Sequential Estimation in Item Calibration with A Two-Stage Design

TL;DR

This paper introduces a two-stage sequential design method for item calibration under a three-parameter logistic model, accounting for measurement errors and ensuring estimates reach a desired accuracy, with theoretical and numerical validation.

Contribution

The paper presents a novel two-stage sequential calibration procedure that incorporates measurement errors and guarantees prescribed accuracy, improving upon conventional methods.

Findings

The proposed method achieves higher accuracy in parameter estimates.

Sequential design reduces the number of examinees needed.

Theoretical properties of the estimates are established.

Abstract

In this paper we apply a two-stage sequential design to item calibration problems under a three-parameter logistic model assumption. The measurement errors of the estimates of the latent trait levels of examinees are considered in our procedure. Moreover, a sequential procedure is employed to guarantee that the estimates of the parameters reach a prescribed accuracy criterion when the iteration is stopped, which fully takes the advantage of sequential design. Statistical properties of both the item parameter estimates and the sequential procedure are discussed. We compare the performance of the proposed method with that of the procedures based on some conventional designs using numerical studies.