2015 Vadim Genin NIT MBA Thesis SEM Defining the state of the art 14122015

Structural Equations Modeling (SEM)
Defining the State of the Art
by
Dipl. Eng. VADIM GENIN
Supervisor: M.Sc. Kai G. Mertens
Hamburg, 15th of December 2015
MBA THESIS DEFENSE
Northern Institute of Technology Management

 Background and Motivation
 Goals of the Thesis
 Introduction into SEM
 Description of the state of art SEM methods
 Classification of the state of art SEM methods
 Comparison and selection of SEM technique
 Conclusion, contribution, limitations & further research
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Outline
Comparison and
selection of SEM
Conclusions &
Future Research
Structural Equation Modeling. Defining the state of the art. 215.12.2015

Many software and authors treat SEM as a “black-box”
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 Before 20th century only qualitative research methods in social sciences, biology and
genetics
 In the 20th century new quantitative methods (e.g. Structural Equations Modeling -
SEM) plus use of mainframes and PC
-> it makes complicated for new business users like me, especially with limited
knowledge in statistics, to get general understanding and to start properly apply
SEM in their research work and evaluate results
What is it
SEM?
How? Can I use it for
my research?
Which SEM
method
should I use?

Outline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Goals
 Provide introduction into SEM
 Describe the state of the art SEM methods
 Classify the state of the art SEM methods
 Elaborate on possible comparison criteria
 Establish simplified SEM selection guideline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Outline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

SEM is more, than just a one method
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 “Structural equation modeling is a growing family of statistical methods for
modeling relations between variables” (Hoyle, 2012)
 SEM “is a multivariate technique combining aspects of multiple regression and
factor analysis to estimate a series of interrelated dependence relationship
simultaneously” (Gefen et al., 2000, p.72)
 In general SEM relates to the combination of so called measurement model and
structural model (Henseler et al., 2009)
 Measurement model shows relationship between observed indicators and
latent variables
 Structural model shows relationship between latent variables
 Observed indicators measure latent (or unobserved) variables (LV)
 Latent variables (or factors) represent abstract phenomena or perception, for
example, social or emotional experiences, behavior patterns that are not
possible to measure or observe directly (Henseler et al., 2009)

3 main alternative depictions of an SEM model
Path diagram
Source: Hoyle (2012)
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Measurement
models
Structural
model
Source:
adopted from Hoyle (2012)
Equations notation
Matrix notation

SEM implementation framework
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Steps in SEM implementation

Outline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

State of the art SEM methods
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Name of SEM method Main contributors
Covariance-based SEM – CBSEM Wright; Jöreskog;
Partial Least Squares Path Analysis - PLS-PA Wright; Wold, H.; Lohmöller; Henseler;
Ringle;
Consistent Partial Least Squares Path Modeling Dijkstra; Henseler;
Generalized structured component analysis - GeSCA Hwang; Takane;
Systems of Regression Equations Cowles; Koopmans; Zellner;

