By
Dr. Ida Rosnita IsmailUKM-Graduate School of Business
Universiti Kebangsaan Malaysia
17 September 2019Seminar Room 1
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Introduction to PLS-SEM and SmartPLS
Data management
Justifications for using PLS-SEM
Measurement model assessment
Structural model assessment
1
2
3
4
5
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Mediation analysis6
Continuous moderator analysis7
IDAISMAIL©IDAISMAIL© 3
Theory
80%
Results
20%
RESEARCH SUCCESS
Data analysis is an important component in a
research but the empirical results are not solely
depending on the data analysis technique:
• Thorough literature review.
• Good underpinning theories.
• Sound theoretical justifications.
• Unquestionable models.
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Structural Equation Modeling (SEM)
• A multivariate analysis technique: application of statistical method that simultaneously analyze
multiple variables.
• A second-generation technique that incorporate unobservable variables measured indirectly by
indicator variables.• Facilitate accounting for measurement error in observed variable.
• Many types of SEM; the ‘famous’ two: • covariance-based structural equation modeling (CBSEM).
• partial least squares structural equation modeling (PLS-SEM).
1Introduction to PLS-SEM and SmartPLS
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• PLS-SEM originator is Herman O. A. Wold.
• Wold (2006) characterized PLS-SEM as an “epoch-making 1960s innovation” that combines
econometric prediction with the psychometric modeling of LVs which multiple indicator
determine.
• Application of PLS-SEM can be found across field of studies including marketing, advertising,
international business, operations management, psychology, accounting, strategic management,
tourism, family business, management information system, human resource management, and
international marketing, education, healthcare, political science, law and others.
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• CBSEM and PLS-SEM are two data analysis techniques that stem from the SEM family –
complement each other.
• Sarstedt et al. (2016) also note that:
• CBSEM follows a common factor model approach in the estimation of the construct
measures, which assumes that the variance of a set indicators can be perfectly explained by
the existence of one unobserved variable (the common factor) and individual random error.
• PLS-SEM follows a composite model approach in the estimation of the construct measures,
whereby indicators can be linearly combined to form composite variables that are
comprehensive representations of the LVs, which serve as valid proxies of the conceptual
variables under investigation. • Note! Differentiate PLS-SEM as composite-based SEM from composite model.
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CBSEM & PLS-SEM
• Reflective indicators are
representative sample of all
possible items available
within the conceptual
domain of a construct.
• Formative indicators form
the construct by means of
linear combination…
BUT!
IDAISMAIL©
• A software that was developed in
2004 by Prof. Dr. Christian M. Ringle
to assist PLS-SEM estimation.
• A leading commercial software that
has received significant attention
among users of various disciplines.
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• A second generation data analysis
technique that is commonly used to
run a complex model.
• A non-parametric approach; thus is
also known as a soft-modelling
technique.
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CBSEM & PLS-SEM: When to Use?
PLS-SEM CBSEM
1. The goal is predicting key target constructs or identifying
key “driver” constructs.
2. Theory is relatively weak or less developed.
3. Formative measured constructs are part of the structural
model.
4. The structural model is complex (many constructs and
many indicators).
5. The sample size is relatively small and/or the data are
non-normally distributed.
6. The plan is to use LV scores in subsequent analyses.
7. Model includes testing the effect of continuous
moderating variable.
1. The goal is theory testing, theory confirmation, or the
comparison of alternative theories.
2. Error terms require additional specification, such as the
covariation.
3. The structural model has circular relationships.
4. The research requires a global goodness-of-fit criterion.
Justifications for Using PLS-SEM
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1. Missing data:
• Occur when a respondent either purposely or inadvertently fails to answer one or more
question(s).
• If amount of missing data on a questionnaire exceeds 15%, remove observation.
• If amount of missing data on a questionnaire do not exceed 15% but there is a high proportion of
responses are missing for a single construct, remove observation.
• Three approaches to missing data treatment:
1. Mean value replacement – use when there are less than 5% values missing per indicator.
2. Casewise deletion
3. Pairwise deletion – not recommended unless the other two options are not possible.
• Other approaches (further details: Hair et al., 2017).
