Introduction to Structural Equation Modeling Partial Least Sqaures (SEM-PLS)

aliasgari1358@gmail.com
January 2016

Ali Asgari aliasgari1358@gmail.com
Outline
• Introduction to SEM
• Requirement of SEM
• PLS versus CB-SEM
• Formative vs. reflective constructs
• Modelling Using PLS
• Evaluation Of Measurement Model
• Higher-order Models
• Mediator Analysis

Statistics Generation Technique
Generation
Techniques
Types
Primarily Exploratory Primarily
Confirmatory
Comparison
1 st
Generation
Techniques
(1980s)
-Multiple regression
-Logistic regression
analysis of variance
cluster analysis
-Exploratory factor
analysis
-Multidimensional
scaling
-Deal with observed
variables
-Regression based
approaches
2 st
Generation
Techniques
(1990s)
PLS-SEM CB-SEM
-Deal with observed variables
-Deal with unobserved variables
(LV)
-Run the model simultaneously

Statistical Methods
• With first-generation statistical methods, the
general assumption is that the data are error
free.
• With second-generation statistical methods,
the measurement model stage attempts to
identify the error component of the data.
• Facilitate accounting for measurement error
in observed variables (Chin, 1998).

Statistical Methods
• Second-generation tools, referred to as
Structural Equation Modeling (SEM).
–Confirmatory when testing the
hypotheses existing theories and
concepts
–Exploratory when they search for latent
patterns or new relationship (how the
variables are related).

 SEM is an advanced technique enables researchers to
assess a complex model that has many relationships,
performs confirmatory factor analysis, and incorporates
both unobserved and observed variables (Barbara 2001; Hair et
al. 2006)
 Furthermore, SEM is such a technique that allows
researcher to measure the contribution of each item in
explaining the variance, which is not possible in
regression analysis (Hair et al. 1998).
 Additionally, SEM can measure the relationship between
construct of interest at the second order level (Hair et al. 2006;
Henseler et al. 2009).
Structural equation modeling (SEM)

 SEM brings together the characteristics of both factor
analysis and multiple regressions which help the
researcher to simultaneously examine both direct and
indirect effects of independent and dependent variables
(Bagozzi & Fornell 1982; Geffen et al. 2000; Hair et al. 2006).
 Whereas, first generation statistical tools which include
techniques such as ANOVA, linear regression, factor
analysis, MANOVA, etc. can examine only one single
relationship at a single point of time (Anderson & Gerbing 1988;
Chin 1998; Gefen et al. 2000; Hair et al. 2006).
Structural equation modeling (SEM)

Structural Equation Modeling (SEM)
• Structural Equation Modeling (SEM) enable
researchers to incorporate unobservable variables
measured indirectly by indicator variables. They
also facilitate accounting for measurement error in
observed variables (Chin, 1998).
• There are two approaches to estimate the
relationships in a structural equation model
(SEM):
• Covariance-based SEM (CB-SEM)
• PLS-SEM (PLS path modeling) / VB-SEM

Measurement error
• Measurement error is the difference between true value of
variable and value obtained by using scale
• Type of measurement error
• random error can affect the reliability of construct
• Systematic error can affect the validity of construct (Hair
et al. 2014)
• Source of error
• 1. poorly world questions in survey
• 2. incorrect application of statistical methods
• 3. Misunderstanding of scaling approach

Ali Asgari aliasgari1358@gmail.comCB-SEM Provider VB-SEM
PLS-SEM
Components-based SEM
Provider
AMOS
Analysis of Moment
Structures
IBM
Developer:
James Arbuckle & Werner
Wothke
SmartPLS Ringle et al., 2005
LISREL
LInear Structural
RELationship
Joreskog 1975
Jöreskog and Sörbom (1989)
PLS-Graph Chin 2005; Chin 2003
MPLUS PLS-GUI Li, 2005
EQS SPADPLS TesteGo, 2006
SAS LVPLS Lohmöller-
R WarpPLS Ned Kock 2012
SEPATH PLS-PM
CALIS semPLS
LISCOMP Visual PLS Fu, 2006
Lavaan PLSPath Sellin, 1989
COSAN XLSTAT Addinsoft, 2008

PLS-SEM
Partial Least Squares (PLS) is an OLS regression-
based estimation technique that determines its
statistical properties.
 The method focuses on the prediction of a
specific set of hypothesized relationships that
maximizes the explained variance in the
dependent variables, similar to OLS regression
models (Hair, Ringle, & Sarstedt, 2011).

