Structural Equation Modelling with Partial Least Squares Using Stata and R

Mehmet Mehmetoglu, Sergio Venturini

• Publisher: Chapman and Hall/CRC
• Year: 2021
• ISBN:
  9780429528859
• Edition: 1
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

Partial least squares structural equation modelling (PLS-SEM) is becoming a popular statistical framework in many fields and disciplines of the social sciences. The main reason for this popularity is that PLS-SEM can be used to estimate models including latent variables, observed variables, or a combination of these. The popularity of PLS-SEM is predicted to increase even more as a result of the development of new and more robust estimation approaches, such as consistent PLS-SEM. The traditional and modern estimation methods for PLS-SEM are now readily facilitated by both open-source and commercial software packages.

This book presents PLS-SEM as a useful practical statistical toolbox that can be used for estimating many different types of research models. In so doing, the authors provide the necessary technical prerequisites and theoretical treatment of various aspects of PLS-SEM prior to practical applications. What makes the book unique is the fact that it thoroughly explains and extensively uses comprehensive Stata (plssem) and R (cSEM and plspm) packages for carrying out PLS-SEM analysis. The book aims to help the reader understand the mechanics behind PLS-SEM as well as performing it for publication purposes.

Features:

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• Intuitive and technical explanations of PLS-SEM methods

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• Complete explanations of Stata and R packages

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• Lots of example applications of the methodology

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• Detailed interpretation of software output

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• Reporting of a PLS-SEM study

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• Github repository for supplementary book material

The book is primarily aimed at researchers and graduate students from statistics, social science, psychology, and other disciplines. Technical details have been moved from the main body of the text into appendices, but it would be useful if the reader has a solid background in linear regression analysis.

Part I

Preliminaries and Basic Methods

1

Framing Structural Equation Modelling

In this chapter we will describe what structural equation modelling (SEM) is by first relating it to traditional single-equation techniques such as regression analysis. We then present the two main approaches to doing SEM analysis, namely covariance-based SEM and partial least squares SEM. Although we assume that the reader has already made her/his decision to use PLS-SEM, we still in a compact manner provide suggestions (mainly based on existing simulation studies) as to when to use PLS-SEM. In so doing, we also present consistent PLS-SEM as a valid method to match CB-SEM. For the reading of this chapter, we also assume that the reader has a sound background in linear regression analysis¹.

1.1 What Is Structural Equation Modelling?

Let us start this section by first defining what a structural equation is. Intuitively put, a structural equation refers to a statistical association whereby one variable (X) influences another one (Y). When there is only one dependent variable predicted by one (or several) independent variables in our statistical model², then the structural equation is univariate and it can be expressed as follows³:

$$\begin{array}{l}{Y}_i={\beta }_0+{\beta }_1·X_i+{\mathrm{ϵ}}_i.\hfill \end{array}$$

(1.1)

Based on your previous statistics knowledge, you will easily recognize equation (1.1). It represents a simple regression model including two variables (X and Y). The significance testing of β₁ will provide the empirical evidence as to whether X (e.g., education level) influences Y (e.g., hourly wage) or not. Incidentally, if X is a dichotomous variable (e.g., gender) or a polytomous variable (e.g., types of occupation), equation (1.1) will then correspond to an independent t-test and analysis of variance (ANOVA) respectively. Extending our regression model in equation (1.1) with one more independent variable will turn it into a multiple regression (or ANCOVA⁴ or two-way ANOVA⁵ for that matter).

1.Appendix A. provides a brief review of the linear regression model, while Section 2.2 summarizes the basics of principal component analysis.

2.A model represents the hypothesized relationships between a set of variables.

3.In this book we will frequently use letters taken from the Greek alphabet. For your convenience, we provide it on page xxxviii.

Increasing the number of independent variables does turn our model into a multivariable one. However, it corresponds still to a univariate model in that we still have just one dependent variable to predict. Examples of such models including only one dependent variable are listed in Table 1.1. Even when we view Table 1.1 at a glance, we will notice that the univariate modelling techniques (e.g., linear regression, logistic regression) are clearly the ones that have been used most commonly in quantitative research regardless of social or natural sciences.

TABLE 1.1: Examples of univariate and multivariate statistical techniques.

Univariate	Multivariate
Multiple regression	Multivariate regression
Logistic regression	Seemingly unrelated regression
Multinomial logistic regression	Path analysis (also called simultaneous equation models)
Discriminant (function) analysis
Survival analysis	Structural equation modelling
Poisson regression
Log-linear analysis
Independent t-test
Analysis of variance
Multilevel regression

Nonetheless, the need to be able to estimate models including more than one dependent variable has also led to the invention of some useful multivariate modelling techniques in quantitative research (see Table 1.1). One of these techniques is multivariate regression (MVREG), which corresponds to a multiple regression facilitating more than one dependent variable. The advantage of this technique is that it allows for cross-equation comparisons. Two limitations of MVREG are that all the dependent variables must be predicted by the same set of predictors, and that the correlations among the residuals are not taken into consideration. Seemingly unrelated regression (SUR) does readily surmount these limitations. These features make SUR a simultaneous⁶ multivariate modelling technique.

Although SUR (and MVREG for that matter) has helped quantitative researchers solve some demanding research questions, its limitation is that it allows for estimating only direct effects. Path analysis (PA) however allows to estimate both direct and indirect effects, making it a technique for es...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Authors
• List of Figures
• List of Tables
• List of Algorithms
• Abbreviations
• Greek Alphabet
• I. Preliminaries and Basic Methods
• II. Advanced Methods
• III. Conclusions
• IV. Appendices
• Bibliography
• Index