3Data Management
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2. Suspicious response patterns:
• Straight lining – when a respondent marks the same response for a high proportion of the
questions.
• Also look out for diagonal lining and alternating extreme pole responses.
• Inconsistency in answers – especially when using screening questions.
• Giving different answers to a same question (that is asked slightly different).
• Deviate from specific instruction – e.g., instructed to check only a 1 on a 7-point scale for the
next question but the respondent check on any other number.
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1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
….
….
….
….
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3. Outliers:
• An extreme response to a particular question, or extreme responses to all questions.
• Why?
1. Data entry errors – e.g., instead of 7, key-in as 77.
2. Part of the reality – e.g., exceptionally high income.
3. Combinations of variable values are particularly rare – e.g., spending 80% of annual income
on holiday trip.
• What should be done?
1. Identify the outliers – boxplot and stem-and-leaf plots.
2. Identify possible solutions by providing explanation, correcting data entry errors, and/or
identifying unique subgroups.
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4. Data distribution:
• PLS-SEM is a soft modeling that does not require normal distribution.
• But extreme non-normal inflates standard errors obtained from bootstrapping; thus, decrease the
likelihood that some relationships will be assessed as significant.
• Hair et al. (2017) suggest examine skewness and kurtosis (two measures of distributions):
1. Skewness:
• Assesses the extent to which a variable’s distribution is symmetrical.
• A distribution is skewed when the distribution of responses for a variable stretches
toward the right or left tail of distribution.
• Guideline: skewed when greater than +1 or lower than -1.
2. Kurtosis:
• Assesses whether the distribution is too peaked.
• Guideline: too peaked if larger than +1 and too flat if less than -1.
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JU
ST
IFIC
AT
ION
S
Stage 1: Measurement Model
Reflective measurement model• Outer loading
• Internal consistency reliability
• Convergent validity
• Discriminant validity
Formative measurement model• Redundancy analysis
• Indicator collinearity
• Outer weight assessment
Stage 2: Structural Model
• Inner collinearity
• Magnitude of path coefficient
• Significance of path coefficient
• Coefficient of determination
• Effect size
• Predictive relevance
BASIC PLS-SEM
Da
ta clea
nin
g
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4Measurement Model Assessment
Measurement model / outer model
of exogenous latent variables
Measurement model / outer model
of endogenous latent variables
Structural model / inner modelAdopted from Hair et al. (2017), p.12
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4PLS-SEM
Y1
Y2
X1
X2
X3
X4
X5
X6
Y3
Y4
X7
X8
X9
X10
Outer weightOuter
loadingPath
coefficient
Manifest
variable
Latent
variable
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Measurement model of
exogenous latent variables
Measurement model of
endogenous latent variables
Y1
Y2
X1
X2
X3
X4
X5
X6
Y3
Y4
X7
X8
X9
X10
Form
ati
ve
Ref
lecti
ve
Sin
gle
ite
m
Structural Model
Y1
Y2
Y3
Y4
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Reflective measurement model
I appreciate this hotel.
I am looking forward
to staying in this hotel.
I recommend this
hotel to others.
SAT
REFLECTIVE
X1
X2
X3
SAT
𝑥 = lY + e
• x is the observed indicator variable
• Y is the latent variable
• l is a regression coefficient quantifying the strength
of the relationship between x and Y, also known as
loading
• e is the random measurement error
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X1
X2
X3
SATThe service is good.
The personnel is
friendly.
The room is clean.
SAT
FORMATIVE
Formative measurement model
𝑌 =
𝑘=1
𝐾
𝑤𝑘 . 𝑥𝑘
Y is a linear combination of indicators, xk (k=1,…,K),
each weighted by an indicator weight wk
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X2
x4
x5
x6
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X1
X2 Y
M
x1
x2
x3
x4
x5
x6
m1
m2
m3
y1
y2
y3
Reflective Measurement Model
Indicator loading: 0.70 and above
Indicator reliability: 0.50 and above
Internal consistency reliability (Cronbach’s
alpha & composite reliability): 0.70 and
above
Convergent validity (average variance
extracted or AVE): 0.50 and above
Discriminant validity:
HTMT: 0.85 or below (convention) or
0.90 or below (relax)
Fornell-Larcker criterion: a construct’s
square root of AVE should be larger
than the construct’s intercorrelations
with other constructs
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• Internal consistency reliability:1. Cronbach’s α
• Reliability estimates based on the intercorrelations of the observed indicator variables.
