Differential Item Functioning by Multiple Variables using Moderated Nonlinear Factor Analysis

In this digital ITEMS module, Drs. Sanford Student and Ethan McCormick discusses an important new methodology for differential item functioning (DIF) that enables analyses with multiple background variables using a moderated nonlinear factor analysis approach.

Module Overview

Moderated Nonlinear Factor Analysis (Bauer, 2017; Bauer & Hussong, 2009) is a general measurement modeling framework with foundations in both IRT and SEM. For the purposes of DIF analysis by multiple background variables, MNLFA incorporates the best features of both multigroup IRT and MIMIC approaches. Like MIMIC models, MNLFA allows for an arbitrary number of background variables (either continuous or categorical). Like multigroup IRT models, MNLFA freely estimates the variance of the theta distribution as a function of variables being analyzed for DIF. Yet, the flexibility of MNLFA also leads to model identification complexities and challenges for estimation. This ITEMS module walks the user through the conceptual foundations of DIF analysis by an arbitrary number of background variables using MNLFA, and describes how penalized maximum likelihood estimation can be used to reduce the complexity of models with many DIF parameters (Bauer et al., 2020; Belzak & Bauer, 2024). Users completing this module will go forward equipped with a powerful new approach to DIF analysis whose flexibility enables analyses that are simply not possible using traditional DIF methods (Bauer, 2023).

Sanford (Sandy) Student

Assistant Professor of Educational Statistics and Research Methods at the University of Delaware
He teaches courses in survey design, educational measurement, Item Response Theory, and structural equation modeling
His research focuses on the relationship between psychometric issues, particularly in the measurement of growth using vertical scales, and broader inferences about student learning made on the basis of test scores.

Ethan McCormick

Assistant Professor of Educational Statistics and Research Methods at the University of Delaware
His research and teaching interests include specializing in longitudinal, time series, and psychometric models, focusing on structural equation modeling, multilevel modeling, Bayesian hierarchical time series modeling, and nonlinear modeling approaches for understanding population heterogeneity in measurement and change over time

Introduction

Upon completion of this ITEMS module, learners should be able to:

Articulate the difference between uniform and non-uniform DIF in the slope-intercept form of the 2PL IRT model
Differentiate DIF from impact, and describe the implications of both for parameters of traditional IRT models
Describe how moderated nonlinear factor analysis can be applied to estimate both DIF and impact in the slope-intercept 2PL
Apply regularized moderated nonlinear factor analysis to simultaneously estimate DIF and impact for multiple covariates of mixed types (i.e., categorical and continuous) using the R package regDIF
Use the results of regularized MNLFA estimation to inform next steps in DIF analysis

Section 1: IRT, DIF, and a More General Model

Upon completion of this section, learners should be able to:

Recognize the isomorphism between the 2PL IRT model and a slope-intercept factor analysis model
Differentiate and define the meaning of DIF versus impact
Contrast the strengths and limitations of multigroup and MIMIC approaches to DIF and impact
Recognize how MNLFA generalizes the slope-intercept model to estimate DIF and impact

Interactive Learning Check – Section 1