A Non-parametric Bayesian Model for Detecting Differential Item Functioning: An Application to Political Representation in the US

TL;DR

This paper introduces a non-parametric Bayesian approach using Dirichlet Process priors in IRT models to detect differential item functioning, revealing that many voters interpret stimuli differently from legislators, affecting representation analysis.

Contribution

It proposes a novel single-model Bayesian method for identifying incomparable subgroups in IRT analysis, improving the detection of differential item functioning in political survey data.

Findings

Identified voter groups with different stimulus interpretations from legislators

Showed ignoring DIF can lead to incorrect assessments of representation quality

Demonstrated the effectiveness of the Dirichlet Process prior in IRT models

Abstract

A common approach when studying the quality of representation involves comparing the latent preferences of voters and legislators, commonly obtained by fitting an item-response theory (IRT) model to a common set of stimuli. Despite being exposed to the same stimuli, voters and legislators may not share a common understanding of how these stimuli map onto their latent preferences, leading to differential item-functioning (DIF) and incomparability of estimates. We explore the presence of DIF and incomparability of latent preferences obtained through IRT models by re-analyzing an influential survey data set, where survey respondents expressed their preferences on roll call votes that U.S. legislators had previously voted on. To do so, we propose defining a Dirichlet Process prior over item-response functions in standard IRT models. In contrast to typical multi-step approaches to detecting DIF, our strategy allows researchers to fit a single model, automatically identifying incomparable sub-groups with different mappings from latent traits onto observed responses. We find that although there is a group of voters whose estimated positions can be safely compared to those of legislators, a sizeable share of surveyed voters understand stimuli in fundamentally different ways. Ignoring these issues can lead to incorrect conclusions about the quality of representation.