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

Structural Equations Modeling (SEM)Defining the State of the Art

byDipl. 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 SEMGoals 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”




methods Classification Comparison and selection of SEM


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






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






Outline






SEM is more, than just a one method






“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)





Measurementmodels

Structuralmodel

Source: adopted from Hoyle (2012)

Equations notation


Matrix notation

SEM implementation framework







Steps in SEM implementation


Outline






State of the art SEM methods






Name of SEM method Main contributorsCovariance-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






Purpose and/or motivation of use: Type of measurement model: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)

Latent variables: Path coefficients: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)

Type of estimators: Popular estimation methods: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)






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)






Consistent Partial Least Squares Path Modeling – PLSc






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

Purpose and/or motivation of use: Type of measurement model:Mainly explanation and conformation of hypothesis (Tenenhaus, 2008);

Formative and reflective (Hwang & Takane, 2004)

Latent variables: Path coefficients:“Components or weights assigned to” manifest indicators (Hwang et al., 2010)

Component weights (Hwang & Takane, 2004)

Type of estimators: Popular estimation methods: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






Purpose and/or motivation of use: Type of measurement model:Data description, parameter estimation, prediction and estimation, and control of models (Montgomery et al., 2012)

Reflective (Westland, 2015)

Latent variables: Path coefficients:Response variables - linear functions of indicators (predictor variables) (Westland, 2015)

Regression coefficients (often used symbol– b) (Tukey, 1954)

Type of estimators: Popular estimation methods: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







Outline






Classification of the SEM state of the art methods - CSEMSAM






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






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






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






3 things that are important to know before comparing SEM methods






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






Source: Adopted from: Goodhue et al. (2012a)

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Comparative simulation study: Feasibility, Conditions, Comparison criteria






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






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.Data Distributions Normal and nonnormal.


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.Data Distributions Normal and nonnormal.


1) convergence - confidence of getting the solution by particular algorithm2) raw bias - consistency between coefficients in a model3) statistical power - occurrence Type-I and Type-II errors .

The result of the analysis of recent comparative studies






Simplified SEM selection guideline


Outline






Conclusions and contributions






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






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

List of References (1 of 3)


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

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