arXiv subjects

Peter F. Halpin

Publications and source records attributed to Peter F. Halpin.

3 recordsLinked to original sources

arXiv2024

Differential Test Functioning via Robust Scaling

In the item response theory (IRT) literature, differential test functioning (DTF) has been conceptualized in terms of how the test response function differs over groups of respondents. This paper presents an alternative approach to DTF that focusses on how the distribution of the latent trait differs over groups, which is referred to as impact. It is proposed to evaluate DTF by comparing two estimates of impact, one that naively aggregates over all test items and a robust alternative that down-weights items that exhibit differential item functioning (DIF). Taking this approach, this paper makes the following three contributions. First it is shown that the difference between the naive and robust estimands provides a convenient effect size for quantifying the extent to which DIF affects conclusions about impact (as opposed to test scores). Second it is shown how to construct a robust estimator that yields consistent estimates of impact whenever fewer than 1/2 of items exhibit DIF. Third, a relatively general purpose Wald test of the difference between two estimates of impact is developed. Using simulations and an empirical example from physics education, it is shown how the proposed effect size and test statistic perform using the proposed robust estimator of impact, as well as estimators that arise from conventional item-by-item tests of DIF.

stat.ME↗

arXiv2023

Multidimensional Item Response Theory in the Style of Collaborative Filtering

This paper presents a machine learning approach to multidimensional item response theory (MIRT), a class of latent factor models that can be used to model and predict student performance from observed assessment data. Inspired by collaborative filtering, we define a general class of models that includes many MIRT models. We discuss the use of penalized joint maximum likelihood (JML) to estimate individual models and cross-validation to select the best performing model. This model evaluation process can be optimized using batching techniques, such that even sparse large-scale data can be analyzed efficiently. We illustrate our approach with simulated and real data, including an example from a massive open online course (MOOC). The high-dimensional model fit to this large and sparse dataset does not lend itself well to traditional methods of factor interpretation. By analogy to recommender-system applications, we propose an alternative "validation" of the factor model, using auxiliary information about the popularity of items consulted during an open-book exam in the course.

stat.ML↗

arXiv2022

Differential item functioning via robust scaling

This paper proposes a method for assessing differential item functioning (DIF) in item response theory (IRT) models. The method does not require pre-specification of anchor items, which is its main virtue. It is developed in two main steps, first by showing how DIF can be re-formulated as a problem of outlier detection in IRT-based scaling, then tackling the latter using methods from robust statistics. The proposal is a redescending M-estimator of IRT scaling parameters that is tuned to flag items with DIF at the desired asymptotic Type I Error rate. Theoretical results describe the efficiency of the estimator in the absence of DIF and its robustness in the presence of DIF. Simulation studies show that the proposed method compares favorably to currently available approaches for DIF detection, and a real data example illustrates its application in a research context where pre-specification of anchor items is infeasible. The focus of the paper is the two-parameter logistic model in two independent groups, with extensions to other settings considered in the conclusion.

stat.ME↗