Stochastic programming for individualized test assembly with mixture response time models

The Law School Admission Council (LSAC) is a nonprofit corporation that provides unique, state-of-the-art products and services to ease the admission process for law schools and their applicants worldwide. Currently, 222 law schools in the United States, Canada, and Australia are members of the Council and benefit from LSAC's services. All law schools approved by the American Bar Association are LSAC members. Canadian law schools recognized by a provincial or territorial law society or government agency are also members. Accredited law schools outside of the United States and Canada are eligible for membership at the discretion of the LSAC Board of Trustees; Melbourne Law School, the University of Melbourne is the first LSAC-member law school outside of North America. Many nonmember schools also take advantage of LSAC's services. For all users, LSAC strives to provide the highest quality of products, services, and customer service. Founded in 1947, the Council is best known for administering the Law School Admission Test (LSAT ®), with about 100,000 tests administered annually at testing centers worldwide. LSAC also processes academic credentials for an average of 60,000 law school applicants annually, provides essential software and information for admission offices and applicants, conducts educational conferences for law school professionals and prelaw advisors, sponsors and publishes research, funds diversity and other outreach grant programs, and publishes LSAT preparation books and law school guides, among many other services. LSAC electronic applications account for 98 percent of all applications to ABA-approved law schools. This study is published and distributed by LSAC. The opinions and conclusions contained in this report are those of the author(s) and do not necessarily reflect the position or policy of LSAC. Executive Summary Many standardized tests are now administered via computer rather than paper and pencil. The computer-based delivery mode brings with it certain advantages, such as the ability to record not only the test taker's response to each item (i.e., question), but also the amount of time the test taker spends considering and answering each item. The analysis of response times (RTs) is still a developing area of research. Early RT research assumed that a test taker would show consistent RTs over the course of a test. Such models may be unrealistic for various reasons—some items require more time than others to answer, a warm-up effect may cause a test taker to respond more quickly after completing the early items, fatigue may cause a test …