#### Partial least squares path modeling: Quo vadis?

Qual Quant
Partial least squares path modeling: Quo vadis?
J o¨rg Henseler 0 1
Nova Information Management School, Universidade Nova de Lisboa, Lisbon, Portugal
0 Faculty of Engineering Technology, University of Twente , P.O. Box 217, 7500 AE Enschede , The Netherlands
1 & Jo ̈rg Henseler
1 Introduction
Partial least squares (PLS) path modeling is a multivariate statistical technique that relies
on an alternating least squares algorithm as invented by
Wold (1974)
. It is regarded as the
‘‘most fully developed and general system’’
(McDonald 1996, p. 240)
among
variancebased estimators for structural equation modeling, and it is applied across a wide range of
disciplines, including information systems research
(Marcoulides and Saunders 2006)
and
marketing
(Hair et al. 2012)
. In its most modern appearance, it can be regarded as a
structural equation modeling (SEM) technique that can handle various forms of construct
operationalizations, including reflective measurement and composite models
(for a
distinction, see Rigdon 2012; Henseler 2017)
.
In recent years, the use of PLS has been the subject of fierce debate between proponents
and opponents. Whereas some researchers strongly advocate the use of PLS and call it a
‘‘silver bullet’’
(Hair et al. 2011)
, others believe PLS should not be used at all
(Antonakis
et al. 2010)
. For researchers who promulgate, extend, or apply PLS, the debate has been
fruitful because it has helped to identify several weaknesses of PLS, for example, the
inconsistency of parameters in the case of reflective measurement models, the lack of
goodness-of-fit measures, and the low sensitivity of the Fornell-Larcker criterion to detect
problems with regard to discriminant validity
(Ro¨ nkko¨ and Evermann 2013)
.
Subsequently, many new developments have led to substantial improvement and enrichment of
PLS, including a correction for attenuation if constructs are modeled as common factors
(consistent PLS, see Dijkstra and Henseler 2015b)
, a new criterion to assess the
discriminant validity called the heterotrait-monotrait ratio of correlations
(HTMT,
Henseler et al. 2015)
, the standardized root mean square residual (SRMR) as an approximate
measure of fit
(Henseler et al. 2014)
, bootstrap-based tests of overall model fit
(Dijkstra
and Henseler 2015a)
, a new approach for estimating and testing second-order constructs
(van Riel et al. 2017)
, a clarification on which auxiliary theories PLS can actually model
(Henseler 2017)
, and updated guidelines for model specification and reporting
(Henseler
et al. 2016)
.
In the past, many papers focused on the question of ‘why should researchers use PLS?’.
Typical answers referred to the alleged advantages of PLS, such as the ability to handle
both formative and reflective measurements, low sample size requirements, and a lack of
distributional assumptions
(c.f. Henseler et al. 2009)
. Unfortunately, the situation is not
that simple, and the generality of these characteristics is limited. Methodologists currently
appear to refrain from making claims about PLS at all
(Rigdon et al. 2017)
or ask for future
research to identify advantages of PLS
(Rigdon 2016)
. At the moment, the question about
the reasons to use PLS remains unanswered. This conclusion is less dramatic for PLS than
it might appear on first sight. Actually, the discussion of why to use PLS could benefit from
a slight reformulation of the question, replacing the ‘‘why?’’ by ‘‘for which purpose?’’. PLS
is nothing but a tool, and tools should be assessed in relation to the task that they are meant
to accomplish
(Goodhue and Thompson 1995)
.
2 For which purpose should one use PLS?
Empirical research in business and social science comes in many varieties. The dominant
types of research are confirmatory, explanatory, exploratory, descriptive, and predictive.
PLS can be of value for all of these types of research.
Confirmatory research aims to understand the causal relationships between variables. In
the special case of structural equation modeling, analysts are interested in the causal
relationships between theoretical concepts. Typically, researchers formulate a theory such
that some effects or relationships are hypothesized to have a fixed value, most often zero.