• Assumes all indicators are equally reliable, i.e. equal outer loadings on the construct.
• Sensitive to the number of items; tends to underestimate the internal consistency reliability.
2. Composite reliability
• Takes into account the different outer loadings of the indicator variables.
• Tends to overestimate the internal consistency reliability.
• Interpretation (Hair et al., 2017):• Below 0.60 – lack of internal consistency reliability.
• 0.60 to 0.70 – acceptable (exploratory research).
• 0.70 to 0.90 – satisfactory (advanced stages of research).
• 0.90 and above (especially 0.95 and above) – not desirable; indicate measuring same phenomenon.
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𝐶𝑟𝑜𝑛𝑏𝑎𝑐ℎ′𝑠 𝛼 =𝐾. 𝑟
[1 + 𝐾 − 1 . 𝑟]
• K is the construct’s number of indicators
• r is the average non-redundant indicator
correlation coefficient
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• lk is the standardized outer loading of the
indicator variable, k, of a specific construct
measured with K indicators
• ek is the measurement error of indicator
variable k
• var(ek) is the variance of measurement error,
defined as 1-lk2
𝜌𝑐 = 𝑘=1𝐾 𝑙𝑘
2
𝑘=1𝐾 𝑙𝑘
2 + 𝑘=1𝐾 𝑣𝑎𝑟(𝑒𝑘)
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• Convergent validity:• The extent to which a measure correlates positively with alternative measures of the same construct.
• Items of a reflective construct should converge or share a high proportion of variance.
• Assessment:
1. Indicator level: indicator reliability – how much of the variation in an item is explained by the
construct, i.e. variance extracted from the item.*• Should be at least 50% – variance shared between the construct and its indicator is larger than the
measurement error variance.
2. Construct level: AVE (average variance extracted) – the degree to which a latent construct explains
the variance of its indicators. • The sum of the squared loadings divided by the number of indicators.
• Threshold: 0.50 and above – which indicates that, on average, at least 50% or half of the variance of its
indicators are explained by the assigned construct.
• Single item construct, indicator outer loading is fixed at 1.00 – AVE is inappropriate measure.
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• Discriminant validity:• The extent to which a construct is truly distinct from other constructs by empirical standards.
• Indicates that a construct is unique and captures phenomena not represented by other constructs in the
model.
• Assessment:
1. Cross-loading• An indicator’s outer loading should be greater than any of its cross-loadings on other constructs.
• The presence of cross-loadings that exceed an indicator’s outer loading indicates a discriminant validity
problem at the item level.
2. Fornell-Larcker criterion• The square root of each construct’s AVE should be greater than its highest correlation with any other
construct – compares the square root of the AVE values with the latent variable correlations.
• A construct shares more variance with its associated indicators than with any other construct.
• In a model that includes formative measure and single item measure, ignore the results for these
measures – AVE value is not meaningful.
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• According to Henseler et al. (2015):• The conventional discriminant validity criteria do not reliably detect discriminant validity issues.
• Examples: constructs are perfectly correlated or indicator loadings vary/differ only slightly.
• Propose: heterotrait-monotrait ratio of the correlations (HTMT).• A ratio between-trait correlations to the within-trait correlations.
• An estimate of what the true correlation (i.e., disattenuated correlation) between two constructs would be if they
were perfectly measured (i.e., perfectly reliable).
• A disattenuated correlation between two constructs close to 1 indicates a lack of discriminant validity; hence, a
conventional threshold value is 0.85 – HTMT0.85
• A value not exceeding 0.90 is acceptable (HTMT0.90) but any value above 0.90 suggests a lack of discriminant
validity.