PLS-SEM
A PLS path model consists of two elements:
–Structural model or inner model
–Measurement model or outer model
The structural model also displays the
relationships (paths) between the
constructs.
–The measurement models display the
relationships between the constructs and
the indicator variables (rectangles).

Introduction to Structural Equation Modeling Partial Least Sqaures (SEM-PLS)

PLS-SEM
Measurement theory specifies how the latent
variables (constructs) are measured.
There are two different ways to measure
unobservable variables.
–Reflective measurement
–Formative measurement

Justification
• According to Hair et al. (2013),
Henseler et al. (2009) and Urbach &
Ahleman (2010) PLS is gaining more
popularity. PLS: In situations where
theory is less developed.

Justification
 If the primary objective of applying structural modeling
is prediction and explanation of target constructs.
 PLS-SEM estimates coefficients (i.e., path model
relationships) that maximize the 𝑹 𝟐
values of the (target)
endogenous constructs.
 small sample sizes
 Complex models
 No assumptions about the underlying data
(Normality assumptions)
 Support reflective and formative measurement
models as well as single item construct.

First-Order Construct
Researchers must consider two types of measurement
specification when he is developing constructs.
Independent/ Predictor Construct
Exogenous latent Construct
Dependent/Outcome Construct
Endogenous latent Construct
FormativeReflectiveMode
A
Mode
B
Items
Indicators
Measures
Variables
Observed Variables
Manifestation Variables

Reflective vs. Formative
• Furthermore, formative indicators are assumed
to be error free (Diamantopoulos, 2006; Edwards & Bagozzi,
2000).
• Reflective measures have an error term
associated with each indicator, which is not the
case with formative measures.

Reflective Construct
• Indicators must be highly correlated
Hulland (1999).
• Direction of causality is from construct
to measure.
• Dropping an indicator from the
measurement model does not alter the
meaning of the construct.
• Takes measurement error into account
at the item level.
• Similar to factor analysis.
• Typical for management and social
science researches.
ξ
𝑥1 𝑥2 𝑥3 𝑥4
𝜀1 𝜀2 𝜀3 𝜀4

Reflective Model
• Reflective measurement model:
– Discussed as Mode A
– According to this theory, measures represent the
effects (or manifestations) of an underlying construct
– Interchangeable; any single item can generally be
removed without changing the meaning of the
construct, as long as the construct has sufficient
reliability.
– Indicators associated with a particular construct should
be highly correlated with each other.
– Causality is from the construct to its measures
(relationship goes from the construct to its measures).

Reflective Model
• The relationships between the reflective construct
and measured indicator variables are called
outer loadings / loadings (l).
– The outer loading (l) coefficients are estimated
through single regressions (one for each indicator
variable) of each indicator variable on its corresponding
construct.

Formative Construct
• Direction of causality is from measure to
construct.
• Indicators are not expected to be correlated.
• Dropping an indicator from the measurement
model may alter alter the meaning of the
construct.
ξ
𝑥1 𝑥2 𝑥3 𝑥4
δ
• No such thing as internal consistency
reliability.
• Based on multiple regression (Hair et al., 2010).
• Need to take care of multicollinearity.
• Typical for success factor research
(Diamantopolous & Winklhofer, 2001).

Formative Model
• The relationships between formative constructs
and indicator variables are considered outer
weights / weights (w).
– The outer weight coefficients (w) are estimated by a
partial multiple regression where the latent construct
represents a dependent variable and its associated
indicator variables are the independent variables.

Formative Model
• Formative measurement models
– Discussed as Mode B
– The indicators cause the construct (Bollen & Lennox, 1991).
– Not interchangeable; each indicator captures a specific
aspect of the construct’s domain.
– Removing an indicator theoretically alters the nature of
the construct (Diamantopoulos & Winklhofer, 2001; Jarvis et al., 2003).
– No intercorrelations between formative indicators
(Diamantopoulos, Riefler, & Roth, 2008), collinearity among formative
indicators can present significant problems .
– No error terms; formative indicators have no individual
measurement error terms (Diamantopoulos, 2011).

