Dealing with Uncertainty about Item Parameters: Expected Response Functions
EDUCATIONAL TESTING SERVICE PRINCETON NJ
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It is a common practice in item response theory IRT to treat estimates of item parameters, say B, as if they were the known, true quantities, B. However, ignoring the uncertainty associated with item parameters can lead to biases and over-confidence in subsequent inferences such as ability estimation, especially when item-calibration samples are small. This paper demonstrates how to incorporate uncertainty about B with Lewiss expected response functions ERFs , pointwise expected values of item response conditional on examinee proficiency averaged over posterior distributions of item parameters. This paper presents ERFs, outlines procedures for computing them and using them in practical work, and gives an illustration with data from the national Assessment of Educational Progress. Advantages of approximating ERFs response curves with members of familiar parametric families of IRT curves are noted. Bayesian estimation, Expected response functions, Item response theory, Multiple imputation, Pseudolikelihood estimation.
- Statistics and Probability