Work

Using Exact Tests from Algebraic Statistics in Sparse Multi-Way Analyses: An Application to Analyzing Differential Item Functioning

Year: 2024

Type: article

Abstract: Asymptotic goodness-of-fit methods in contingency table analysis can struggle with sparse data, especially in multi-way tables where it can be infeasible to meet sample size requirements for a robust application of distributional assumptions. However, algebraic statistics provides exact alternatives to these classical asymptotic methods that remain viable even with sparse data. We apply these methods to a context in psychometrics and education research that leads naturally to multi-way contingency tables: the analysis of differential item functioning (DIF). We explain concretely how to apply the exact methods of algebraic statistics to DIF analysis using the R package algstat, and we compare their performance to that of classical asymptotic methods.

Source: The American Statistician

DOI: 10.1080/00031305.2024.2388526

Authors: Shishir Agrawal, Luis David Garcia Puente, Minho Kim, Flavia Sancier-Barbosa

Institutions: University of California San Diego, Colorado College

Language: English

Topic: Psychometric Methodologies and Testing

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funder: National Science Foundation

Award: LEAPS-MPS: Foundational Connections in Number Theory, Coding Theory, Graphs, and Their Applications