Purpose and/or motivation of use: Type of measurement model:
Hypothesized model validation vis-à-vis observed data
(Tenenhaus, 2008); “theory oriented, and emphasizes the
transition from exploratory to confirmatory analysis”
(Henseler et al., 2009)
Both formative (but identification problems often may
occur) and reflective (Jarvis et al., 2003; Henseler et al.,
2009)
Latent variables: Path coefficients:
“True latent variables (i.e. hypothetically existing entities or
constructs” (Marcoulides et al., 2009). Common factors
(therefore random) (Hwang et al., 2010)
Covariance and variances (Henseler et al., 2009; Bowen &
Guo, 2011)
Type of estimators: Popular estimation methods:
Full information methods (Tenenhaus, 2008; Westland,
2015) – “Full information methods estimate the full
network model equations jointly using the restrictions on
the parameters of all the equations as well as the variances
and covariances of the residuals” (Westland, 2015, p.20)
Maximum Likelihood (ML), generalized least squares (GLS),
Unweighted least squares (ULS), Weighted least squares
(WLS), Asymptotically distribution-free (ADF) (Dijkstra &
Henseler, 2015; Bowen & Guo, 2011; Westland, 2015)
Model fit statistical measures: Sampling characteristics:
Overall and local model fit (Hwang et al., 2010; Gefen et al.,
2000); Many statistical measures, for examples see
(Westland, 2015)
Usually needs a large sample (Tenenhaus, 2008); non-
convergence issues in relatively small samples (less than
200) (Boomsma & Hoogland, 2001)
Main disadvantage:
Usually requires larger sample size and normally distributed data (Gefen et al., 2000). But nowadays problems with non-
normal distribution can be mitigated by special estimation options (Muthen & Muthen, 2010; Gefen et al., 2011)
Covariance-based SEM - CBSEM
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Exploration and prediction (oriented research) - creation of
causal models and theory building (Gefen et al., 2000,
Gefen et al., 2011, Ringle et al., 2012; ); Score computation
(Tenenhaus, 2008); Rare - confirmatory research (Gefen et
al., 2000);
Both formative and reflective (Henseler et al., 2009; Ringle
et al., 2012)
Components or weighted sums of observed variables
(Hwang et al., 2010); possible both linear (usually) and not
linear (seldom) combination of observed indicators (Bollen,
1989) – composite variables (Henseler et al., 2009)
Loadings, inner regression weights (Hwang et al., 2010,
Henseler et al., 2009); Pearson correlations (Wright, 1921);
Regression coefficients (Wold, 1975)
It is a „limited information method“ (Westland, 2015;
Tenenhaus, 2008). “Limited information methods estimate
individual node pairs or paths in a network separately using
only the information about the restrictions on the
coefficients of the particular equation. The other equations’
coefficients may be used to check for identifiability, but are
not used for estimation purposes” (Westland, 2015, p.19)
Combination of methods OLS for path estimates and PLS
for weights (Goodhue et al., 2012a). OLS (Westland, 2015;
Hwang et al., 2010) with goal “to maximize the explanation
of variance in a structural model’s dependent constructs”
(Henseler et al., 2009) and PLS – for estimation of weights
(in a measurement model).
Partial Least Squares Path Analysis - PLS-PA (1 of 2)
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Model fit statistical measures: Two sets of equations:
Local (Hwang et al., 2010) First, for structural model – scores are computed via OLS
regressions (Tenenhaus, 2008); second, for measurement
model (Lohmöller, 1989) - “computed using the PLS
algorithm” (Tenenhaus, 2008)
Sampling characteristics: Sample distribution characteristics:
Possible to use relatively small sample size for
complex models (Reinartz et al., 2009; Hair et al.,
2011; Ringle et al., 2012), but this point isn’t
without critic and frequently debated, (e.g.,
Goodhue et al., 2006; Marcoulides et al., 2009;
Gefen et al., 2011)
Possible to work with both standard and non-standard
distribution (Reinartz et al., 2009); For rules of thumb see
(Barclay et al., 1995)
Convergence: Main disadvantage:
Calculations usually converge, because algorithm is
relatively simple (Tenenhaus, 2008)
Absence of global optimization function and measures of
GOF (Henseler et al., 2009)
Partial Least Squares Path Analysis - PLS-PA (2 of 2)
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Consistent Partial Least Squares Path Modeling – PLSc
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 PLSc is a Refined PLS-PA algorithm, which overcomes the problem in of adverse
consequences for hypothesis testing, because of inconsistency of PLS path
coefficient estimates in case of reflective measurement.
 PLSc provides a correction for estimates when PLS is applied to reflective constructs
 In Classification of PLSc is defined as PLS sub-method, and inherits all main
distinctive features of its ancestor