• The procedure can also serve as the basis of statistical discriminant test – use bootstrapping procedure but
confidence interval containing the value 1 indicates a lack of discriminant validity.
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Within-trait
correlations
Between-trait
correlations
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DA1 DA2 DA3 DA4 DA5
DA1
DA2 0.907
DA3 0.864 0.895
DA4 0.773 0.813 0.906
DA5 0.755 0.787 0.859 0.907
DimensionDimension A1 Dimension A2
Item A01 A02 A03 A04 A05 A06 A07 A08
DA1
A01 1
A02 0.705 1
A03 0.632 0.651 1
A04 0.582 0.644 0.619 1
DA2
A05 0.645 0.641 0.633 0.641 1
A06 0.600 0.622 0.584 0.584 0.747 1
A07 0.592 0.612 0.638 0.572 0.690 0.719 1
A08 0.569 0.601 0.582 0.615 0.644 0.686 0.741 1
HTMT Heterotrait-heteromethod Correlations
𝐻𝑇𝑀𝑇 𝐷1, 𝐷2 =𝐴𝑣𝑒𝑟𝑎𝑔𝑒 ℎ𝑒𝑡𝑒𝑟𝑜𝑡𝑟𝑎𝑖𝑡 − ℎ𝑒𝑡𝑒𝑟𝑜𝑚𝑒𝑡ℎ𝑜𝑑 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠
𝑀𝑒𝑎𝑛 𝑜𝑓 𝑎𝑙𝑙 𝑝𝑎𝑖𝑟𝑤𝑖𝑠𝑒 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠 𝐷1 ×𝑀𝑒𝑎𝑛 𝑜𝑓𝑎𝑙𝑙 𝑝𝑎𝑖𝑟𝑤𝑖𝑠𝑒 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠 𝐷2
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DEMONSTRATION
Corporate Reputation model:
reflective measurement model assessment
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X1
X2 Y
M
x1
x2
x3
x4
x5
x6
m1
m2
m3
y1
y2
y3
Formative Measurement Model
Convergent validity (redundancy analysis:
correlation): 0.70 and above
Collinearity of indicators: VIF < 5
Outer weight assessment: significance test
Outer weight is significant → outer weight’s
absolute and relative size.
Outer weight is not significant:
Outer loading is 0.50 or larger → keep
the indicator though not significant.
Outer loading is lower than 0.50: look
at the significance of the outer loading
Outer loading is lower than 0.50
but significant → consider
removing the item.
Outer loading is lower than 0.50
and not significant → delete the
item.
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DEMONSTRATION
Corporate Reputation model:
formative measurement model assessment
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5Structural Model Assessment
Bootstrapping
• PLS-SEM does not rely on distributional assumptions.• It relies on non-parametric bootstrap procedure to make statistical inferences.
• Bootstrapping in PLS-SEM is a non-parametric resampling procedure that assesses the variability
of a statistic by examining the variability of the sample data rather than using parametric
assumptions to assess the precision of the estimates (Streukens & Leroi-Werelds, 2016).
• Streukens & Leroi-Werelds (2016):
• Bootstrapping results provide good approximation of the population parameter of interest if
the sample is good approximation of the population. That is, • Bootstrapping needs good data.
• Bootstrapping is not a miracle cure for bad data and/or (too) small samples.
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Adopted from Hair et al. (2017), p.152
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• Test of significance for PLS-SEM coefficient estimates is derived from sampling distribution.
• Is a relationship statistically different from zero? • H0: β = 0
• H1: β ≠ 0
𝑡 =β
𝑠𝑒β• Test statistic:
Significant if the empirical t-value > critical t-value1.96
(5% sig. level, two-tailed)
• Hair et al. (2017) recommend reporting bootstrap confidence interval• Provide additional information on the stability of a coefficient estimate.
• Confidence interval, CI, is the range within which the true population parameter will fall assuming a
certain level of confidence (e.g., 95%).
• Significant if does not include a zero value.
