Optimal sampling design for IRT linking with bimodal data

Abstract

Optimal sampling designs for an IRT linking with improved efficiency are often sought in analyzing assessment data. In practice, the skill distribution of an assessment samplemay be bimodal, and this warrants special considerationwhen trying to create these designs. In this study we explore optimal sampling designs for IRT linking of bimodal data. Our design paradigm is modeled to gain the efficiency in linking and equating in analyzing assessment data and presents a formal setup for optimal IRT linking. In an optimal sampling design, the sample structure of bimodal data is treated as being drawn from a stratified population. The optimum search algorithmproposed is used to adjust the stratum weights and form a weighted compound sample that minimizes linking errors. The initial focus of the current study is the robust mean–mean transformation method, though the model of IRT linking under consideration is adaptable to generic methods.