Mainly explanation and conformation of hypothesis
(Tenenhaus, 2008);
Formative and reflective (Hwang & Takane, 2004)
“Components or weights assigned to” manifest indicators
(Hwang et al., 2010)
Component weights (Hwang & Takane, 2004)
Full information method (Tenenhaus, 2008; Hwang &
Takane, 2004; Hwang et al., 2010)
Alternating least squares (ALS) algorithm (Hwang &
Takane, 2004); for ALS see (Leeuw et al., 1976)
Model fit statistical measures:
Global (e.g., FIT and AFIT indices) and local because GeSCA “can handle the relationships among components and
observed variables in a unified algebraic framework” which distinct it from PLS-PA methods (Hwang & Takane, 2004;
Hwang et al., 2010)
Generalized structured component analysis - GeSCA
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Data description, parameter estimation, prediction and
estimation, and control of models (Montgomery et al.,
2012)
Reflective (Westland, 2015)
Response variables - linear functions of indicators
(predictor variables) (Westland, 2015)
Regression coefficients (often used symbol– b) (Tukey,
1954)
Both full (e.g., 3SLS) and limited (e.g., 2SLS) information
methods are possible
Two-stage least squares (2SLS) described by (e.g.,Theil,
1953); Three-stage least squares (3SLS) described by
(Zellner, 1962; Zellner & Theil, 1962); Limited information
maximum likelihood developed by (Anderson, 1983)
Model fit statistical measures: Special features:
Performance fit statistics and well defined hypothesis tests
(Westland, 2015)
Multi-equation regression model with not diagonal
covariance matrix (Westland, 2015)
Systems of Regression Equations
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Outline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Classification of the SEM state of the art methods - CSEMSAM
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Name of SEM
method:
CBSEM GSCA PLS-PA Systems of Regression Equations
Type: Covariance based SEM Component based SEM Systems of regression approaches
Latent Variables: Common factors (therefore
random)
Components or weighted sums of observed
variables
Variables - linear functions of
indicators
Purpose and/or
motivation of use:
Hypothesis model
validation and
conformation of theory
Exploration and prediction - creation of new
hypothesis.
And Confirmatory research (Rare use)
Data description, parameter
estimation, prediction and
estimation, and control of models
Sub-Methods: Software based e.g.:
LISREL, AMOS, TETRAD,
Mplus, etc.
N/A PLSC Software based e.g.:
SAS, STATA, system fit (R), SPSS,
MATLAB, etc.
Measurement
model:
Reflective
and Formative (rare use)
Formative and reflective
indicators
Formative and reflective Reflective
Path coefficients: Covariance's and variances Parameters or correlations, Regression coefficients Regression coefficients
Type of Estimators: Full Information Methods Full Information
Methods
Limited Information
Methods
Limited
Information
Methods
Full Information
Methods
Popular estimation
methods:
ML (most popular), ULS,
GLS, WLS, ADF
Alternating least
squares (ALS)
Fixed point OLS
regressions and PLS
algorithm
2SLS, OLS 3SLS
Model fit statistical
measures:
Overall and local Overall and local Local Local Overall and
local
Founders/Main
contributors:
Wright; Jöreskog; Hwang; Takane; Wright; Wold, H.;
Lohmöller; Dijkstra;
Henseler; Ringle;
Cowles; Koopmans; Zellner;

Structure of the Classification of the SEM state of the art methods
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 7 criteria are used as a basis to classify SEM methods and create rows of this
classification
 5 SEM methods are clustered and placed in 4 main columns and 1 sub-column
 SEM methods are divided into 3 main types:
1) Covariance based SEM - most frequently used methods are
LISREL and AMOS
2) Component based SEM – PLS-PA, PLSc, GeSCA
3) Systems of regression approaches
 These 3 types are coming from the type of latent variables

Criteria used in the Classification of the SEM
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 The type of LV is a “cornerstone” of the whole Classification of the SEM state of
the art methods
 Purpose and/or motivation of use - there is ambiguity and redundancy between
methods
Type of “Measurement model”:
1) reflective models are primarily used in CBSEM
2) formative model, can help to derive and depict new phenomena out of
observed indicators’ scores – mainly used for PLS-PA
 The rest of criteria: path coefficients, type of estimators, estimation methods and
model of fit measures, are more technical and are more in focus of interest of
professional statistical and mathematical specialists, rather than social or business
science researches
 Modern software often allows users to choose between several estimation
methods

