Sébastien Béland

A general framework and an R package for the detection of dichotomous differential item functioning.

Differential item functioning (DIF) is an important issue of interest in psychometrics and educational measurement. Several methods have been proposed in recent decades for identifying items that function differently between two or more groups of examinees. Starting from a framework for classifying DIF detection methods and from a comparative overview of the most traditional methods, an R package for nine methods, called difR, is presented. The commands and options are briefly described, and the package is illustrated through the analysis of a data set on verbal aggression.

A Didactic Presentation of Snijders’s lz* Index of Person Fit With Emphasis on Response Model Selection and Ability Estimation:

This paper focuses on two likelihood-based indices of person fit, the index lz and the Snijders’s modified index lz *. The first one is commonly used in practical assessment of person fit, although its asymptotic standard normal distribution is not valid when true abilities are replaced by sample ability estimates. The lz * index is a generalization of lz , which corrects for this sampling variability. Surprisingly, it is not yet popular in the psychometric and educational assessment community. Moreover, there is some ambiguity about which type of item response model and ability estimation method can be used to compute the lz * index. The purpose of this article is to present the index lz * in a simple and didactic approach. Starting from the relationship between lz and lz *, we develop the framework according to the type of logistic item response theory (IRT) model and the likelihood-based estimators of ability. The practical calculation of lz * is illustrated by analyzing a real data set about language skill assessment.

A generalized logistic regression procedure to detect differential item functioning among multiple groups

We present an extension of the logistic regression procedure to identify dichotomous differential item functioning (DIF) in the presence of more than two groups of respondents. Starting from the usual framework of a single focal group, we propose a general approach to estimate the item response functions in each group and to test for the presence of uniform DIF, nonuniform DIF, or both. This generalized procedure is compared to other existing DIF methods for multiple groups with a real data set on language skill assessment. Emphasis is put on the flexibility, completeness, and computational easiness of the generalized method.

A Test-Length Correction to the Estimation of Extreme Proficiency Levels

In this study, the estimation of extremely large or extremely small proficiency levels, given the item parameters of a logistic item response model, is investigated. On one hand, the estimation of proficiency levels by maximum likelihood (ML), despite being asymptotically unbiased, may yield infinite estimates. On the other hand, with an appropriate prior distribution, the Bayesian approach of maximum a posteriori (MAP) yields finite estimates, but it suffers from severe estimation bias at the extremes of the proficiency scale. As a first step, a simple correction to the MAP estimator is proposed to reduce this estimation bias. The correction factor is determined through a simulation study and depends only on the length of the test. In a second step, some additional simulations emphasize that the corrected estimator behaves like the ML estimator and outperforms the standard MAP method for extremely small or extremely large abilities. Although based on the Rasch model, the method could be adapted to other logistic item response models.