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• 5 options of bootstrapping approach in SmartPLS 3.
• Both SmartPLS developers and Streukens & Leroi-Werelds (2016) recommend using bias-
corrected and accelerated percentile bootstrap confidence interval, or BCa bootstrap.• Confidence intervals may be asymmetrically distributed around the mean parameter estimate.
• Avoid forced symmetry—as in standard normal bootstrap confidence interval—that may have negative
influence on estimation accuracy, Type I error, and statistical power.
• Adjust for bias due to non-symmetric distribution and the shape (i.e., skewness) of the distribution.
• The most stable method that does not need excessive computing time.
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• Bootstrapping results reporting (recommendation):
Topic Recommendation
Resampling method Bootstrapping
Number of bootstrap samples Min: 5,000 or 10,000
Size of bootstrap samples Equal to the size of the original sample (i.e., number of valid
observations)
Parameter evaluation Bootstrap t-values
Bias-corrected percentile bootstrap confidence intervals
Software setting (SmartPLS3) No sign change option
Bias-corrected and accelerated (BCa) boostrap
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Blindfolding
• PLS-SEM is used for prediction purposes; hence, a measure of predictive capability is required.
• Stone-Geisser’s Q2-value: an indicator of the model’s out-of-sample predictive power or
predictive relevance. • Predictive relevance (Q2 value larger than zero) indicates that the PLS model accurately predicts data
not used in the model estimation.
• Q2 value is obtained from the blindfolding procedure.
• Blindfolding is a sample reuse technique that omits every dth data point in the endogenous
construct’s indicators and estimates the parameters with the remaining data point. • Omitted data points are treated as missing values – estimates
• The process repeats until each data point has been omitted and the model reestimated.
• Applicable endogenous construct with reflective measurement model or having single-item only.
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ObservationsIndicators of the
Reflective (Endogenous) Construct
X1 X2 X3
1 d1 d2 d3
2 d1 d2 d3
3 d1 d2 d3
4 d1 d2 d3
5 d1 d2 d3
6 d1 d2 d3
7 d1 d2 d3
Omission distance (D) allows for systematic pattern data
point to be eliminated and predicted.• Recommended omission distance value is between 5 and 10,
and should not result in an integer when the number of
observations is divided by the chosen omission distance. Why?
• Example: D = 3 means every third data point of the indicators
X1, X2, and X3 is eliminated in a single blindfolding.
• The number of blindfolding rounds always equals the chosen
omission distance.
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ObservationsIndicators of the
Reflective (Endogenous) Construct
X1 X2 X3
1 d1 d2 d3
2 d1 d2 d3
3 d1 d2 d3
4 d1 d2 d3
5 d1 d2 d3
6 d1 d2 d3
7 d1 d2 d3
ObservationsIndicators of the
Reflective (Endogenous) Construct
X1 X2 X3
1 d1 d2 d3
2 d1 d2 d3
3 d1 d2 d3
4 d1 d2 d3
5 d1 d2 d3
6 d1 d2 d3
7 d1 d2 d3
ObservationsIndicators of the
Reflective (Endogenous) Construct
X1 X2 X3
1 d1 d2 d3
2 d1 d2 d3
3 d1 d2 d3
4 d1 d2 d3
5 d1 d2 d3
6 d1 d2 d3
7 d1 d2 d3
Omission distance = 3
5
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• A set of data is subject to parameter estimation to generate an outcome.
• Is it possible to use the same set of data to generate a predicted value using the established
parameter estimation?
• Fitting ≠ prediction
• Prediction is using a new set of data on established parameter estimation.
• A whole set of data is divided into training data AND holdout data.
• Use the training data to generate parameter estimation [training phase].
• Use the holdout data to generate predictive outcomes using the parameter estimation [prediction phase].
• Compare predictive outcomes to actual outcomes – predictive validity [validation phase].