Reflective Vs. Formative
• Reflective measurement approach aims at maximizing
the overlap between interchangeable indicators.
• Formative measurement approach tries to fully cover
the construct domain by the different formative
indicators, which should have small overlap.
• The estimated values of
outer weights in
formative measurement
models are frequently
smaller than the of
reflective indicators.

Reflective vs. Formative
Satisfaction Satisfaction
I am looking
forward staying in
this hotel
I recommend this
hotel to others
Formative Measurement ModelReflective Measurement Model
I appreciate this
hotel
The rooms are
clean
The personnel
is friendly
This Service is
good
The decision of whether to measure a construct
reflectively or formatively is not clear-cut (Hair et al., 2014).

Case Study
• Clarify Endogenous, Exogenous, Reflective and
Formative Constructs.
IT
Performance
IT_1
Quality
Delivery
Flexibility
IS
IT_3
IT_4
IT_5
IT_2
IS_1
IS_1
IS_1
Cost

Reflective MEASUREMENT MODEL
• The goal of reflective measurement model
assessment is to ensure the reliability and
validity of the construct measures and
therefore provide support for the suitability
of their inclusion in the path model.

Reliability & Validity
• Reliability is the extent to which an assessment tool
produces stable and consistent results.
• While reliability is necessary, it alone is not sufficient.
For a test to be reliable, it also needs to be valid.
• Validity refers to the
extent to which the
construct measures what it
is supposed to measure.

Reflective MEASUREMENT MODEL
Reflective Measurement Model
 Internal Consistency Reliability
 Composite Reliability (CR> 0.708 - in exploratory research
0.60 to 0.70 is acceptable).
 Cronbach’s alpha (α> 0.7 or 0.6)
 Indicator reliability (> 0.708)
 Squared Loading
 Convergent validity
 Average Variance Extracted (AVE>0.5)
 Discriminant validity
 Fornell-Larcker criterion
 Cross Loadings
Reliability&Validity

Internal Consistency Reliability
• N = number of indicators assigned to the factor
• 2
i = variance of indicator i
• 2
t = variance of the sum of all assigned indicators’
scores
• j = flow index across all reflective measurement
model

Internal Consistency Reliability
• i = loadings of indicator i of a latent variable
• i = measurement error of indicator i
• j = flow index across all reflective measurement
model

Indicator Reliability
• The indicator reliability denotes the
proportion of indicator variance that is
explained by the latent variable
• However, reflective indicators should be
eliminated from measurement models if their
loadings within the PLS model are smaller
than 0.4 (Hulland 1999, p. 198).

Convergent validity
• An established rule of thumb is that a latent
variable should explain a substantial part of
each indicator's variance, usually at least
50%.
• This means that an indicator's outer loading
should be above 0.708 since that number
squared (0.7082) equals 0.50.

Convergent validity
• Convergent validity is the extent to which a
measure correlates positively with other
measures (indicators) of the same construct.
• To establish convergent validity, researchers
consider the outer loadings of the
indicators, as well as the average variance
extracted (AVE).

Average Variance Extracted (AVE)
• 2
i = squared loadings of indicator i of a latent
variable
• var(i ) = squared measurement error of indicator i

Discriminant validity
• Discriminant validity is the extent to
which a construct is truly distinct from other
constructs by empirical standards.
 Cross-Loadings
 Fornell-Larcker criterion

Discriminant validity
Discriminant validity:
–Cross-Loadings: An indicator's outer
loadings on a construct should be higher
than all its cross loadings with other
constructs.
–Fornell-Larcker criterion: The square root
of the AVE of each construct should be
higher than its highest correlation with any
other construct (Fornell and Larcker, 1981).

