Analyzing Responses and Response Times in Time-Limit Tests: A Mixture Cure-Rate Model Approach

• Activity Number: 165
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Committee on Applied Statisticians
• Author(s): Yi-Hsuan Lee*+ and Zhiliang Ying
• Companies: Educational Testing Service and Columbia University
• Keywords: survival analysis ; response time ; censoring ; cure model ; time limit ; power test

Abstract

Many large-scale standardized tests are intended to measure skills related to proficiency rather than the rate at which examinees can work. Time limits imposed on these tests make it difficult to distinguish between the effect of low proficiency and the effect of lack of time. This paper proposes a mixture cure-rate model approach to address this issue. Maximum likelihood estimation is proposed for parameter and variance estimation for three cases: when examinee parameters are to be estimated given precalibrated item parameters, when item parameters are to be calibrated given known examinee parameters, and when item parameters are to be estimated without assuming known examinee parameters. Large-sample properties are established for the cases under suitable regularity conditions. Simulation studies suggest that the proposed approach is appropriate for inferences concerning model parameters. In addition, not distinguishing the effect of low proficiency and the effect of lack of time is shown to have considerable consequences for parameter estimation. A real data example is presented to demonstrate the new model. Choice of survival models for the response times is also discussed.