The Use of Regression Mixture Modeling With a Social Justice Lens

• In Event: The Utility of Mixture Modeling to Understanding Heterogeneous Effects in Educational Studies

Abstract

There has been a call for research with social justice orientated in all areas of educational research. Statistical methods are not immune to incorporating intersectional applications into empirical research (Else-Quest & Hyde, 2016). Intersectionality is a theoretical framework that considers the multiple memberships in social categories (e.g., race, ethnicity, class, gender, sexual orientation) which can reflect systems of privilege and oppression (Crenshaw, 1989, 1991). Intersectionality in the education field has been presented as a conceptual aspiration and a research imperative (Tefera et al., 2018). These researchers suggest that requiring researchers to account for complexity and diversity within the education field that incorporates quantitative methods is a strength of intersectionality. This paper focuses on incorporating intersectionality using person-centered methods, or mixture models. More specifically, researchers interested in applying mixture models, or latent class analysis (LCA), may include auxiliary variables (e.g., covariates and distal outcomes) to incorporate an intersectional approach into their research.

Mixture models are person-centered statistical approaches used to identify and model unobserved subgroups of a population using a set of items in a measure. Mixture models can be utilized as a moderating variable in order to understand the more complex relationships in social science research. Moderation with mixture models, or regression mixture models, applies a three-step method (i.e., ML three-step or BCH) to estimate the relationships of the auxiliary variables with the latent class variable while leaving the measurement parameters of the latent class variable unchanged. Auxiliary variables used in the analyses may be observed, latent, or treatment variables. The current paper builds on the foundation of mixture regression, extending to the application of intersectionality examples.

Applying LCA and regression mixture models can illustrate the intersections of multiple identities of individuals through various social contexts. For example, Garnett et al. applied a latent class model to understand the intersectionality of discrimination attributes and bullying among youth. A four-class solution included classes that subgroups of individuals with marginalized identities, one of which is described as “Intersectional Discrimination”. The four-class latent variable was then used to determine associations between class membership and various distal outcomes. Similarly, this paper will frame mixture modeling as a tool for intersectionality research.

This paper is an extension of previous work which provided a pedagogical approach to understanding, interpreting and visualizing moderation in the context of mixture modeling. This paper builds on the example using the Longitudinal Survey of American Life (LSAL) to demonstrate the use of regression mixture models and provide examples of how to incorporate intersectional methods in quantitative research. While this paper will provide a walkthrough of the 3-step method noted above, the focus will be on demonstrating this method using an applied example with an intersectional lens. Demonstrations of the statistical methods are using the R and the MplusAutomation package within R and R Studio.

Authors

• Dina Naji Arch, University of California - Santa Barbara

• Karen L. Nylund-Gibson, University of California - Santa Barbara