Discriminant Validity
• The AVE values are obtained by squaring each outer loading,
obtaining the sum of the three squared outer loadings, and then
calculating the average value.
• For example, with respect to construct 𝒀 𝟏, 0.60, 0.70, and 0.90
squared are 0.36, 0.49, and 0.81. The sum of these three numbers is
1.66 and the average value is therefore 0.55 (i.e., 1.66/3).
𝒀 𝟏
𝐶𝑜𝑟𝑟.2=0.64
𝒀 𝟐
𝐶𝑜𝑟𝑟.2=0.64
𝑪𝒐𝒓𝒓.=0.80
𝑋1
𝑋2
𝑋3
𝑋6
𝑋5
𝑋4
AVE=0.55 AVE=0.65
0.60
0.70
0.90
0.70
0.80
0.90

Discriminant Validity
• The correlation between constructs 𝒀 𝟏, and 𝒀 𝟐 is
0.80.
• Squaring the correlation of 0.80 indicates that 64%
(i.e., 0.802² = 0.64) of each construct's variation is
explained by the other construct.
• 𝒀 𝟏 explains less variance in its indicator measures
𝒙 𝟏 to 𝒙 𝟑 than it shares with 𝒀 𝟐.
• This implies that the two constructs (𝒀 𝟏, and 𝒀 𝟐),
which are conceptually different, are not sufficiently
different in terms of their empirical standards.
– Thus, in this example, discriminant validity is not
established.

Formative MEASUREMENT MODEL
• Any attempt to purify formative indicators
based on correlation patterns can have
negative consequences for a construct's
content validity.
• Assessing convergent and discriminant
validity using criteria similar to those
associated with reflective measurement
models is not meaningful when formative
indicators and their weights are involved
(Chin, 1998).

• This notion especially holds for PLS-SEM, which
assumes that the formative indicators fully
capture the content domain of the construct
under consideration.
• The statistical evaluation criteria for reflective
measurement scales cannot be directly
transferred to formative measurement models
where indicators are likely to represent the
construct's independent causes and thus do not
necessarily correlate highly.

• Instead, researchers should focus on establishing
content validity before empirically evaluating
formatively measured constructs.
• This requires ensuring that the formative
indicators capture all (or at least major) facets of
the construct.

Formative Measurement Model
Assess Convergent Validity (Redundancy
Analysis)
Assess Collinearity Among Indicators
Assess the Significance and relevance of
outer weights
Validity

Assess1: Convergent Validity
• The first step on assessing the empirical PLS-
SEM results of formative measurement
models involves;
 assessing the formative measurement model's
convergent validity by correlating the
formatively measured construct with a
reflective measure of the same construct.

Assess1: Convergent Validity
• When evaluating formative measurement models, we have
to test whether the formatively measured construct is
highly correlated with a reflective measure of the same
construct.
• This type of analysis is also known as redundancy
analysis (Chin, 1998).
• Note that to execute this approach, the reflective
latent variable must be specified in the research
design phase and included in data collection for
the research.

Assess 1: Convergent Validity
Redundancy Analysis for convergent validity Assessment
𝐘𝐥
𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐯𝐞
𝐘𝐥
𝐫𝐞𝐟𝐥𝐞𝐜𝐭𝐢𝐯𝐞
X1
X2
X3
X4
Global_item
 Ideally, a magnitude of 0.90 or at least 0.80 and above is
desired (Chin, 1998) for the path between 𝒀𝒍
𝒇𝒐𝒓𝒎𝒂𝒕𝒊𝒗𝒆
and
𝒀𝒍
𝒓𝒆𝒇𝒍𝒆𝒄𝒕𝒊𝒗𝒆
, which translates into an R² value of 0.81 or at
least 0.64.
 The correlation between the constructs should be 0.80 or
higher.

Assess 2: Collinearity Issues
• High correlations of items are not accepted in
formative models.
• In fact, high correlations between two
formative indicators, also referred to as
collinearity, can prove problematic from a
methodological and interpretational
standpoint.
• When more than two indicators are involved,
this situation is called multi-collinearity.
• Collinearity boosts the standard errors.

Assess 2: Collinearity Issues
• A related measure of collinearity is the variance
inflation factor (VIF), defined as the reciprocal of
the tolerance (i.e., VI𝐹𝒙 𝟏
=1 TO𝐿 𝒙 𝟏
).
• In the context of PLS-SEM, a tolerance value of
0.20 or lower and a VIF value of 5 and higher
respectively indicate a potential collinearity
problem (Hair, Ringle, & Sarstedt, 2011).

