Exploratory Factor Analysis and Structural Equation Modeling

Abstract

This chapter discusses exploratory factor analysis (EFA) and structural equation modeling (SEM) techniques, two quantitative analytic methods commonly used in the field of language assessment. EFA is a data‐driven approach which is generally used as an investigative technique to identify relationships among variables. SEM is an a priori theory approach which is most often used to determine the extent to which an already established theory about relationships among variables is supported by empirical data. The chapter provides guidelines for using each of the techniques. Conducting an EFA requires screening and preparing the data for analysis, extracting eigenvalues, determining the number of factors for a solution, rotating the factors to a more interpretable solution, and providing an interpretation for the solution. Conducting an SEM analysis requires identifying the model, collecting and screening data appropriate for the analyses, estimating the parameters of the model, assessing the fit of the model to the data, interpreting the model's parameters, and evaluating the plausibility of competing models.To illustrate the principles and concepts of EFA, a self‐assessment of academic abilities data set is analyzed. A four‐factor model is found to be the most defensible factor structure. A second self‐assessment of academic abilities data set is then analyzed with an SEM approach with the aim of confirming or disconfirming the four‐factor structure identified with the EFA approach. Discussion and justification for decisions made during each step in the two analyses, along with an interpretation of the results, are provided. Common uses of EFA and SEM in language testing along with a brief historical overview of these techniques are also included in the chapter. The chapter concludes with a call for researchers to follow appropriate guidelines and principles when using one or the other of the techniques.