Outline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

3 things that are important to know before comparing SEM methods
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Therefore, before comparing SEM methods important:
1) to understand, when in research process should a researcher to choose which
SEM technique to apply
2) to understand how to compare performance of SEM methods and is it indeed
possible to compare different SEM methods
3) what can be the conditions during the application of SEM and what are criteria
to compare efficiency
In order to establish a set of rules of thumb or a guideline (e.g., Gefen et al., 2011;
Hair et al., 2011), many scholars compare different SEM methods in different
sample size and distributional conditions
(e.g. Hwang et al.,2010; Goodhue et al. ,2012b; Dijkstra & Henseler ,2015)

CBSEM
type
Component
based SEM
type
Regression
Equations
type
(SEM technique)
Note: Research Model:
Measurement + Structural
Models
The selection of SEM method in social and business researches
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Source: Adopted from: Goodhue et al. (2012a)
InputOutput

Comparative simulation study: Feasibility, Conditions, Comparison criteria
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 Is it indeed possible to compare different SEM types with each other?
 It’s possible to perform comparative simulation study, the best way -
Using Monte Carlo simulation.
Feasibility
 Normal or non-normal distribution
 Sample size
 Model Complexity
Conditions
 Convergence
 Raw bias
 Statistical power
Criteria to compare efficiency

Analysis of recent comparative studies
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
1
(Authors, Year) (Hwang et al., 2010)
SEM types / methods CBSEM; PLS-PA; GeSCA.
Sample size N= 100, 200, 300, 400 and 500.
Data Distributions Normal and nonnormal.
Criteria of compared
efficiency
Loading and path coefficient estimates: 1) relative bias; 2) standard
deviation; 3) mean square error.
2
(Authors, Year) (Goodhue et al., 2012b)
SEM types / methods PLS, multiple regression, CBSEM (LISREL).
Sample size N= 20, 40, 90, 150 and 200, generation 500 data sets for each sample size.
efficiency
1) arriving at a solution (convergence), 2) producing accurate path
estimates,
3) avoiding false positives (Type 1 errors), 4) avoiding false negatives (Type 2
errors, related to statistical power).
3
Authors (Year) (Dijkstra & Henseler, 2015)
SEM types / methods PLS-PA, PLSc, regression equations and CBSEM (FIML, GLS, WLS, DWLS, ULS).
Sample size N= 100, 200 and 500.
efficiency
1) convergence - confidence of getting the solution by particular algorithm
2) raw bias - consistency between coefficients in a model
3) statistical power - occurrence Type-I and Type-II errors .

The result of the analysis of recent comparative studies
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Simplified SEM selection guideline

Outline
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research

Conclusions and contributions
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
 Description of the theoretical bases of SEM & Description of SEM methods;
 Contribution:
1) Creation of Classification of the SEM state of the art methods;
2) Analysis of : Feasibility, Conditions, criteria to compare efficiency; of comparative
studies;
3) Newly established simplified SEM guideline;
 The analysis of 3 comparative studies showed that there is no “magical silver bullet”,
and selection of the method should be based on many factors, for example :
1) research goal; 2) data, sample, distribution and model specification;
Conclusion: The initial goals of this thesis have been achieved

Limitations and opportunities for further research
Background
and Motivation
Introduction
into SEM
Goals
SEM
methods
Classification
Comparison and
selection of SEM
Conclusions &
Future Research
Based on the existing literature and studies performed by other researchers
Limited the number of SEM methods, complexity of the models and variety of
sample sizes
Focused on amateur SEM users with limited knowledge in statistics
Only existing state of the art SEM techniques
Limitations
Extensive Monte Carlo simulation studies with all existing SEM types with all
possible estimators in models of different complexity and with different sample size.
To establish of more sophisticated SEM selection guidelines, focused on both
amateur and experts in this field
Creation of new SEM techniques or a refinement of existing SEM methods
Focus on how to use a bundle of SEM methods in research
Opportunity for further research

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