In that way, they obtain degrees of freedom (one per fixation/constraint) and make their
theory accessible to empirical testing. In the measurement model, this can mean that the
axiom of local independence holds, which entails that the correlations among indicators of
a common factor can be fully attributed to the existence of an underlying latent variable
(Lazarsfeld and Henry 1968)
. In the structural model, researchers may look for mediation,
which means that a certain variable has only an indirect effect on another variable, and the
direct effect is zero
(Nitzl et al. 2016)
. Confirmatory research requires a test of global
goodness of model fit based on the discrepancy between the empirical and the
modelimplied variance-covariance matrix. Only since the advent of global goodness of fit tests
(Dijkstra and Henseler 2015a; Henseler et al. 2014)
can PLS be employed for confirmatory
research.
Explanatory research also aims to understand the causal relationships between
variables; both confirmatory and explanatory research are sometimes referred to as causal
research. As in the case of confirmatory research, analysts wish to obtain consistent
estimates of the relationships among constructs. The distinguishing aspect of explanatory
research is that analysts are interested in explaining a specific phenomenon that is treated
as a dependent variable. Consequently, the structural equation models used for explanatory
research typically consist of one endogenous and one or more exogenous constructs. Since
structural models of this type are saturated (i.e., they have zero degrees of freedom), the
structural model is not assessable in terms of goodness of fit but only in terms of strength of
fit
(Henseler and Sarstedt 2013)
, i.e., the R-squared value of the endogenous construct.
Nevertheless, in explanatory research, the measurement models of multi-item constructs
can and should be tested for goodness of fit. Thus, explanatory research using PLS relies to
some extent on confirmatory research to test the auxiliary theory. If an analyst finds it
difficult to distinguish between confirmatory and explanatory research, the following
heuristic may help: If analysts have a eureka experience because they find empirical
support for a model that tries to explain a part of the world without a specific effect or
relationship, they are most likely conducting confirmatory research. If the empirical
support of an effect creates a eureka experience, then the analysts are most likely conducting
explanatory research.
Exploratory research aims to pinpoint possible relationships between constructs and can
best be understood as a heuristic for theory building. As such, it is an inductive way of
reasoning. Herman Wold, the inventor of PLS, regarded model building as the core task of
PLS
(Wold 1989)
. In his view, a researcher should design an exploratory structural
equation model ‘‘on the joint basis of his rudimentary theoretical knowledge, his
experience and intuition about the problems explored, and the data that are at his disposal’’
(Wold
1980, p. 70)
. PLS path models are developed ‘‘in dialogue with the computer’’
(Wold
1985, p. 240)
. For analysts, it can be tempting to continuously adapt a structural equation
model to the data at hand and then report hypothesis tests of the model fit and parameter
estimates. Adapting a model to the data implies that the model itself becomes a random
variable; consequently, any hypothesis test of a presumably fixed model will provide
misleading results. Researchers using PLS for exploratory research should regard PLS at
that stage as a tool for theory building not theory testing. In analogy to other exploratory
research techniques, such as cluster analysis or qualitative research, PLS should be
considered an atheoretical technique as long as it is used for exploratory research. Since
exploratory research tends to probe for possible explanations and hypotheses, analysts
strive for high sensitivity and are willing to compromise specificity. In this situation, the
somewhat higher sensitivity of PLS
(Reinartz et al. 2009)
is beneficial. To ensure
specificity, exploratory research should be followed by causal research.
Descriptive research is mainly interested in quantities that describe a population. The
dominant applications are national customer satisfaction indices, such as the Swedish
Customer Satisfaction Index
(Fornell 1992)
, the American Customer Satisfaction Index
(Fornell et al. 1996)
, and the European Customer Satisfaction Index
(Tenenhaus et al.
