studies used this method only because of having low sample sizes.
Tenenhaus, Pages, Ambroisine, & Guinot (2005) even did research based on just six subjects.
Even though PLSSEM has the edge over
CBSEM, CBSEM also has few comparative advantages over PLSSEM. PLSSEM allows
for only recursive relationships in the structural models with no causal loops
allowed. Whereas, CBSEM does not have any such restriction and can also work
well with the nonrecursive models; CBSEM can deal with bidirectional
relationships unlike in PLSSEM where relationships tend to unidirectional only
(Hair, Ringle, & Sarstedt, 2011). CBSEM gives better global goodness of
fit criterion (Hair, Ringle, & Sarstedt, 2011) compared to PLSSEM with no
global measure of goodness of model fit.
As PLSSEM output does not give any
overall model fit in, therefore Goodness of fit (GoF) proposed by Tenenhaus,
Vinzi, Chatelin, & Lauro (2005) can be used to assess the structural model.
The geometric mean (G.M.) of the Average Variance Extracted (AVE) and the
average Coefficient of Determination (R^{2}) is used for the
calculation of Goodness of fit value. Wetzels, OdekerkenSchröder, & Van
Oppen (2009) proposed the cutoff values for assessing the result of GoF
analysis as ‘GoF=0.10 (small); GoF=0.25
(medium); and GoF=0.36 (large)’. Still,
these cut off values are not widely accepted by the majority of researchers.
Selection between PLSSEM Vs CBSEM
As the researcher has already discussed
the positive and negative aspects of both the methods in this study; now will
discuss the situations in which they should be applied.
CBSEM should be selected when the prior
theory is strong and additional testing &validation are the research objectives.
CBSEM should also be applied when either the model is nonrecursive, or when the assumptions of parametric tests are
fulfilled, or when bidirectional paths are used in the model (Wong, 2013; and
Hair, Ringle, & Sarstedt, 2011).
Whereas, PLSSEM should be selected, if
the research is more of exploratory in nature or if it is an extension to an
existing theory. PLSSEM should be used with the goal of predicting key target and
driver constructs, i.e. more for theory development rather than theory
confirmation (Hair, Ringle, & Sarstedt, 2011), notably when the sound
theory base is missing. PLSSEM should be used when available theories on the
subject are insufficient (Wong, 2013). Especially during the early stage of
theory development (Sosik, Kahai, & Piovoso, (2009). PLSSEM is strongly
prescribed when the model under study are complex or when formative constructs
are part of the structural model (Ringle, Sarstedt, & Straub, 2012). Moreover,
of course, its usage becomes must when
the underlying assumptions of CBSEM are violated (Reinartz, Haenlein, &
Henseler, 2009), or when there is single item per construct (Ringle, Sarstedt,
& Straub, 2012).
However, in the condition when the sample size is considerably large, then both
the techniques give similar results,
irrespective of the assumptions or anything else (Sosik, Kahai, & Piovoso,
2009). As according to the Figure: 1, PLSSEM and Figure: 2, CBSEM same
manifest variables (USEF3, EOU3, BI3, ATT2, USE1) had maximum loadings for the
Latent Variables (USEF, EOU, BI, ATT, USE). Also, Path EOUàUSEF
followed by USEFàBI had maximum and second highest
coefficient values, and the sequence of other paths were also the same in both the models. The results were the same; only the values were different. The
reason for this could be because the
dataset was huge as in this hypothetical it was of 1,190 responses.
Figure:
1 Partial least squares (PLS) results
Source: (SmartPLS, 2018)
Figure:
2 CBSEM Maximum likelihood (ML) based results (AMOS; standardized
coefficients)
Source: (SmartPLS, 2018)
Steps to be followed in PLSSEM concerning
reflective scale:
First of all, the objectives should be
clearly defined and if they suit for
PLSSEM, then only it should be applied. Additionally,
the assumption of the CBSEM should be
checked before proceeding further with the PLSSEM
if the data set fails to satisfy the assumptions than one would be forced to
move towards the PLS Techniques. One
should mention the reasons for using PLS Technique in their research.
There are two submodels in a PLS
Structural Equation Model; (Sosik, Kahai, & Piovoso, 2009). The first component of PLSSEM model is the
structural model or inner loop, having endogenous constructs which are
explained by relationships in structural model with the other constructs (Hair,
Ringle, & Sarstedt, 2011). It stipulates the relationships among the
independent and dependent latent variables. The second
component is an outer loop or measurement
model having exogenous constructs with no structural path relationship between
them (Hair, Ringle, & Sarstedt, 2011). It represents the relationships
between the latent variables and their manifest variables.
It cannot be said that there are no
restrictions on the sample size of the data
set while performing PLS Techniques. Sample size in case of PLSSEM should be atleast
equal to or more than ten times highest formative variables measuring one
construct. (Hair, Ringle, & Sarstedt, 2011). Alternatively,minimum ten
times the highest statistical paths directed at a latent construct in the
structural model. According to Marcoulides & Saunders (2006) as cited in
Wong (2013); minimum sample size should be 91 ifmaximum
number of arrows pointing towards a latent variable is 10.
Checking validity and reliability is the mostcrucial step while performing PLS Techniques:
• For
Internal consistency/reliability (Nunnally
& Bernstein, 1994): in place of Cronbach alpha, Composite
Reliability is the better method in PLSSEM, as it does not assume all the
indicators to be equally reliable (Bagozzi & Yi, 1988). Composite
reliability of more than 0.60 isregarded as
satisfactory.
