A general framework for modeling missing data due to item selection with item response theory

In education testing, the items that examinees receive may be selected for a variety of reasons, resulting in missing data for items that were not selected. Item selection is internal when based on prior performance on the test, such as in adaptive testing designs or for branching items. Item selection is external when based on an auxiliary variable collected independently to performance on the test, such as education level in a targeting testing design or geographical location in a nonequivalent anchor test equating design. This paper describes the implications of this distinction for Item Response Theory (IRT) estimation, drawing upon missing-data theory (e.g., Mislevy & Sheehan, 1989, https://doi.org/10.1007/BF02296402; Rubin, 1976, https://doi.org/10.1093/biomet/63.3.581), and selection theory (Meredith, 1993, https://doi.org/10.1007/BF02294825). Through mathematical analyses and simulations, we demonstrate that this internal versus external item selection framework provides a general guide in applying missing-data and selection theory to choose a valid analysis model for datasets with missing data.