Best Practices in Measurement Invariance Testing with Ordinal-Level Data in Mplus

Social work constructs are commonly measured using sets of items with ordinal response options, such as, “never,” “sometimes,” “often,” or “agree,” “neutral,” “disagree.” The rigorous validation of these sets of questions, or scales, often includes confirmatory factor analysis (CFA), in which scores on scale items are modeled as effects of a latent variable and measurement error. In addition, when latent variables are used to test hypotheses about relationships among constructs in general structural equation models (SEM), a first step is to ascertain the quality of the measures through CFA. Therefore, many social work researchers are likely to encounter CFA. Because social workers work with populations of all ages and backgrounds, furthermore, social work researchers must pay special attention to the validity of their measures across groups. In the SEM framework, it is possible to conduct sophisticated and detailed tests of whether measures collect comparable data from different groups.  

The presence of ordinal data increases the complexity of CFA. Default CFA estimation procedures and input matrices, for example, are not appropriate for ordinal data (Jöreskog, 1993; Muthén, 1984). When social workers conduct multiple group tests, or tests of measurement invariance, to determine the quality of their measures across age, race/ethnic, or other subgroups, the analysis procedures required and the literature describing them becomes even more complex (e.g., Millsap & Yun-Tein, 2004;  Muthén & Muthén, 1998-2012; Sass, 2011).

Workshop Content. This workshop is designed to serve as a comprehensive guide to invariance testing with ordinal variables for social work researchers who have at least a basic understanding of latent variable modeling. First, a general explanation of how ordinal data differ from interval level and continuous data will be presented. Information on how programs like Mplus generate an analysis matrix from ordinal data will be provided. Then, a framework for analyzing and evaluating measurement invariance for ordinal data will be presented. Parameters unique to ordinal models, appropriate estimators, and issues of model identification will be addressed. A recommended sequence of model tests for assessing invariance will be outlined and demonstrated. Examples of output will be provided along will guidance in how to interpret results. The issue of partial measurement invariance will also be discussed. A shortcut feature for invariance testing that was introduced to Mplus 7.11 will be highlighted.

Pedagogical techniques include: (1) a presentation of major concepts; (2) interactive discussion of participants’ experiences with measurement invariance and how it applies to their research questions; (3) presentation and discussion of 3 examples that illustrate various outcomes of invariance testing (noninvariance, invariance, and partial invariance); (4) demonstration of analysis techniques in Mplus; (5) interpretation of results; and (6) concluding remarks. Participants will receive a detailed handout including Powerpoint slides, syntax, and annotated output.

Audience. This workshop will be suitable for researchers and doctoral students with a basic understanding of CFA or SEM. Basic knowledge of Mplus is helpful, but not required.