Using Functional Clustering to Diagnose Person Misfit

Abstract

The purpose of this study is to demonstrate clustering methods within a functional data analysis (FDA) framework for identifying subgroups of individuals that may be exhibiting categories of misfit. Person response functions (PRFs) estimated within a FDA framework (FDA-PRFs) provide graphical displays that can aid in the identification of persons that have responded unexpectedly to items comprising an achievement test. Typical person fit statistics are also useful for detecting unexpected response patterns, but they do not provide insight into the underlying behaviors responsible for those responses. However, different responding behaviors tend to produce FDA-PRFs of different shapes, and may provide additional information regarding the reasons for misfit. Functional clustering methods are useful for categorizing respondents into subgroups based on the shapes of their FDA-PRFs. In this study, a small simulation illustrates the potential of clustering FDA-PRFs for identifying persons displaying common types of responding behaviors. The methodology is also applied to data from a high school biology assessment and a mathematics achievement test. Clustering FDA-PRFs offers a promising methodology for operationalizing person fit evaluations in large-scale assessments, and may be a valuable step in person fit assessment when used in conjunction with traditional indices of psychometric quality.