Exploring the Robustness of a Unidimensional Item Response Theory Model With Empirically Multidimensional Data

• Published in: Applied measurement in education Vol. 30; no. 3; pp. 163 - 177
• Main Authors: Anderson, Daniel, Kahn, Joshua D., Tindal, Gerald
• Format: Journal Article
• Language: English
• Published: Philadelphia Routledge 03-07-2017; Taylor & Francis Ltd
• Subjects: Educational tests & measurements; Factor Analysis; Grade 6; Grade 7; Grade 8; Item Response Theory; Mathematics Tests; Maximum Likelihood Statistics; Robustness (Statistics)
• ISSN: 0895-7347; 1532-4818
• DOI: 10.1080/08957347.2017.1316277

Unidimensionality and local independence are two common assumptions of item response theory. The former implies that all items measure a common latent trait, while the latter implies that responses are independent, conditional on respondents' location on the latent trait. Yet, few tests are truly unidimensional. Unmodeled dimensions may result in test items displaying dependencies, which can lead to misestimated parameters and inflated reliability estimates. In this article, we investigate the dimensionality of interim mathematics tests and evaluate the extent to which modeling minor dimensions in the data change model parameter estimates. We found evidence of minor dimensions, but parameter estimates across models were similar. Our results indicate that minor dimensions outside the primary trait have negligible consequences on parameter estimates. This finding was observed despite the ratio of multidimensional to unidimensional items being above previously recommended thresholds.