2005)
. However, customer satisfaction is not the only application of indices. Researchers
have created a plethora of other indices, for instance, the Air Force Warehouse Logistics
Index (Sohn et al. 2007), the Global Competitiveness Index (Petrarca and Terzi
forthcoming), the Respondent Burden Index
(Fricker et al. 2012)
, and the Technology
Commercialization Success Index
(Sohn and Moon 2003)
. Descriptive research using PLS also
encompasses a prescriptive element. In particular, the PLS algorithm provides a
prescription for dimension reduction
(Dijkstra and Henseler 2011)
i.e., it prescribes how
variable values should be aggregated to proxy scores.
Predictive research aims to make predictions for individual cases. It differs from causal
and descriptive research in two important ways
(Shmueli et al. 2016)
. First, whereas causal
and descriptive research attempt to explain or describe the data at hand, predictive research
focuses on providing a prognosis for new data. Second, whereas causal and descriptive
research make aggregate statements such as effects and average levels, predictive research
makes individual statements for each case. PLS is well suited for prediction purposes.
Wold
(Wold 1982)
emphasized the ‘‘causal-predictive’’ nature of the structural paths, and a
recent special issue of the Journal of Business Research was dedicated to ‘‘PLS and
prediction’’
(Cepeda Carrio´ n et al. 2016)
. While there are other statistical techniques that
outperform PLS with regard to prediction capability, PLS is transparent about how the
prediction is produced. Thus, in contrast to many other techniques, PLS is not a black box.
As Shmueli et al (2016, p. 4552) stated, PLS ‘‘aims to maintain interpretability while
engaging in predictive modeling.’’
In practice, the distinction between the five aforementioned types of research is not
always that clear-cut. Combinations of research types are common, e.g., making
predictions based on an explanatory model. Nevertheless, distinguishing between the five types
of research can help to identify certain purposes for which PLS is an adequate statistical
tool. For each type of research, one can identify situations in which PLS can be of value for
an analyst. These are expressed in the form of the following five propositions:
PLS is a suitable technique for confirmatory purposes if a structural equation model
contains one or more constructs operationalized as a composite. The analyst’s focus
will predominantly lie on the model’s goodness of fit.
PLS is a suitable technique for explanatory purposes if a structural equation model
contains one or more constructs operationalized as a composite. The analyst’s focus
will predominantly lie on the endogenous variables’ R-squared, the statistical
inference of path coefficients, and effect sizes.
PLS is a suitable technique for exploratory purposes if researchers are searching for a
quick, graphic-supported indication of whether there might be a relation between two
proxies. The analyst’s focus will predominantly lie on the path coefficients.
PLS is a suitable technique for predictive purposes if the analyst is also interested in
understanding how the prediction is made. The analyst’s focus will predominantly lie
on the prediction errors of the model and the predictive relevance of each effect.
PLS is a suitable technique for descriptive purposes if the weights of a focal index take
into account the nomological net. The analyst’s focus will predominantly lie on the
(average) proxy scores and the proxy weights.
Finally, PLS can be used for auxiliary purposes. In such situations, PLS is not directly
applied to answer a research question but as a preparatory analytical step within a more
extensive analytical design. Researchers predominantly apply PLS to obtain construct
scores or inter-construct correlations that can be used in follow-up analyses. For instance,
Benitez et al. (2018)
use covariance-based structural equation modeling to estimate a
nonrecursive structural model using an inter-construct correlation matrix obtained through
PLS. PLS construct scores play a pivotal role in two-step procedures for estimating
moderating effects
(see, e.g., Dijkstra and Schermelleh-Engel 2014; Fassott et al. 2016;
Henseler and Fassott 2010)
, non-linear effects
(see, e.g., Henseler et al. 2012)
, and
higherorder constructs
(see, e.g., van Riel et al. 2017)
. Moreover, they form the basis for various
segmentation approaches
(see, e.g., Sarstedt and Ringle 2010)
. PLS can also serve as an
emulator of canonical correlation analysis (Wold 1966) and various generalizations thereof
(Tenenhaus and Esposito Vinzi 2005)
.
