Issues and Best Practices in Multiple Group Analysis With Ordinal-Level Data in Mplus

Multiple-group analysis (MGA) in structural equation modeling (SEM) is a flexible technique to test invariance of measures and validity of theoretical models across different populations. In the context of confirmatory factor analysis (CFA), MGA is a test of measurement invariance. For example, MGA can be used to test whether measures operate equivalently for males and females. In the context of substantive theory and general structural equation models, MGA allows tests of whether hypothesized relationships between latent variables are moderated by group membership (e.g., gender, race/ethnicity). For example, researchers may seek to determine whether an intervention improves outcomes for high school students to the same extent it does for middle school students.

MGA has been widely used in social work research. However, studies often use default software procedures which are sometimes inappropriate for the measurement level of study data. Ordinal-scaled indicators – common in social work research – require specific procedures to appropriately conduct MGA. Procedures based on assumptions of multivariate normal distribution with continuous variables are not the optimal approach when data are ordinal. The limitations of linear models with ordinal data have long been studied. However, recent methodological advances have provided guidance of how to proceed in testing measurement invariance for ordinal data (Hoyle, 2012; Millsap & Yun-Tein, 2004; Sass, 2011). This workshop emphasizes key analytical considerations associated with conducting ordinal-data MGA and presents best practices for common methodological challenges. First, a multiple-group CFA model for ordinal data is presented, and identification and estimation issues are discussed. Second, procedures for assessing measurement invariance for ordinal-scaled indicators are outlined. Workshop attendees will gain knowledge and skills in the application of best practices, including selection of an appropriate estimator (e.g., weighted least-squares), achieving model identification through constraint of thresholds, and testing invariance of thresholds. Because of its ability to appropriately handle clustered and ordinal-level scale data, Mplus software will be used throughout the workshop.  

Workshop Content. This workshop will provide an overview of the issues related to moderation in measurement and theoretical models as a foundation. Then, best practices in conducting MGA using Mplus software will be demonstrated and discussed. Information on how to carry out a MGA and interpret results will be covered. Specific attention will be given to modeling ordinal-level and/or non-normally distributed data. Presentation plans and pedagogical techniques include: 1. An introduction to major concepts (presentation); 2. Interactive discussion of participants’ experiences with multiple-group analysis and how these techniques might apply to their research questions; 3. Presentation and discussion of two to three research examples that illustrate the various applications of multiple-group analyses with ordinal-level and/or clustered data; 4. Demonstration of analysis techniques in Mplus; 5. Practice interpreting analysis results; and 6. Concluding questions and answers. Participants will receive a detailed handout containing Powerpoint slides, Mplus syntax for conducting multiple-group analyses, and annotated Mplus output.

Audience. This workshop will be suitable for researchers and PhD students with a basic understanding of measurement and/or structural equation models. Basic knowledge of Mplus software is helpful, but not required.