The Basics behind Structural Equation Modeling

Structural equation modeling (SEM) is a method for analyzing data in which relationships between observed and latent constructs are tested and depicted.  While SEM is often thought of as a single type of modeling, it is a class of analysis whose exact methods depend upon the objectives of the research.  SEM is used to test complicated theory-driven hypotheses including how observed variables relate to latent constructs and, often simultaneously, how latent constructs relate to one another.  One of the main reasons for using SEM is that it can help researchers make causal inferences (Joreskog, 1993; Kline, 2016).

SEM has been used with increasing frequency in social work research.  In a systematic review conducted by Guo and colleagues (2009), it was found that social worker researchers were primarily using SEM to conduct confirmatory factor analyses and full SEM models.  Less frequently, researchers used it for path analysis and latent growth curves.

In addition to traditional statistical output, SEM models are traditionally illustrated graphically.  Software, then, to analyze SEM models should, ideally, be able to generate the visual depictions associated with the models.  Some software programs, such as MPlus and AMOS, can do both, but are expensive.  Other programs, such as Stata, are more moderately priced, but have built capability more slowly. 

R, the open-source statistical programming language, has many advantages over proprietary statistical   software packages.  It is freely available, works well on any operating system, and produces outstanding graphics.  R has a number of packages that can build SEM models, the first of which was sem, that was developed by Fox and colleagues in 2006 (Fox et al., 2017).  Other packages have been developed for fitting SEM models, including OpenMx, lavaan, semPLS, and plspm (Monecke, 2013; Rosseel, 2012; Sanchez, Trinchera, & Russolillo, 2017; The OpenMx Project, 2017). 

While each has its strengths, lavaan has emerged as one of the most robust SEM packages available in R. lavaan has the capacity to estimate confirmatory factory analysis, full SEM models, path analysis, and t growth curves.  It has syntax that is similar to MPlus, making it easy to use for those familiar with that package.  It has the capacity to model categorical dependent variables and can support multiple groups.  Additionally, lavaan produces myriad fit statistics, enabling users to evaluate and compare models. It also has multiple estimators, many of which of robust variants.  The result is a free package that has the capabilities of commercial-grade software (Rosseel, 2012).

Because of its popularity and its robustness, a host of free resources are available for using lavaan.  These include tutorials, videos, teaching materials, and external projects, many of which are dedicated to easily diagramming lavaan models.

This paper presentation will present a brief overview of SEM, in general, and then will showcase how SEM models are used in social work research with examples taken from the field.  Resources for getting started with both R and lavaan will be presented so that symposium attendees can further explore SEM and lavaan at their convenience.