Exploratory Structural Equation Modeling, Integrating CFA and EFA: Application to Students' Evaluations of University Teaching

Abstract

This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching (SETs). For these data, there is a well established ESEM structure but typical CFA models do not fit the data and substantially inflate correlations among the nine SET factors (median rs = .34 for ESEM, .72 for CFA) in a way that undermines discriminant validity and usefulness as diagnostic feedback. A 13-model taxonomy of ESEM measurement invariance is proposed, showing complete invariance (factor loadings, factor correlations, item uniquenesses, item intercepts, latent means) over multiple groups based on the SETs collected in the first and second halves of a 13-year period. Fully latent ESEM growth models that unconfounded measurement error from communality showed almost no linear or quadratic effects over this 13-year period. Latent multiple indicators multiple causes models showed that relations with background variables (workload/difficulty, class size, prior subject interest, expected grades) were small in size and varied systematically for different ESEM SET factors, supporting their discriminant validity and a construct validity interpretation of the relations. A new approach to higher order ESEM was demonstrated, but was not fully appropriate for these data. Based on ESEM methodology, substantively important questions were addressed that could not be appropriately addressed with a traditional CFA approach.

Notes

¹Although not a focus of this investigation, it is also useful to consider issues of measurement invariance in relation to the terminology from item response theory (see Marsh, 2007a; Marsh & Grayson, 1994). Each measured variable (t) is related to the latent construct (T) by the equation t = a + bT where b is the slope (or discrimination) parameter that reflects how changes in the observed variable are related to changes in the latent construct and a is the intercept (or difficulty) parameter that reflects the ease or difficulty in getting high manifest scores for a particular measured variable. Unless there is complete or at least partial invariance of both the a and b parameters across the multiple groups, the comparison of mean differences across the groups might be unwarranted. In relation to the taxonomy of models in Table 1, tests of the IRT a parameter are represented by tests of the invariance of factor loadings, and the IRT b parameter is represented by tests of the item intercepts.

*p < .05;

**p, .001.

*p < .05;

**p, .001.