# Structural Equation Modelling with Partial Least Squares Using Stata and R

Structural equation modeling (SEM) is a statistical framework that can model both observed and unobserved (latent) variables through complex relationships. While the traditional covariance-based SEM aims to find parameter estimates that minimize the distance between the observed and model-implied covariances of the observed variables, partial least-squares SEM (PLS-SEM) aims to find parameter estimates that maximize explained variance.

Structural Equation Modelling with Partial Least Squares Using Stata and R, by Mehmet Mehmetoglu and Sergio Venturini, offers a comprehensive tutorial on conducting PLS-SEM and consistent PLS-SEM through the author’s open-source plssem package.

The authors begin with theoretical introductions to PLS-SEM and various multivariate statistical prerequisites. The following chapters provide a step-by-step guide to conducting PLS-SEM in Stata, including model specification, estimation, assessment, and interpretation. The remaining chapters introduce concepts and examples for mediation, moderation, and detecting unobserved heterogeneity in PLS-SEM and close with some advice and an example of writing up a PLS-SEM study. The datasets and do-files from all the examples are available as a GitHub repository at https://github.com/sergioventurini/SEMwPLS.

Structural Equation Modelling with Partial Least Squares Using Stata and R is a useful resource for researchers interested in learning more about PLS-SEM and for more advanced researchers interested in learning how to fit PLS-SEM models in Stata.

Preface
Authors
List of Figures
List of Tables
List of Algorithms
Abbreviations
Greek Alphabet

I Preliminaries and Basic Methods
1 Framing Structural Equation Modelling
1.1 What is Structural Equation Modelling?
1.2 Two Approaches to Estimating SEM Models

1.2.1 Covariance-based on SEM
1.2.2 Partial least squares SEM
1.2.3 Consistent partial least squares SEM

1.3 What Analyses Can PLS-SEM Do?
1.4 The Language of PLS-SEM
1.5 Summary

2 Multivariate Statistics Prerequisites
2.1 Bootstrapping
2.2 Principal Component Analysis
2.3 Segmentation Methods

2.3.1 Cluster analysis

2.3.1.1 Hierarchical clustering algorithms
2.3.1.2 Partitional clustering algorthms

2.3.2 Finite mixture models and model-based clustering
2.3.3 Latent class analysis

2.4 Path Analysis
2.5 Getting to Partial Least Squares Structural Equation Modelling
2.6 Summary
Appendix: R Commands

The bootstrap
Principal component analysis
Segmentation methods
Latent class analysis
Path analysis

Appendix: Technical Details

More Insights on the bootstrap
The algebra of principal components analysis
Clustering stopping rules
Finite mixture models estimation and selection
Path analysis using matrices

3 PLS Structural Equation Modelling: Specification and Estimation
3.1 Introduction
3.2 Model specification

3.2.1 Outer (measurement) model
3.2.2 Inner (structural) model
3.2.3 Application: Tourists satisfaction

3.3 Model Estimation

3.3.1 The PLS-SEM algorithm
3.3.2 Stage I: Iterative estimation of latent variable scores
3.3.3 Stage II: Estimation of measurement model parameters
3.3.4 Stage III: Estimation of structural model parameters

3.4 Bootstrap-based Inference
3.5 The plssem Stata Package

3.5.1 Syntax
3.5.2 Options
3.5.3 Stored results
3.5.4 Application: Tourists satisfaction (cont.)

3.6 Missing Data

3.6.1 Application: Tourists satisfaction (cont.)

3.7 Effect Decomposition
3.8 Sample Size Requirement
3.9 Consistent PLS-SEM

3.9.1 The plssemc command

3.10 Higher Order Constructs
3.11 Summary
Appendix: R Commands

The plspm package
The cSEM package

Appendix: Technical Details

A formal definition of PLS-SEM
More details on the consistent PLS-SEM approach

4 PLS Structural Equation Modelling: Assessment and Interpretation
4.1 Introduction
4.2 Assessing the Measurement Part

4.2.1 Reflective measurement models

4.2.1.1 Unidimensionality
4.2.1.2 Construct reliability
4.2.1.3 Construct validity

4.2.2 Higher order reflective measurement models
4.2.3 Formative measurement models

4.2.3.1 Content validity
4.2.3.2 Multicollinearity
4.2.3.3 Weights

4.3 Assessing the Structural Part

4.3.1 R-squared
4.3.2 Goodness-of-fit
4.3.3 Path coefficients

4.4 Assessing a PLS-SEM Model: A Full Example

4.4.1 Setting up the model using plssem
4.4.2 Estimation using plssem in Stata
4.4.3 Evaluation of the example study model

4.4.3.1 Measurement part
4.4.3.2 Structural part

4.5 Summary
Appendix: R Commands
Appendix: Technical Details

Tools for assessing the measurement part of a PLS-SEM model
Tools for assessing the structural part of a PLS-SEM model

5 Mediation Analysis With PLS-SEM
5.1 Introduction
5.2 Baron and Kenny’s Approach to Mediation Analysis

5.2.1 Modifying the Baron-Kenny approach
5.2.2 Alternative to the Baron-Kenny approach
5.2.3 Effect size of the mediation

5.3 Examples in Stata

5.3.1 Example 1: A single observed mediator variable
5.3.2 Example 2: A single latent mediator variable
5.3.3 Example 3: Multiiple latent mediator variables

5.4 Moderated Mediation
5.5 Summary
Appendix: R Commands

6 Moderating/Interaction Effects Using PLS-SEM
6.1 Introduction
6.2 Product-Indicator Approach
6.3 Two-Stage Approach
6.4 Multi-Sample Approach

6.4.1 Parametric test
6.4.2 Permutation test

6.5 Example Study: Interaction Effects

6.5.1 Application of the product-indicator approach
6.5.2 Application of the two-stage approach

6.5.2.1 Two-stage as an alternative to product-indicator
6.5.2.2 Two-stage with a categorical moderator

6.5.3 Application of the multi-sample approach

6.6 Measurement Model Invariance
6.7 Summary
Appendix: R Commands

Application of the product-indicator approach
Application of the two-stage approach
Application of the multi-sample approach
Measurement model invariance

7 Detecting Unobserved Heterogeneity in PLS-SEMM
7.1 Introduction
7.2 Methods for the Identification and Estimation of Unobserved Heterogeneity in PLS-SEM

7.2.1 Response-based unit segmentation in PLS-SEM
7.2.2 Finite mixture PLS (FIMIX-PLS)
7.2.3 Other methods

7.2.3.1 Path modelling segmentation tree algorithm (Pathmox)
7.2.3.2 Partial least squares genetic algorithm segmentation (PLS-GAS)

7.3 Summary
Appendix: R Commands
Appendix: Technical Details

The math behind the REBUS-PLS algorithm
Permutation tests

III Conclusions
8 How to Write Up a PLS-SEM Study
8.1 Publication Types and Structure
8.2 Example of PLS-SEM Publication
8.3 Summary

IV Appendices
A Basic Statistics Prerequisites
A.1 Covariance and Correlation
A.2 Linear Regression Analysis

A.2.1 The simple linear regression model
A.2.2 Goodness-of-fit
A.2.3 The multiple linear regression model
A.2.4 Inference for the linear regression model

A.2.4.1 Normal-based inference

A.2.5 Categorical predictors
A.2.6 Multicollinearity
A.2.7 Example

A.3 Summary
Appendix: R Commands

Covariance and correlation
Bibliography
Index
Author: Mehmet Mehmetoglu and Sergio Venturini
ISBN-13: 978-1482-22781-9