Assess 3: Significance and Relevance
• Does formative indicators truly
contribute to forming the construct?
• To answer this question, we must test if the outer
weights in formative measurement models are
significantly different from zero via the
bootstrapping procedure.
• With this information, t values are calculated to
assess each indicator weight's significance.

• With larger numbers of formative indicators
used to measure a construct, it becomes more
likely that one or more indicators will have low or
even nonsignificant outer weights.
• Analyze the Outer Weights for their significant
and relevance.

Interpretation of Indicator's Relative
Contribution to the Construct:
When an indicator's weight is significant, there is
empirical support to retain the indicator.
When an indicator's weight is not significant but the
corresponding item loading is relatively high (> 0.50),
the indicator should generally be retained.
If both the outer weight and outer loading are
nonsignificant, there is no empirical support to
retain the indicator and it should be removed from the
model.

Interpret Outer Weight:
1. Significantly Important (Significantly Contribution)
 Outer weight is significant
2. Absolutely Important (Absolutely Contribution)
 Outer weight is Nonsignificant
 Outer Loading is Significant (t value) or above 0.5
3. Relatively important (Absolutely Contribution)
 Outer weight is Nonsignificant
 Outer loading is below 0.50 or nonsignificant

3. Relatively important (Relatively Contribution)
 The researcher should decide whether to retain or
delete the indicator.
 The researcher decide by examining its
theoretical relevance and potential content.
 If the theory-driven conceptualization of the
construct strongly supports; retain indicator.
 If the conceptualization does not strongly
support an indicator's inclusion; remove
indicator.

PLS-SEM
• The relationships between the latent variables in
the structural model are called path coefficients in
the structural model that are labeled as p are also
initially unknown and estimated as part of solving
the PLS-SEM algorithm.
• After the algorithm calculated the construct
scores, the scores are used to estimate each partial
regression model in the path model.

Path Models
• Path models are made up of two elements:
–The Structural Model (Inner Model), which
describes the relationships between the latent
variables.
–The Measurement Models (Outer Model),
which describe the relationships between the
latent variables and their measures (their
indicators).

Path Models

PLS-SEM Evaluation
• Rules of thumb for evaluating PLS-SEM
results:
If the measurement characteristics of
constructs are acceptable, continue with the
assessment of the structural model results.
Path estimates should be statistically
significant and meaningful.

PLS-SEM Evaluation
 Moreover, endogenous constructs in the
structural model should have high levels of
explained variance—R² (coefficients of
determination).
• The goal of the PLS-SEM algorithm is to
maximize the R² values of the endogenous
latent variables and thereby their prediction.
• The R² values are normed between 0 and +1
and represent the amount of explained
variance in the construct.*

• PLS-SEM allows the user to apply three structural
model weighting schemes:
(1) the centroid weighting scheme,
(2) the factor weighting scheme,
(3) the path weighting scheme.
PLS Algorithm

PLS-SEM Evaluation
• The path weighting is the recommended
because it provides the highest 𝑹 𝟐
value for
endogenous latent variables and is
generally applicable for all kinds of PLS path
model specifications and estimations
(Hair et al., 2014).

PLS Algorithm
• The PLS-SEM algorithm draws on
standardized latent variable scores.
• Thus, PLS-SEM applications must use
standardized data for the indicators (more
specifically, z-standardization, where each
indicator has a mean of 0 and the variance is
1) as input for running the algorithm.
• When running the PLS-SEM method, the
software package standardizes both the raw
data of the indicators and the latent variable
scores.

PLS Algorithm
• As a result, the algorithm calculates
standardized coefficients between -1 and +1
for every relationship in the structural model
and the measurement models.
• For example, path coefficients close to +1
indicate a strong positive relationship (and
vice versa for negative values).
• The closer the estimated coefficients are to 0,
the weaker the relationships. Very low values
close to 0 generally are not statistically
significant.

Assess structural model for collinearity issues
Assess the level of R²
Assess the significance and relevance of the
structural model relationship
Step 1
Step 2
Step 3
Assess the predictive relevance the level of Q² and the level of
q² effect size
Assess the level of f²Step 4
Step 5
Structural Model Assessment Procedure

STEP 1: Collinearity issues
Before we describe these analyses, however,
we need to examine the structural model
for collinearity (Step 1).
The reason is that the estimation of path
coefficients in the structural models is based
on OLS regressions of each endogenous
latent variable on its corresponding
predecessor constructs.