• For
indicator reliability (Hair, Ringle, & Sarstedt, 2011 and Bagozzi & Yi,
1988): Indicator loadings should be more than 0.70 and loadings that are less
than 0.4 should not be included inreflective
scale.
• For
Convergent validity (Hair, Ringle, & Sarstedt, 2011) and (Bagozzi & Yi,
1988): Average Variance Extracted (AVE) should be more than 0.5,meaning that
the latent variable explains more than half of the variance of its indicators.
• For
Discriminant validity (Hair, Ringle, & Sarstedt, 2011): all crossloadingsshould be lowerthan indicator loadings and AVE should be more than
the construct’s highest squared correlations with any other latent construct
(FornellLarcker Criterion) (Fornell & Larcker, 1981).
Measuring ‘Coefficient of determination’
(R^{2}),i.e.model’s predictive
accuracy is primary evaluation criteria for the structural model. R^{2} values of 0.2 are
considered high in consumer behaviour
studies. Values of 0.7, for endogenous
latent construct is called as substantial, 0.5 as moderate and 0.25 asweek
(Hair, Ringle, & Sarstedt, 2011). Additionally, PLS Algorithm must converge
in maximum of 300 iterations, if it does not converge
in 300 iterations it would have meant that data were abnormal due to the
reasons such as the sample size could be too small, evidence of the existence of outliers, data having too many
identical values in indicator and this would require further investigation (Wong, 2013).
Bootstrapping, which is a nonparametric
method, allows for the testingnull hypothesis
that a coefficient equals to zero, through this,
the significance of the coefficient can
be analyzed. Bootstrapping should be
done with samples of at least 5,000 wherenumber
of cases should not be less than the number
of original observations. Omission distance (d) should be chosen between 5 and
10. Critical tvalues for a twotail test
are 1.65 (significance at the level of 10 percent),
1.96 (significance at the level of 5 percent),
2.58 (significance at the level of 1 percent)
(Hair, Ringle, & Sarstedt, 2011).
Model’s capacity to predict is significant
(Rigdon, 2014) and can be
measured through StoneGeisser’s (Q^{2}) (Stone, 1974) obtained through
Blindfolding, which gives ‘crossvalidated
redundancy’ and ‘crossvalidatedcommunality’.
Hair, Ringle, & Sarstedt (2011) suggested using
crossvalidated redundancy (Q^{2}) of endogenous latent variable
and its value to be more than zero for explaining the construct’s predictive relevance.
With the significance,
it is also f^{2} value indicates the effect of the construct removed
for a particular endogenous construct. The values of 0.02 represent small, 0.15
medium and 0.35 large effects (Cohen, 1988). If an exogenous construct strongly
contributes to explaining an endogenous construct, the difference between R^{2}
included and R^{2} excluded should be high, leading to high effect size (f^{2} value).essential
to measure the magnitude of the influence, which can be done through Cohen’s f^{2 }or Effect size.
f^{2 }= (R^{2}_{AB }–R^{2}_{A})
/ (1 R^{2}_{AB})
Where;
R^{2}_{A} 
= 
variance accounted for in the
population by variable set A 
R^{2}_{AB} 
= 
Variance accounted for in the
population by variable set A and B Together 
Conclusion:
Data itself is not the solution to any
problem; it is the analysis of data which shows the decision path to any
manager. For the analysis, several techniques could be used. Comparisons among
the techniques would be wrong as none of them is better than another. Their
usage should depend upon the objectives of any particular study. In a
situation, one could be better whereas in another case the other one. The
relation between both is more complementary rather than competitive. As also
found by Tenenhaus (2008) and cited in
Hair, Ringle, &
Sarstedt(2011) –When the study is using suitable measures and data or
when CBSEM assumptions were met then in that situation both the approaches
practically yield the same results. That is if before the application of
PLSSEM if measurement model characteristics are checked,then it will give similar results as of CBSEM
(Hair, Ringle, & Sarstedt, 2011).
If precisely discussing the strength of
PLS, then it is statistically more robust, sensitive, and simpler with less
strict assumptions. However, its inability to deal with nonrecursive
relationships and causal loops; and the absence of global goodness of fit acts
as its weakness.
In the dynamic business environment,
VUCA is quite high, and almost every data in the social sciences follows
Pareto’s principle. It does not showcase normality and is mainly skewed, also
as the life cycle of every product and service is shortening due to
technological advancements, it becomes imperative to finish the marketing
research very rapidly. Therefore, it becomes difficult to fulfil all the
assumptions of the CBSEM and to have a large sample size, which acts as an
opportunity for the usage of PLS. seeing the dynamic nature of the everchanging
business scenario, this methodology facilitates the researcher with appropriate
judgmental decision choices.
However, every researcher should first
identify her or his objectives and then decide the bettersuited method for her or his study. Dijkstra &Henseler (2015)
gave consistent PLS (PLSc) model, which is an extension of PLS and is comparable
to covariancebased SEM, in future,the researchers suggest a study
differentiating PLSc and CBSEM. Researchers believe that PLSSEM usage has
been overly used or indeed misused due to its simplicity or they believe that
it will require less pain due to lesser strict assumptions. Whereas, they must
be considering their objectives as their selection criterion to choose any
method.
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