Using MIMIC Methods to Detect and Identify Sources of DIF among Multiple Groups

This study investigated the efficacy of multiple indicators, multiple causes (MIMIC) methods in detecting uniform and nonuniform differential item functioning (DIF) among multiple groups, where the underlying causes of DIF was different. Three different implementations of MIMIC DIF detection were studied: sequential free baseline, free baseline, and constrained baseline. In addition, the robustness of the MIMIC methods against the violation of its assumption, equal factor variance across comparison groups, was investigated. We found that the sequential-free baseline methods provided similar Type I error and power rates to the free baseline method with a designated anchor, and much better Type I error and power rates than the constrained baseline method across four groups, resulting from the co-occurrence background variables. But, when the equal factor variance assumption was violated, the MIMIC methods yielded the inflated Type I error. Also, the MIMIC procedure had problems correctly identifying the sources DIF, so further methodological developments are needed

Item Parameter Estimation With the General Hyperbolic Cosine Ideal Point IRT Model

Over the last decade, researchers have come to recognize the benefits of ideal point item response theory (IRT) models for noncognitive measurement. Although most applied studies have utilized the Generalized Graded Unfolding Model (GGUM), many others have been developed. Most notably, David Andrich and colleagues published a series of papers comparing dominance and ideal point measurement perspectives, and they proposed ideal point models for dichotomous and polytomous single-stimulus responses, known as the Hyperbolic Cosine Model (HCM) and the General Hyperbolic Cosine Model (GHCM), respectively. These models have item response functions resembling the GGUM and its more constrained forms, but they are mathematically simpler. Despite the apparent impact of Andrich’s work on ensuing investigations, the HCM and GHCM have been largely overlooked by applied researchers. This may stem from questions about the compatibility of the parameter metric with other ideal point estimation and model-data fit software or seemingly unrealistic parameter estimates sometimes produced by the original joint maximum likelihood (JML) estimation software. Given the growing list of ideal point applications and variations in sample and scale characteristics, the authors believe these HCMs warrant renewed consideration. To address this need and overcome potential JML estimation difficulties, this study developed a marginal maximum likelihood (MML) estimation algorithm for the GHCM and explored parameter estimation requirements in a Monte Carlo study manipulating sample size, scale length, and data types. The authors found a sample size of 400 was adequate for parameter estimation and, in accordance with GGUM studies, estimation was superior in polytomous conditions

MIMIC Methods for Detecting DIF Among Multiple Groups: Exploring a New Sequential-Free Baseline Procedure

A simulation study was conducted to investigate the efficacy of multiple indicators multiple causes (MIMIC) methods for multi-group uniform and non-uniform differential item functioning (DIF) detection. DIF was simulated to originate from one or more sources involving combinations of two background variables, gender and ethnicity. Three implementations of MIMIC DIF methods were compared: constrained baseline, free baseline, and a new sequential-free baseline. When the MIMIC assumption of equal factor variance across comparison groups was satisfied, the sequential-free baseline method provided excellent Type I error and power, with results similar to an idealized free baseline method that used a designated DIF-free anchor, and results much better than a constrained baseline method, which used all items other than the studied item as an anchor. However, when the equal factor variance assumption was violated, all methods showed inflated Type I error. Finally, despite the efficacy of the two free baseline methods for detecting DIF, identifying the source(s) of DIF was problematic, especially when background variables interacted

APM-17-03-060.R3_Online_Supplemental_Material_(1) – Supplemental material for Item Parameter Estimation With the General Hyperbolic Cosine Ideal Point IRT Model

<p>Supplemental material, APM-17-03-060.R3_Online_Supplemental_Material_(1) for Item Parameter Estimation With the General Hyperbolic Cosine Ideal Point IRT Model by Seang-Hwane Joo, Seokjoon Chun, Stephen Stark, and Olexander S. Chernyshenko in Applied Psychological Measurement</p