Promise of Mixture Modeling to Disability Research

• In Event: A Novel Methodological Approach to Understanding Disabilities

Abstract

Traditional statistical modeling approaches often make assumptions that do not coincide with the theoretical perspectives of disability research. For example, the assumption of normality often does not hold for outcomes of interest with samples who have been identified as having a disability, especially when standard scores are based on a normative sample. Mixture modeling provides multiple advantages. It is a multivariate approach that is amenable to special education research because it does not make distributional assumptions, provides useful heuristics for educational practitioners, is flexible in terms of how variables are examined, and allows for the identification of variables most salient to diagnosis and intervention.

Mixture modeling describes a family of modeling approaches (including cross-sectional and longitudinal), which share the assumption that a given population might be composed of a mixture of qualitatively different subpopulations. Further, mixture models do not assume that these subpopulations are observable, unlike gender or clinical diagnosis, these subpopulations are derived by a set of responses. As there is often considerable heterogeneity among students with disabilities - including heterogeneity among students with the same diagnosis - mixture models represent an important methodological tool that explicitly recognizes and models such heterogeneity. As it is a multivariate technique, researchers are able to identify subpopulations using variables that represent multiple components of a disability. Furthermore, subpopulation membership can be linked to auxiliary variables. These include covariates that can describe the characteristics of the subpopulations and outcome variables that enable researchers to understand how the subpopulations differ with respect to a given outcome of interest.

This paper provides a non-technical overview of mixture models, introducing possible models and the utility of them across a range of substantive disability research areas. By highlighting the range of applications that are possible, the intent of this paper is to highlight ways mixture models can and have been used to help stimulate new findings in disabilities research. These models are particularly salient for special educators and other educational practitioners who often encounter limited resources and need to group students together who exhibit similar skill profiles, but also provide tailored intervention that addresses individual needs. Beyond empirically identifying subpopulations of students, mixture models can be used to compare variables in terms of their ability to distinguish students. Thus, educational practitioners and researchers can gain a better understanding of which academic skills to prioritize for individual students when designing interventions.

Mixture modeling has the potential to provide a more nuanced understanding of special education research questions compared to traditional analytic approaches as it explicitly models heterogeneity, which is critical to understanding the needs of students with disabilities. Mixture modeling is a flexible, multivariate technique that enables the examination of how subpopulations differ with respect to any number of outcomes of interest. The focus of this paper is on the application of mixture models to special education research. While traditional analytic approaches are certainly of value, this paper seeks to identify pressing special education research questions, and explain how mixture models might be useful in answering them.

Author

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