A penalized heteroskedastic ordered probit model for DIF (measurement invariance) testing of single-item assessments in cross-cultural research

TL;DR

This paper introduces a novel penalized heteroskedastic ordered probit model to test measurement invariance in single-item assessments, addressing a gap in DIF analysis for cross-cultural research.

Contribution

It proposes a new statistical approach for DIF/MI testing in single-item measures, which was previously unfeasible due to methodological limitations.

Findings

The model enables DIF testing with single-item assessments.

Current methods are still recommended when multiple items are available.

Single-item DIF testing is now possible with the proposed approach.

Abstract

Differential item functioning (DIF) or measurement invariance (MI) testing for single-item assessments has previously been impossible. Part of the issue is that there are no conditioning variables to serve as a proxy for the latent variable--regression-based DIF methods. Another reason is that factor-analytic approaches require multiple items to estimate parameters. In this technical working paper, I propose an approach for evaluating DIF/MI in a single-item assessment of a construct. The current methods should NOT replace using multiple-indicator MG-CFA/IRT analyses of DIF/MI or regression mased methods when possible. More items generally provide significantly better construct coverage and provide more rigorous DIF/MI evaluation.