Estimation of IRT Parameters over a Small Sample. Bootstrapping of the Item Responses

2000 Mathematics Subject Classification: 97C40.

Estimation of the parameters of the Item Response Theory model is reasonable only on a relatively large samples. Applying this methodology for small samples is a common problem in practice. In this paper a bootstrapping technique for a small samples is presented. Additional item responses are added to the original dataset, according to the posterior probability of the correct item response. The same is used in generation of additional items needed when the cognitive attributes are studied.