Chapter 10: Exploratory Structural Equation Modeling

In a seminal publication, Cohen (1968) presented multiple regression as a generic data-analytic system for quantitative dependent variables (outcomes) encompassing classical analyses of variance and covariance, interactive effects, and predictive non-linearity among quantitative and qualitative predictors. However, multiple regression and most of the General Linear Model procedures were later shown to represent special cases of the even more encompassing framework of canonical correlation analysis, allowing for the inclusion of multiple outcomes within the same model (Knapp, 1978). Similarly, Structural Equation Modeling (SEM) was proposed as an even more flexible framework (Bagozzi, Fornell, & Larker, 1981; Fan, 1997; Graham, 2008), covering any relation that could be studied with canonical correlation analysis, but also allowing for the simultaneous estimation of chains of direct and indirect effects (i.e., path analysis) based on latent variables that implicitly correct the estimated relations for measurement error (i.e., confirmatory factor analysis [CFA]). Then, Muthén (2002; also see Skrondal & Rabe-Hesketh, 2004) incorporated all of these methods into an even more generic framework (generalized SEM [GSEM]), allowing for the estimation of relations between any type of quantitative or qualitative observed and latent variables. Although exploratory factor analyses (EFAs) have been around for more than a century (Spearman, 1904) and represent an important precursor of CFAs (Cudeck & MacCallum, 2007), and thus of SEM and GSEM, it was until recently excluded from these generalized frameworks.