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In This Chapter
-
Missing Responses in Item Response Modeling
- Missing Responses in Item Response Theory
- Notation, Concepts, and General Results
- Notation
- Inference under Ignorability
- Definition 10.1
- Definition 10.2
- Definition 10.3
- Definition 10.4
- Definition 10.5
- Definition 10.6
- Theorem 10.1 (Rubin, 1976, p. 581)
- Inference When Missingness Is Not Ignorable
- Predictive Distributions for Missing Responses
- Markov Chain Monte Carlo Estimation
- Imputation for Missing Responses
- Theorem 10.2
- Definition 10.8
- Definition 10.9
- Definition 10.10 (Known-value imputation)
- Definition 10.11 (Expected-value imputation (or corrected mean imputation; Sijtsma and van der Ark, 2003))
- Definition 10.12 (Single imputation)
- Definition 10.13 (Multiple imputation (Rubin, 1987))
- Theorem 10.3
- Theorem 10.4 (Inference from multiple imputations (Rubin, 1987))
- Common Types of Missingness
- Random Assignment
- Targeted Testing
- Adaptive Testing
- Theorem 10.12
- Theorem 10.13 (Mislevy and Chang, 2000; Mislevy and Wu, 1996)
- Theorem 10.14
- Theorem 10.15
- Theorem 10.16
- Theorem 10.17
- Theorem 10.18
- Not-Reached Items
- Intentionally Omitted Items
- Definition 10.14 (Zwick, 1990)
- Scoring Rules, Omitting Behavior, and Ignorability
- Lord’s 1974 Recommendation
- Intentional Omits as an Additional Response Category
- Model v with Correctness and Missingness Processes
- Examinee Choice
- Item-Parameter Estimation
- Ignorability Results
- Full Bayesian Model
- Inference from Conditional-on-m Expected Likelihoods
- Specialized Models
- Conclusion
- References
Abstract
Missing responses occur in item response theory (IRT) applications in ways that may or may not have been intended by the examiner and may or may not be related to people’s ability ?. The mechanisms that produce missingness must be taken into account to draw correct inferences. This chapter addresses missingness in IRT through the lens of Rubin’s (1976, 1977) missing-data framework. Implications for Bayesian and likelihood estimation are discussed for (a) random assignment of items, including alternate test forms and matrix sampling, (b) targeted testing, including vertical linking, (c) adaptive testing, (d) not-reached items, (e) intentional omits, and (f) examinee choice of items.
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