The document provides a comprehensive overview of structural equation modeling (SEM) using Partial Least Squares Structural Equation Modeling (PLS-SEM) with SmartPLS software. It discusses theoretical foundations, model assessments, and practical guidelines for applying SEM techniques, including measurement and structural model evaluations for different validity types. Key topics include the importance of indicator reliability, internal consistency, and hypotheses testing via bootstrapping, exemplifying the process with a study on mobile money services in Ghana.

1. Analyzing Research Data with PLS-SEM
using SmartPLS
Awuni Emmanuel, PhD, MSc (Comp. Sc), MBA, PGCE
QES Scholar: McGill University, Montreal, Canada/University of Ghana, Legon
Prof. Richard Boateng, QES Collaborator/University of Ghana,
Workshop Enquiries: qesknowledgesharing@gmail.com
Venue: UGBS Graduate Campus, 1w1
Dr. Emmanuel Awuni, University of Ghana 1

2. Structural Equation Modeling: Introduction
• Structural equation modeling (SEM) is a
multivariate statistical analysis technique
that is used to analyze structural
relationships.
• Cases of SEM:
• Factor analysis
• Exploratory factor analysis
• Confirmatory factor analysis
• Multiple regression analysis
• Path Analysis
• Schools of thought:
• Covariance-Based SEM: Lisrel, Amos etc.
• Partial Least Square SEM: SmartPLS, XLSTAT..
• Generalized Structured Component Analysis
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Developers
of SmartPLS
for PLS_SEM

4. Model Element
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5. Formative vs Reflective
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6. Formative vs Reflective
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7. Models Assessment (Reflective)
• Measurement Model: shows how items
measure a particular construct.
• Reflective Indicator Reliability
• Internal Consistency
• Convergent Validity
• Discriminant Validity
• Structural Model: Regression equivalent
which shows how construct relates to
each other.
• Collinearity issues
• Hypothesis testing (Direct effect)
• Effect sizes f2
• Goodness of fit with R2
• Predictive relevance Q2
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8. Measurement Model Assessment (Formative)
• For the formative
indicators:
• Outer weight and T-
statistics for testing
indicator reliability
• Composite Reliability for
is used as a test criteria
for for the convergent
validity.
• Assessment of the
Collinearity with VIF.
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9. SmartPLS: An overview
• WHY PLS?
• The sample size is small and/or the data are
non-normally distributed.
• PLS enhances sampling distribution to
approach normality
• For theory development and prediction
• Models can use fewer indicators (1 or 2
• Model can(up to 50+)
• All variances including errors are useful for
testing the causal relationships.
SmartPLS is a software with
graphical user interface for
variance-based structural
equation modeling using the
Partial Least Squares path
modeling method.
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1. First: Download and
Install Java Runtime
>>Download
SmartPLS
https://www.smartpls.com/downloads

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>>Download
SmartPLS
https://www.smartpls.com/downloads

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Conceptual Model
for Effect of
Gratification on
user attitude and
continuance use of
Mobile Money
services in Ghana
using Uses and
Gratification Theory
with income and
Education as a
Moderating factors.
Example of a Conceptual Model

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Assess the Measurement
Model with
PLS Algorithm
Models Assessment

16. Measurement Model Assessment
• Indicator Reliability : is the
proportion of Indicator
variance that is explained by
the Latent variable.
• Criterion: Outer loading:
Threshold> .70
• Indicator reliability is the extent
to which a variable or set of
variables is consistent regarding
what it intends to measure.
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• Click on the outer loading after running
the PLS algorithm
• Click on the Construct Reliability and
validly for all the measurements regarding
the measurement assessment

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18. Measurement Model Assessment
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Reporting Indicator Reliability: The
study assessed indicator loading using
PLS algorithm. The result, as indicated
in Table 1, shows all the indicators
loaded well into their construct.
However, CG3 was deleted after first
running the PLS algorithms. This is
because the indicator loaded weakly
below the 0.70 threshold.
Table 1

19. Measurement Model Assessment
• Internal Consistency: refers to the general agreement between
multiple items (often Likert scale items) that make-up a composite
score of a survey measurement of a given construct.
• This agreement is generally measured by the correlation between
items.
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CRITERIA
Threshold:
• Cronbach alpha (𝛼): Threshold> .70
• Composite Reliability (CR):
Threshold> .70
Table 2

20. Measurement Model Assessment
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Reporting: The study tested internal consistency with Cronbach's alpha using PLS
algorithm. All the latent constructs, shown in Table 3 yielded over 0.70 Cronbach
alpha values. This indicates a strong internal reliability among the indicator.
Table 3: Construct reliability

