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A Monte Carlo Approach to the Design, Assembly, and Evaluation of Multistage Adaptive Tests

Law School Admission Council, dbelov{at}lsac.org, belovd{at}mail.ru

Ronald D. Armstrong

Rutgers, The State University of New Jersey

This article presents an application of Monte Carlo methods for developing and assembling multistage adaptive tests (MSTs). A major advantage of the Monte Carlo assembly over other approaches (e.g., integer programming or enumerative heuristics) is that it provides a uniform sampling from all MSTs (or MST paths) available from a given item pool. The uniform sampling allows a statistically valid analysis for MST design and evaluation. Given an item pool, MST model, and content constraints for test assembly, three problems are addressed in this study. They are (a) the construction of item response theory (IRT) targets for each MST path, (b) the assembly of an MST such that each path satisfies content constraints and IRT constraints, and (c) an analysis of the pool and constraints to increase the number of nonoverlapping MSTs that can be assembled from the pool. The primary intent is to produce reliable measurements and enhance pool utilization.

Key Words: computer adaptive testing • test assembly • Monte Carlo methods • item response theory • testlet • automated test assembly • test construction

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