title: Non-ignorable missingness item response theory models for choice effects in examinee-selected items.
abstract: Examinee-selected item (ESI) design, in which examinees are required to respond to a fixed number of items in a given set, always yields incomplete data (i.e., when only the selected items are answered, data are missing for the others) that are likely non-ignorable in likelihood inference. Standard item response theory (IRT) models become infeasible when ESI data are missing not at random (MNAR). To solve this problem, the authors propose a two-dimensional IRT model that posits one unidimensional IRT model for observed data and another for nominal selection patterns. The two latent variables are assumed to follow a bivariate normal distribution. In this study, the mirt freeware package was adopted to estimate parameters. The authors conduct an experiment to demonstrate that ESI data are often non-ignorable and to determine how to apply the new model to the data collected. Two follow-up simulation studies are conducted to assess the parameter recovery of the new model and the consequences for parameter estimation of ignoring MNAR data. The results of the two simulation studies indicate good parameter recovery of the new model and poor parameter recovery when non-ignorable missing data were mistakenly treated as ignorable.
authors.affiliation: Department of Psychology, The Education University of Hong Kong, Hong Kong.
authors.forename: Chen-Wei
authors.initials: CW
authors.lastname: Liu
authors.affiliation: Department of Psychology, The Education University of Hong Kong, Hong Kong.
authors.forename: Wen-Chung
authors.identifier: http://orcid.org/0000-0001-6022-1567
authors.initials: WC
authors.lastname: Wang
mesh_terms: D002755:Choice Behavior; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004521:Educational Measurement / Q000379:methods* / Q000706:statistics & numerical data; D006801:Humans; D015233:Models, Statistical; D012044:Regression Analysis
keywords: choice effect; examinee-selected items; missing not at random; multidimensional item response theory