STEP 1: Collinearity Issues
• In the context of PLS-SEM, a tolerance
value of 0.2 or lower and VIF value of 5
and higher respectively indicate a potential
collinearity problem (Hair, Ringle & Sarstedt,
2011).

STEP 2: Path Coefficients
• Running the PLS-SEM algorithm to
estimate the structural model relationships
(the path coefficients), which represent the
hypothesized relationships among the
constructs.
• The path coefficients have standardized
values (Coefficients) between -1 and +1 for
every relationship in the structural model
and the measurement models.

STEP 2: Path Coefficients
• Path coefficients close to +1 indicate a strong
positive relationship (and vice versa for negative
values).
• The closer the estimated coefficients are to 0, the
weaker the relationships. Very low values close
to 0 generally are not statistically significant.
• When interpreting the results of a path model, we
need to test the significance of all structural
model relationships.

STEP 2: Significance And Relevance
• Reporting results: examine the empirical t value,
the p values, or the bootstrapping confidence
interval.
• The goal of PLS-SEM is to identify not only
significant path coefficients in the structural
model but significant and relevant effects.
• After examining the significance of relationships,
it is important to assess the relevance of
significant relationships.

STEP 2:Total Effect
• The sum of direct and indirect effects is referred
to as the total effect.
 The direct effect indicating the relevance of 𝒀 𝟏 in
explaining 𝒀 𝟑.
𝒀 𝟐
𝒀 𝟏 𝒀 𝟑
p 𝟏𝟐
p 𝟐𝟑
p 𝟏𝟑
 Total effect= direct + indirect
= p 𝟏𝟑
+ p 𝟏𝟐
• p 𝟐𝟑

STEP 3: Coefficient of Determination (R²)
• The most commonly used measure to evaluate the
structural model is the coefficient of
determination (R² value).
• The coefficient represents the exogenous latent
variables' combined effects on the endogenous
latent variable.
• It also represents the amount of variance in the
endogenous constructs explained by all of the
exogenous constructs linked to it.

STEP 3: Coefficient of Determination (R²)
• The R² value ranges from 0 to 1.
• In scholarly research as a rough rule of thumb
– 0.75 is substantial
– 0.50 is moderate
– 0.25 is weak
(Hair, Ringle, & Sarstedt, 2011; Chin, 20110; Henseler et al., 2009).

STEP 4: Effect Size ƒ²
• The change in the R² value when a specified
exogenous construct is omitted from the
model can be used to evaluate whether the
omitted construct has a substantive impact
on the endogenous constructs. This measure
is referred to as the ƒ² effect size.

STEP 4: Effect Size ƒ²
• The effect size can be calculated as
ƒ² =
𝑹²
𝒊𝒏𝒄𝒍𝒖𝒅𝒆𝒅 −𝑹²
𝒆𝒙𝒄𝒍𝒖𝒅𝒆𝒅
𝟏−𝑹²
𝒊𝒏𝒄𝒍𝒖𝒅𝒆𝒅
• Guidelines for assessing ƒ² :
– 0.02 → small
– 0.15 → medium
– 0.35 → large effects (Cohen, 1988)

STEP 5: Blindfolding and Predictive
Relevance Q²
• In addition to the evaluation of R² values,
researchers frequently revert to the cross-
validated redundancy measure Q² (Stone–
Geisser test), which has been developed to
assess the predictive validity of the exogenous
latent variables and can be computed using the
blindfolding procedure.
• This measure is an indicator of the model's
predictive relevance.

Relevance Q²
• Stone-Geisser's Q² value (Geisser, 1974; Stone,
1974).
• Q² values larger than zero for a certain reflective
endogenous latent variable indicate the path
model's predictive relevance for this particular
construct.
• This procedure does not apply for formative
endogenous constructs.
• The number between 5 and 10 should be used in
most applications (Hair et al., 2012).