21. Measurement Model Assessment
• Convergent Validity: is degree to which individual
items reflecting a construct converge in
comparison to items measuring different
constructs.”
• Average Variance Extracted (AVE): Threshold >= 0.50.
• Composite reliability (CR): Threshold >= 0.60 or 0.70
• To measure the AVE, each indicator loading on a
construct must be squared and the mean value
determined.
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• Reporting: Table 4 shows
that the AVE values are
higher than the threshold
of 0.50 which indicates
adequate convergent
validity. This means that
the latent construct
explains at least 50
percent of the variability
of its items and thus
demonstrates sufficient
convergent validity.
Table 4

22. Measurement Model Assessment
• Discriminant Validity: is referring to the
extent in which the construct is actually
differing from one another empirically
• Outer Loadings: Threshold >= 0.70
• Fornell- Lacker: Threshold >= 0.50
• Heterotrait-monotrait: Threshold < 0.85 or
0.90.
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Reporting: As indicated in Table 5, all
the HTMT values did not exceed the
0.9 threshold which indicates the
presence of discriminant validity. The
implication is that the various latent
variables are distinct and different
from each other.
HTMT table for
Discriminant
validity
Table 5

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Reporting: Where each indicator
loading is higher for its construct
than for any other construct and
each of the constructs or latent
variables loads highest with its
indicators or assigned items, it can
be generalized that, the indicators of
the latent variable or construct are
discriminant of each other. That is,
they are not interchangeable. From
that 5.3, it can be inferred that the
latent variables are discriminant of
each other as they load the highest
on their assigned constructs than
any other construct (s).

24. Measurement Model Assessment
Measurements Criteria Threshold Reference
Indicator Reliability indicator loadings >=0.5 Henseler et al. (2009)
Internal Consistency Cronbach Alpha (𝛼) >=0.6 or 0.7 Nunnally, (1978)
Composite reliability (CR) >=0.6 or 0.7 Joreskog (1971)
Rho_A >=70 Dijkstra and Henseler
(2015)
Convergent Validity *Average Variance Extracted (AVE) >=0.5 Fornell and Larcker (1981)
Composite reliability (CR) >=0.6 or 0.7
Discriminant Validity *Indicator Cross loadings >=0.7 Hair et al. (2019, p.9)
*Heterotrait-monotrait (HTMT) <= 0.85 0r 0.90, above
this threshold indicates
absent of discriminant
validity
Gold, Malhotra, and
Segars, (2001) Henseler et
al., (2015)
Fornell and Larcker 0.5 across the diagonal Fornell and Larcker (1981)
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Table 7

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Table 8. Some
Guidelines for
using SmartPLS

26. Assessment of the Structural Model
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Collinearity Issues
Significance and relevance
Effect Size, f2
Goodness of fit with R2
Predictive Relevance, q2

27. Assessment of Collinearity
• In SEM, A minimum
threshold of 5 or lower
is needed to avoid
issues of collinearity
(Hair, Ringle, & Sarstedt,
2011).
• A very high
multicollinearity is
above 20.
In PLS_SEM, Multicollinearity is assessed by analyzing
the Variance Inflation Factor (VIF) for each independent
construct
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28. Assessing Multicollinearity
• After running the PLS algorithm click on the VIF beneath.
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29. From Table 9, all VIF values are below the value of 5, indicating that there
are no issues with collinearity. That latent variables are independent of each
other and that change in one does not affect the other variables and vice
versa.
Reporting Multicollinearity
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Table 9

30. Hypothesis testing: Bootstrapping for Direct effect
• Bootstrap estimates the spread, shape and bias of the sampling distribution
of the population from which the sample under study is drawn from.
Bootstrapping is
non-parametric
procedure that
allows testing
the statistical
significance of
various
PLS_SEM results
such as Path co-
efficient etc.
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31. Reporting test of significance (Direct effect)
In order to test the hypothesis for significance,
bootstrapping procedure is performed using a two-tailed t-
distribution. The bootstrapping was run using 5000
iterations (subsamples). The result is presented in Table 9.
NOTE:
Sample mean
after the running
bootstrapping
algorithm is the
Standardized beta
(std. beta)
Standard
deviation after the
running
bootstrapping
algorithm is the
standard error
(std. error) on the
table.
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Table 9

32. Reporting:
All five hypotheses proposed
in this study were
supported. This was done
through bootstrapping with
bias-corrected 95%
confidence intervals. The
findings related to the
individual hypotheses are
discussed in the following
section below.
Since a 95% confidence interval is
assumed, a minimum critical value
of 1.65 as ideal for a significance
level of 10% (two-tailed).
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33. Effect Size, Cohen’s f2
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• The effect size shows how much an exogenous
latent variable contributes to an endogenous
latent variable’s R2 value.
• In simple terms, effect size assesses the
magnitude or strength of relationship between
the latent variables.
• Effect size helps researchers to assess the overall
contribution of a research study.

