# Composite Based SEM

## by Jörg Henseler

### Companion website

Jörg Henseler introduces the types of research questions that can be addressed with composite-based SEM and explores the differences between composite- and factor-based SEM, variance- and covariance-based SEM, and emergent and latent variables. Advanced topics include confirmatory composite analysis, mediation analysis, second-order constructs, interaction effects, and importance–performance analysis. Most chapters conclude with software tutorials for ADANCO and the R package cSEM. This companion website includes data files and syntax for the book's examples, along with presentation slides.

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**Introduction**

This chapter provides a general introduction to structural equation modeling (SEM) and an overview of various SEM techniques. It introduces composite-based SEM as those SEM techniques that involve composites in the estimation phase. Composite-based SEM can help answer research questions of various nature: confirmatory research, explanatory research, exploratory research, predictive research, and descriptive research.

**Auxiliary Theories**

The key difference between SEM and other statistical techniques is SEM’s ability to model substantial theories in combination with auxiliary theories. This chapter throws a glimpse on auxiliary theories and makes analysts aware that they have several options. Firstly, this chapter explores the nature and general anatomy of auxiliary theories. Secondly, it distinguishes between the sciences of the existing and the sciences of the artificial as well as their main components, theoretical concepts and forged concepts. Thirdly, it portrays measurement theory as the workhorse of behavioral sciences, which is based on the axiom of local independence assuming the existence of a latent variable. Finally, it introduces synthesis theory as a viable auxiliary theory for design sciences, which hypothesizes that an emergent variable acts as a whole instead of a mere heap of parts based on the axiom of unity.

**Model specification**

SEM starts with the model specification. A structural equation model is essentially a set of structural equations that puts constraints on the model-implied variance-covariance matrix of observed variables. It can be subdivided in the inner model and the outer model. The inner model captures the relationships among the constructs. The outer model entails the relationships between the constructs and the observed variables. The employed auxiliary theory dictates a certain type of outer model: composite model vs. reflective measurement model. The chapter also explains causal-formative measurement. Single-indicator constructs can be modeled as well as categorical exogenous variables. Finally, various forms of inner models are discussed.

**Model Identification**

Structural equation models must be identified in order to provide meaningful results. Composite-based SEM entails several mechanisms to safeguard the identification of models. In addition, researchers must ensure empirical identification, which means that the data contain enough information to provide a sufficiently strong nomological net for every construct whose outer model parameters are meant to be estimated. A construct’s nomological net encompasses its antecedents, its conse- quences, other correlated constructs, and the interrelationships among them. Moreover, in order to overcome the sign indeterminacy inherent to factor-analytical methods, analysts should define one dominant indicator for every construct that is operationalized by means of more than one indicator. The chapter concludes with a set of rules that can inform analysts about whether their models are identified or not.

**Model Estimation**

This chapter presents a variety of methods that can be employed to estimate structural equation models. They fall into three categories. The first category encompasses methods that create construct scores and can help to estimate structural equation models whose outer models only consist of composite models: sum scores and other preset weights, PLS path modeling, and GSCA. The second is in fact an extension of the first one; allowing them also to estimate structural equation models with reflective measurement models consistently. Preset weights with a correction for attenuation and consistent PLS are the major contenders. The third category is formed by the discrepancy functions of covariance-based SEM. Finally, this chapter explains the estimation options provided by ADANCO and cSEM.

**Global Model Assessment: Model Fit**

In order to test a structural equation model, researchers can examine its fit. A structural equation model’s goodness of fit expresses how similar the empirical and the model-implied variance-covariance matrix are. Composite-based SEM offers non-parametric and parametric tests of exact fit. Moreover, there are fit measures that indicate a structural equation model’s approximate fit. If the fit of a structural equation model is not satisfactory, analysts can employ model diagnostics and eventually adapt their model. Since econometrics and psychometrics have a different understanding of fit, there are some alleged fit measures in literature that should not be understood and used as measures of goodness of fit. Finally, this chapter demonstrates how a structural equation model’s fit can be tested using ADANCO or cSEM.

**Local Model Assesment**

This chapter explains how to assess a model locally, i.e., part by part. It captures outer and inner models separately and provides analysts with a set of means to examine the auxiliary and substantial theories encapsulated in their structural equation models. It discusses the difference between reliability and validity and shows how to assess both. It covers the assessment of composite models of emergent variables as well as reflective and causal-formative measurement models of latent variables. Inner models can be assessed with regard to ability to explain the variance of the endogenous constructs as well as the sign and strength of effects between constructs. Confidence intervals for all model parameters can be obtained through the bootstrap. Finally, this chapter provides a tutorial on how to assess structural equation models using ADANCO as well as cSEM.