Relevance Q²
• The Q² of blindfolding procedure represent a
measure of how well the path model can predict
the originally observed values.
• The relative impact of predictive relevance can
be compared by means of the measure to the q²
effect size, formally defined as follows:
q² =
𝑸²
𝒊𝒏𝒄𝒍𝒖𝒅𝒆𝒅 − 𝑸²
𝒆𝒙𝒄𝒍𝒖𝒅𝒆𝒅
𝟏−𝑸²
𝒊𝒏𝒄𝒍𝒖𝒅𝒆𝒅

Higher-Order Models
• Higher-order models or hierarchical component
models (HCM) most often involve testing second-
order structures that contain two layers of
components (e.g., Ringle et al., 2012; Wetzels,
Odekerken-Schroder & van Oppen, 2009).
• Instead of modeling the attributes of satisfaction as
drivers of higher-order modeling involves
summarizing the lower-order components
(LOCs) into a single multidimensional higher-
order construct (HOC).

Higher-Order Models
Personnel
Service-
scape
Satisfaction
Price
Service
Quality
First (Lower)
Order Components
Second (Higher)
Order Components

Higher-Order Models
• According Law et al (1998) we refer to construct as
Multidimensional when it consist of number of
interrelated dimensions.
• For example Customer Satisfaction consist of Price,
Service Quality, Personnel, and Service-scape.
• Researchers (see Edwards 2001; MacKenzie,
Podaskoff, and Jarvis 2005) suggested that using
higher-order construct allows to reduce complexity.
• According to Jenkins and Griffith (2004) the border
the construct is better to predict of criterion.

Higher-Order Models
• An important condition for a multidimensional construct
to identify it is relationship with its underlying dimensions
based on theoretical evidence and empirical considerations
(Law et al 1998).
• More clearly, it is crucial to understand whether the
higher order construct affect lower level dimensions in
which the indicators are manifestation of the construct
(reflective construct), or the indicators are affecting the
higher order construct in which the indicators are defining
characteristic of the construct (formative construct)
(Jarvis et al. 2003).
• There are 4 possible types of second-order constructs.

Reflective-Reflective type I
Reflective-Formative type II
Lower Construct/
First-order
Construct
Higher Construct/
Second-order Construct
Higher level of abstraction

Formative-Reflective type III
Formative-Formative type IV
Higher level of abstraction

Mediation Purpose
• We can determine the extent to which the
variance of the dependent variable is
directly explained by the independent
variable and how much of the target
construct's variance is explained by the
indirect relationship via the mediator
variable.

Mediator
• A mediating effect is created when a third variable
or construct intervenes between two other related
constructs.
• The role of the mediator variable then is to clarify
or explain the relationship between the two
original constructs.
• Indirect effects are those relationships that involve
a sequence of relationships with at least one
intervening construct involved.

Mediator
• Baron & Kenny (1986) has formulated the steps
and conditions to ascertain whether full or partial
mediating effects are present in a model.
Reputation
Satisfaction
Loyalty
X
M
YP12 P23
P13

Mediator: Baron & Kenny, 1986
• Technically, a variable functions as a mediator
when it meets the following conditions (Baron &
Kenny, 1986):
– Variations in the levels of the independent variable
account significantly for the variations in the presumed
mediator (i.e., path p 𝟏𝟐).
– Variations in the mediator account significantly for the
variations in the dependent variable (i.e., path p 𝟐𝟑).
– When paths p 𝟏𝟐 and p 𝟐𝟑 are controlled, a previously
significant relation between the independent and
dependent variables (i.e., path p 𝟏𝟑) changes its value
significantly.

Mediation
• When testing mediating effects, researchers
should rather follow Preacher and Hayes
(2004,2008) and bootstrap the sampling
distribution of the indirect effect, which works
for simple and multiple mediator models.

Email: aliasgari1358@gmail.com
Please feel free to contact me if you
have any questions or comments.

Introduction to Structural Equation Modeling Partial Least Sqaures (SEM-PLS)

More Related Content

What's hot (20)

Viewers also liked (13)

Similar to Introduction to Structural Equation Modeling Partial Least Sqaures (SEM-PLS) (20)

Recently uploaded (20)

Introduction to Structural Equation Modeling Partial Least Sqaures (SEM-PLS)