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Run the PLS Algorithm
Algorithm for the effect
size and make changes
here to give your results
on the indirect effect

35. Effect Size, Cohen’s f2
Reporting: From Table 10, the independent constructs such as cognitive,
convenience, ease of use, hedonic and integrative are found to have a small
effect on attitude towards use. In addition, usefulness as an independent
construct has a moderating effect on Attitude towards use. Attitude towards
use is termed to have a large effect on continuance use intention.
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Table 10

36. Assessing Goodness of Fit with R-Squared
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• The assessment of the goodness of fit
indicates whether the model is well-fitted or
ill-fitted.
• The GOF test helps the researcher to identify
misspecifications of the measurement and
structural model.
• R2 measures the model’s explanatory power.
• It represents the combined effects of the
exogenous latent variables on the
endogenous latent variable.
• R2 varies from 0 to 1
0.25: weak
0.50: moderate
0.75: Strong or
substantial

37. Assessing Goodness of Fit with R-Squared
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Find the R2

38. Reporting Goodness of Fit
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• From Table 11, the R2 of the model
is 0.649 and 0.556. This implies that
the combined exogenous latent
variables account for 65%
endogenous factor variations
(Attitude) and and 56% of the
Attitude on continuance use. This
indicates that the model is well
fitted given that it is beyond the
acceptable threshold of 0.5.
Table 11

39. Mediation
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• Direct Effect: Relationship linking two constructs with a single arrow
• Indirect Effect (also Mediating effect): A sequence of relationships with at
least one intervening construct involved
Students IQ
Classroom
Academic
performance
x1
x2 x3

40. Mediation
• Mediation explains the relationship between the
constructs/latent variables (exogeneous and endogenous)
• Conditions:
• Exogeneous variations account for the variations in
endogenous construct
• Exogeneous variations account for the variations in Mediator
• Mediator accounts for the variations in endogenous construct
• When mediator is added to the model the relationship
between the Exogeneous and endogenous constructs
decreases.
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41. Mediating Effect
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Run the Bootstrapping
Algorithm for the
Mediating effect and
make changes here to
give your results on the
indirect effect

42. Moderation
• Moderation changes the strength or direction of the relationship between
the constructs/latent variables (exogeneous and endogenous).
• They do not explain why there is a relationship between the constructs.
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Hedonic Hedonic
Income Education Gender
• Does income increase or decrease the relationship between hedonic and Attitude
• Does education increase or decrease the relationship between hedonic and Attitude
• Does Gender play role in the relationship between hedonic and Attitude

43. Moderation
• Two types:
• Categorical moderation
• Continuous moderation
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44. Moderation Effect
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1. Add the moderating variable by
connecting formatively to the
dependent variable.
2. Run the Bootstrapping Algorithm
for the Moderating effect

45. Moderation Effect
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1. Add the moderating variable
by connecting formatively to
the dependent variable.
2. Right click on the dependent
variable and select
moderating effect.
3. Make changes to add the
moderating effect.
4. If the variable is Categorical
make these changes in the
figure.
5. Run the Bootstrapping
Algorithm for the
Moderating effect

46. Moderation Effect
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1. If the variable is Categorical
make these changes in the
figure.
2. After that run the
Bootstrapping Algorithm for
the Moderating effect

47. Mediating Effect
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Run the
Bootstrapping
Algorithm for
the
Moderating
effect

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49. Practice: Drafting of Research paper
1. Introduction
2. Literature Review
3. Hypothesis and Research Model
3.1 Research Theory
3.2 Hypothesis development and Model
4. Methodology
5. Results
5.1 Demographic characteristics
5.2 Measurement Model Assessment
- Indicator reliability (outer loading)
- Internal consistency (CR, Rho_A)
- Convergent Validity (AVE)
- Discriminant Validity (HTMT)
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5.3 Structural Model Assessment
-Assess Multicollinearity (VIF)
-Test of Significance (T-value/p-value)
-Effect size (Chen f2)
-Goodness of Fit (R2)
6. Discussion and implication
6.1 General discussion
6.2 Implications
5. Conclusion
Reference

50. Areas to explore in SmartPLS
• Multigroup Analysis
• Higher Order Construct
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51. Areas to Explore in SmartPLS
Analyzing Data with
Data Mining and Machine Learning
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