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TEST
Training
Training
Training
Training
TEST
Training
Training
Training
Training
TEST
Training
Training
Training
Training
TEST
Training
Training
Training
Training TEST
Training
Training
Training
TrainingC
OM
PL
ET
E
DA
TA
TEST
TEST
TEST
TEST
TEST
Fold 1 Fold 2 Fold 3 Fold 4 Fold 5
Example: k = 5
Pre
dic
tion
sta
tist
ics
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• PLS modelcomp_1
comp_2
comp_3
cusa
like_1
like_2
like_3
• Linear model
5
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RMSE = standard deviation of the prediction error
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Variable IndicatorPLS predict LM predict LM - PLS (LM – PLS)/ PLS (%)
RMSE MAE RMSE MAE RMSE MAE RMSE MAE
Customer satisfaction cusa 5.798 1.298 5.818 1.328 0.02 0.03 0.34 2.31
Customer loyalty cusl_1 9.837 2.404 9.957 2.465 0.12 0.06 1.22 2.50
cusl_2 9.893 2.473 9.972 2.617 0.079 0.14 0.79 5.66
cusl_3 11.371 2.954 11.489 2.991 0.118 0.04 1.04 1.35
• Manifest variables (items) are good not only in explaining the endogenous variables but also in predicting them.
• Negative differences or percentages indicate that there are problems with the items. Good at explaining but bad
at predicting. Why?
• Include qualitative questions to get further insights about the phenomenon under investigation.
• Note: PLS prediction works well when the model is less complex – do you agree?
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X1
X2 Y
M
Structural Model
Inner (predictor) collinearity: VIF < 5
Path coefficient
Significance of path coefficient: one-tailed (t >
1.65) or two-tailed (t > 1.96)
Coefficient of determination, R2 depends on
research field; but in general:
0.75 (substantial), 0.50 (moderate), 0.25 (weak)
Effect size, f 2 : 0.35 (large), 0.15 (moderate), 0.02
(small)
Predictive relevance, Q2 (Stone-Geisser): value
should be larger than 0
Predictive relevance, Q2 (PLS predict): value
should be larger than 0
Assess the MV prediction summary:
PLS < LM
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DEMONSTRATION
Corporate Reputation model:
structural model assessment
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6Mediation Analysis
• Assumes a sequence of relationships in which an antecedent variable affects a mediation variable,
which then affects a dependent variable – focus: underlying process (Nitzl, Roldán, & Cepeda Carrión, 2016).
M
YXYX
M
YXc
Direct effect Indirect effectFull mediation
Direct and indirect effects Partial mediation
c'
a b a b
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M
YX
MX
No direct effect: one mediator
Indirect effect: one mediator
c
a b
Y
M1
YX
M2
a b
c
a1b1
a2b2
MX Ya b
Z
d
Two mediator mediation
model
Simple moderated mediation
model
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Path Model Coefficients:
• Mediation: direct effect, indirect effect, and total effect.• Important in studies that aimed at exploring the differential impact of several driver constructs on a
criterion construct via one or more mediating variables.
• Example: • Direct effect (P13) = 0.20.
• Indirect effect (P12·P23) = 0.80 × 0.50 = 0.40.
• Total effect (P13 + P12·P23) = 0.20 + 0.40 = 0.60.
• Although the direct relationship is not very strong, the total effect
is quite pronounced. This indicates the relevance of Y1 in
explaining Y3.
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Is
ρ1*ρ2
sig.?
Is
ρ3
sig.?
Is
ρ3
sig.?
Is
ρ1*ρ2*ρ3
positive.
?
Complementary
(partial mediation)
Competitive
(partial mediation)
Direct only
(no mediation)
No effect
(no mediation)
Indirect only
(full mediation)
Yes
Yes
Yes
Yes
No
NoNo
No
Neither the direct
effect nor the
indirect effect are
significant.
The direct effect is
significant but not
the indirect effect.
The indirect effect
is significant but
not the direct
effect.
Adapted from:
Hair, Hult, Ringle & Sarstedt (2017) and
Nitzl, Roldán, & Cepeda Carrión, (2016).
Mediation analysis procedure
Both direct and
indirect effects are
significant but
point in opposite
directions.
Both direct and
indirect effects are
significant and
point in the same
direction.
