Seminar 2022-09-14: Flexible Latent Variable Model Framework for Latent DIF Detection

2022-09-05

Speaker: Gabriel Wallin, Umeå University and London School of Economics. Date and location: 2022-09-14 at 10:15–12:00, Ekonomikum room H317.

Abstract

In psychometrics, a field concerned with theory and techniques for psychological and educational measurement, it is standard procedure to assess the presence of differential item functioning (DIF). DIF means that questionnaire/test items function differently for different groups of respondents, after controlling for the latent construct that is intended to be measured. It for example occurs in educational testing when groups such as defined by e.g., gender or ethnicity have different probabilities of answering a given item correctly, after controlling for the latent ability that the exam is intended to measure. As such, it relates to fairness in educational testing.

When DIF detection is not based on known groups such as gender or ethnicity but on unknown, homogeneous subgroups, the problem is typically referred to as latent DIF detection, which will be the focus of this talk. To that end, I will present a flexible modelling framework that combines a general latent factor model with a latent class model to capture both normal response behaviour for non-DIF items and deviant behaviour for DIF items. In the proposed model, a sparse DIF effect parameter is introduced that is allowed to vary between the latent classes identified by the model.

Our main contributions are two-folded: Firstly, unlike previous research on DIF detection, no prior knowledge of DIF-free items is required. Instead, they are identified through an 1 penalty on the DIF effect parameter in the marginal likelihood function of the model. Secondly, the proposed model considers a multiple latent group setting, whereas only two groups (a so called manifest and a focal group) are typically facilitated in current DIF detection methods. We propose an EM algorithm for model estimation, where the maximization step is carried out using a quasi-Newton proximal algorithm. Results based on both simulated and empirical data together with theoretical results will be presented.

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