As Fig. 1 illustrates, PLS is at a crossroads. Awareness about the concrete purpose for
which one wants to use PLS is not only important for analysts seeking their way but also
for methodologists who are dedicated to improving and enhancing PLS. Whenever they are
strengthening the method, they should ask themselves which type of research question they
help PLS answer. By devoting research efforts to certain aspects of PLS, methodologists
can have a substantial impact on when and how intensively PLS will be used in the future.
3 The papers of the special issue
This special issue contains four papers that extend or apply PLS. They cover a wide
spectrum with regard to the type of research. The four papers all provide a unique
contribution to the further development and application of PLS.
The article ‘‘Partial least squares path modeling using ordinal categorical indicators’’ by
Schuberth et al. departs from the notion that researchers would sometimes like to apply
PLS but face the problem that their data is not metric but ordinal. This can occur in
questionnaire-based research if scales with too few options were selected. As a solution,
the authors introduce ordinal consistent partial least squares (OrdPLSc), a new consistent
variance-based estimator that makes use of polychoric correlations. OrdPLSc enables
estimation of the structural equation models of composites and common factors if some or
all indicators are measured on an ordinal categorical scale. A Monte Carlo simulation
validates the efficacy of the new method and confirms that OrdPLSc provides almost
unbiased estimates. If all constructs are modeled as common factors, OrdPLSc’s estimates
are close to those obtained from mean- and variance-adjusted weighted least squares
(WLSMV). OrdPLSc is most helpful for models that contain common factors as well as
composites. As can be derived from the quest for consistent and unbiased estimates,
Schuberth et al. are mainly concerned with confirmatory and explanatory research.
In their article titled ‘‘What matters most: importance-performance matrix analysis of
the factors influencing international postgraduate students psychological and sociocultural
adaptations,’’ Shafaei and Razak present the design and outcomes of an empirical study
explaining a relevant phenomenon of international higher education, namely, cross-cultural
adaptation. Based on their sample of international postgraduate students from major
research universities in Malaysia, the authors conclude that perceived stereotype images
and adjustment attitude affect the psychological and sociocultural adaptations of students
in Malaysia, whereas attachment attitude does not have an influence. English language
proficiency is not related to psychological adaptation. The use of importance-performance
matrix analysis underlines the combined application of explanatory and descriptive
research.
In contrast to the previous paper, the article written by Rodr´ıguez-Entrena et al. titled
‘‘Assessing statistical differences between parameter estimates in Partial Least Squares
path modeling’’ does not provide an immediate answer to the question ‘‘What matters
most?’’. Instead, it provides a technique that helps researchers to study research questions
of this type in general. Concretely, it introduces bootstrap-based confidence intervals to
statistically assess differences among structural model parameters using PLS. The authors
illustrate the applicability of their approach with the example of an established information
systems theory (technology acceptance model) to assess whether two parameter estimates
derived from the same sample are statistically different. Business success factor research in
particular can benefit from this approach because it enables discrimination of effective
management instruments from less effective ones.
The paper by Schreier et al. titled ‘‘Question order effects in partial least squares path
modelling: an empirical investigation’’ studies how a particular factor of research design
impacts the results of PLS analyses. The paper focuses on question order effects that may
be found in product or service quality studies—a typical domain of PLS path modeling. A
central finding is that when there are questions about details as well as overall questions, it
does matter in which order they are asked. The implications of this paper are particularly
valuable during the design phase of an empirical study.
I would like to thank the editor of Quality & Quantity, Vittorio Capecchi, for providing
the opportunity to publish this special issue. Moreover, I would like to express my
gratitude to the editorial assistant Massimiliano Geraci and Springer’s production editor
Ambiga Selvaraj for all their support in preparing the special issue. Special thanks goes to
the reviewers, who did an excellent job in guiding the authors. Finally, I wish that the four
papers are well received by the academic community.
Acknowledgements The special issue editor acknowledges a financial interest in the variance-based
structural equation modeling software ADANCO and its distributor, Composite Modeling. He thanks
Florian Schuberth for valuable comments on a previous version of this editorial.
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