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• Hair, Hult, Ringle & Sarstedt (2014):
• Variance accounted for (VAF) determines the size of the indirect effect in relation to total effect.
𝑉𝐴𝐹 =(𝜌12 · 𝜌23)
(𝜌12 · 𝜌23 + 𝜌13)
What about VAF?
• Helps to explain how much of the target construct’s variance is explained by the indirect relationship.
• Rule of thumbs:
1. VAF > 80% Full mediation
2. 20% ≤ VAF ≤ 80% Partial mediation
3. VAF < 20% No mediation
• VAF is calculated only when the absolute value of standardized total effect is at least 0.2.
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Direct
Effect
95% CIs of
the Direct
Effect
t
value
Significance
(p < 0.05)?
Indirect
Effect
95% CIs of
the Indirect
Effect
t
value
Significance
(p < 0.05)?
Mediation
type
COMP→ CUSL 0.006 [-0.101,
0.112]
0.105 No 0.074 [0.007, 0.143] 2.162 Yes ?
LIKE → CUSL 0.344 [0.235,
0.452]
6.207 Yes 0.220 [0.152, 0.293] 6.207 Yes ?
Sample reporting format for mediation analysis:
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• Moderating effects are evoked by variables whose variation affects the strength of a relation
between an independent and a dependent variable (Baron & Kenny, 1986 in Fassott, Henseler & Coelho, 2016).
Z
YX
• Two types:
1. Categorical moderator: group comparison
2. Continuous moderator: interaction terms
a. Product indicator approach
b. Two-stage approach
c. Orthogonalizing approach
ρ3
ρ1
ρ2
Continuous Moderation Analysis
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• Product indicator approach
Z
YX
ρ3
ρ1
ρ2
X·Z
z2
z1
x2
x1
y2
y1
x1·z2
x2·z1
x1·z1
x2·z2
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• Two-stage approach
Z
YX ρ1
ρ2
z2
z1
x2
x1
y2
y1
ρ3
X·Z
Z
YX ρ1
ρ2
LVS(Z)
LVS(X)
LVS(X)×LVS(Z)
LVS(Y)
STAGE 1 STAGE 2
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• Orthogonalizing approach
Z
YX ρ1
ρ2
z2
z1
x2
x1
y2
y1
ρ3
X·Ze12
e11
e22
e21
x1·z1 = b1,11·x1+ b2,11·x2+b3,11·z1+b4,11·z2+e11
x1·z2 = b1,12·x1+ b2,12·x2+b3,12·z1+b4,12·z2+e12
x2·z1 = b1,21·x1+ b2,21·x2+b3,21·z1+b4,21·z2+e21
x2·z2 = b1,22·x1+ b2,22·x2+b3,22·z1+b4,22·z2+e22
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Moderator and/or
exogenous constructs
are formative.
Inspect the mode of measurement
model of the moderator and
exogenous constructs.
Moderator and
exogenous constructs
are reflective.
Determine the goal of the
analysis.
Reveal the
significance of the
moderating effect.
Minimize estimation
bias of the
moderating effect.
Maximize prediction.
Two-stage approach Orthogonalizing
approach
Orthogonalizing
approach
Two-stage approach
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Effect Size, f 2 :
• Assessing an exogenous construct’s contribution to an endogenous LV’s R2.
𝑓2𝑥𝑧 → 𝑦 =𝑅 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑2 − 𝑅 𝑒𝑥𝑐𝑙𝑢𝑑𝑒𝑑
2
1 − 𝑅 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑2
R2 value of the endogenous LV when the interaction term is included in the model.
R2 value of the endogenous LV when the interaction term is excluded in the model.
𝑅 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑2
𝑅 𝑒𝑥𝑐𝑙𝑢𝑑𝑒𝑑2
• Guidelines: 0.005 (small), 0.01 (medium), 0.025 (large)
𝑓2𝑥𝑧 → 𝑦 Effect size interaction effect (XZ) on endogenous LV (Y).
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Dr. IDA ROSNITA ISMAIL
03-89214969
THANK YOU & ALL THE BEST!
