Structural equation models: from paths to networks (Westland 2019)

Abstract

Structural equation modeling (SEM) is a statistical analytic framework that allows researchers to specify and test models with observed and latent (or unobservable) variables and their generally linear relationships. In the past decades, SEM has become a standard statistical analysis technique in behavioral, educational, psychological, and social science researchers’ repertoire. From a technical perspective, SEM was developed as a mixture of two statistical fields—path analysis and data reduction. Path analysis is used to specify and examine directional relationships between observed variables, whereas data reduction is applied to uncover (unobserved) lowdimensional representations of observed variables, which are referred to as latent variables. Since two different data reduction techniques (i.e., factor analysis and principal component analysis) were available to the statistical community, SEM also evolved into two domains—factor-based and component-based (e.g., Jöreskog and Wold 1982). In factor-based SEM, in which the psychometric or psychological measurement tradition has strongly influenced, a (common) factor represents a latent variable under the assumption that each latent variable exists as an entity independent of observed variables, but also serves as the sole source of the associations between the observed variables. Conversely, in component-based SEM, which is more in line with traditional multivariate statistics, a weighted composite or a component of observed variables represents a latent variable under the assumption that the latter is an aggregation (or a direct consequence) of observed variables.