Structural Equation Modeling, 2nd Edition

2 Confirmatory factor analysis

2.1 Introduction

As discussed in Chapter 1, the key difference between path analysis and structural equation modeling (SEM) is, the former analyzes relationships among observed variables, while the latter focuses on relationships among latent variables (latent constructs or factors). In order to conduct SEM, latent variables/factors must be defined appropriately using a measurement model before they are incorporated into a structural equation model. Latent variables are unobservable and can only be indirectly estimated from observed indicators/items. Traditionally, the exploratory factor analysis (EFA) technique is applied to determine the underlying factorial structure of a measurement instrument (Comrey and Lee 1992; Gorsuch 1983; Mulaik 1972). EFA extracts unobserved factors from a set of observed indicator variables without specifying the number of factors or without determining how the observed indicator variables load onto specific factors; instead, factors are defined after they are extracted. In other words, EFA is applied in situations where the factorial structure or the dimensionality of an instrument for a given population is unknown, usually in the situation of developing new instruments. In contrast, confirmatory factor analysis (CFA) (Bollen 1989; Brown 2015) is used in situations where one has some knowledge of the dimensionality of the instrument under study, based either on a theory or on empirical findings. The factors ...