**Confirmatory Composite Analysis**

CCA is a subtype of composite-based SEM that aims at assessing composite models of emergent variables. Composite models are an implementation of synthesis theory as presented in Section 2.4. They hypothesize that all information between blocks of observed variables is conveyed solely by the composites formed of these observed variables. Both variance-based and covariance-based SEM techniques can be used to estimate composite models. The composite model can be tested by both parametric and non-parametric approaches. In doing so, the discrepancy between the empirical and the model-implied variance-covariance matrix of the observed variables is assessed. A non-significant discrepancy provides evidence that the composites behave as emergent variables, which means that synthesis theory holds. Finally, a tutorial illustrates how ADANCO as well as cSEM can be used to conduct CCA.

**Mediation Analysis**

As soon as a structural equation model contains constructs that play the role of both dependent and independent variable, indirect effects emerge. Researchers may want to analyze to what extent relationships between variables are indirect, i.e., mediated. This section discusses why it is important to analyze mediating effects, explains how to model them using composite-based SEM, and provides a tutorial using ADANCO as well as cSEM.

**Second-Order Constructs**

Second-order constructs are variables on a higher level of abstraction. Their indicators are not directly observable but again constructs. Firstly, this chapter introduces a typology of second-order constructs consisting of six types: latent variables measured by latent variables (Type I), emergent variables made of latent variables (Type II), latent variables measured by emergent variables (Type III), emergent variables made of emergent variables (Type IV), latent variables measured by different types of variables (Type V), and emergent variables made of different types of variables (Type VI). For each type of second-order construct, there are typical research questions that it can help answer. For each type of second-order construct, this chapter presents at least one approach how to consistently estimate the model parameters and to test the model. Finally, this chapter shows how to model second-order constructs using ADANCO as well as cSEM.

**Analyzing Interaction Effects**

Interaction effects (also called moderating effects) overcome the assumption that the relationships between constructs are exactly the same for all individuals. Rather, they are a special form of nonlinear effects that allow the strength of effects to depend on the level of so-called moderator variables. Analysis of interaction effects permits researchers to take into account contingencies as well as heterogeneity of subpopulations. This chapter presents several ways that interaction effects can be specified, estimated, reported, and interpreted using composite-based SEM. If the moderator variable is of categorical nature as is often the case with data stemming from experimental designs, multigroup analysis is a viable option. If the moderator variable is of continuous nature, the two-stage approach allows analysts to model interaction effect among emergent and latent variables. In light of the additional layer of complexity introduced by interaction effects, a graphical visualization of model results is recommended, as, e.g., done in a surface analysis, a spotlight analysis, or a floodlight analysis. The penultimate section discusses how the approaches to model interaction effects can also be used to model other nonlinear effects, particularly quadratic and higher polynomial effects. Finally, a tutorial illustrates how ADANCO and cSEM can be employed to specify, estimate, and test interaction effects.

**Importance-Performance Analysis**

Importance-performance analysis is an additional analytical step to report model results in a graphical fashion. Combining descriptive and predictive research, importance-performance analysis plots the location parameters of independent variables against their total effects. ADANCO and cSEM provide all the required numerical output to conduct importance-performance analysis.

# About

**Jörg Henseler**, PhD, is Full Professor and Chair of Product–Market Relations in the Faculty of Engineering Technology of the University of Twente in The Netherlands. He is also Visiting Professor at NOVA Information Management School, NOVA University of Lisbon, Portugal, and Distinguished Invited Professor in the Department of Business Administration and Marketing at the University of Seville, Spain.

His broad-ranging research interests encompass empirical methods of marketing and design research as well as the management of design, products, services, and brands. A highly cited researcher, Dr. Henseler is a leading expert on partial least squares (PLS) path modeling, a composite-based structural equation modeling (SEM) technique that bridges design and behavioral research. He has written dozens of scholarly articles, edited or authored several books, served as guest editor for three special journal issues, and chaired conferences on PLS. He serves on several journal editorial boards and has been an invited speaker on SEM at universities around the world. Dr. Henseler chairs the scientific advisory board for the ADANCO software program and regularly provides seminars on PLS path modeling at the PLS School.