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Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing

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Pubblicato in:Psychometrika vol. 89, no. 1 (Mar 2024), p. 317
Autore principale: van Rijn, Peter W.
Altri autori: Ali, Usama S., Shin, Hyo Jeong, Joo, Sean-Hwane
Pubblicazione:
Springer Nature B.V.
Soggetti:
Statistics
Statistical inference
Models
Statistical analysis
Item Response Theory
Adaptive Testing
Accesso online:Citation/Abstract
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Abstract:The key assumption of conditional independence of item responses given latent ability in item response theory (IRT) models is addressed for multistage adaptive testing (MST) designs. Routing decisions in MST designs can cause patterns in the data that are not accounted for by the IRT model. This phenomenon relates to quasi-independence in log-linear models for incomplete contingency tables and impacts certain types of statistical inference based on assumptions on observed and missing data. We demonstrate that generalized residuals for item pair frequencies under IRT models as discussed by Haberman and Sinharay (J Am Stat Assoc 108:1435–1444, 2013. <ext-link xlink:href="https://doi.org/10.1080/01621459.2013.835660" ext-link-type="doi">https://doi.org/10.1080/01621459.2013.835660</ext-link>) are inappropriate for MST data without adjustments. The adjustments are dependent on the MST design, and can quickly become nontrivial as the complexity of the routing increases. However, the adjusted residuals are found to have satisfactory Type I errors in a simulation and illustrated by an application to real MST data from the Programme for International Student Assessment (PISA). Implications and suggestions for statistical inference with MST designs are discussed.
ISSN:0033-3123
1860-0980
DOI:10.1007/s11336-023-09935-4
Fonte:ABI/INFORM Global