Structural Equation Modeling, 2nd Edition

3 Structural equation models

3.1 Introduction

In Chapter 2, we discussed and demonstrated confirmatory factor analysis (CFA) models. Once the factorial structure of the underlying constructs is validated using CFA, the measurement model is ready to be used for further studies of relationships involving latent variables/factors. Covariates can be included in the CFA model to study relationships between latent variables and observed covariates. A CFA model with covariates is also called a multiple indicators, multiple causes (MIMIC) model and can be used to study not only the relationships between factors and covariates, but also measurement invariance. When any covariance/correlation between latent variables/factors (represented by a curved line with an arrow in both directions in the model diagram) is replaced with a causal effect (represented by a line with an arrow in one direction in the model diagram), the model becomes a structural equation model (SEM), in which a specific latent variable/factor can be specified to predict other latent variables/factors or is influenced by other latent variables/factors. In addition, observed exogenous variables or covariates can be included to predict latent variables/factors, and the latter can also be used to predict observed endogenous dependent variables in the structural equation model.

We begin this chapter with the multiple indicators, multiple causes (MIMIC) model – a special case of the structural equation model – in ...