Stochastic programming for individualized test assembly with mixture response time models

Early research on response time modeling assumed that a test taker would show consistent response time behavior, often referred to as working speed, over the course of a test. Such models may be unrealistic for various reasons — a warm-up effect may cause a test taker to respond more slowly than expected to the early items, fatigue may cause a test taker to respond more slowly than expected toward the end of a test, or as time runs out the test taker may quickly guess the answers to the last items on a test. To take these variations in working speed into account, mixture response time models have recently been investigated. Until now, mixture response time models have only been applied for post hoc analyses. This research expands the use of these models by exploring their application in the context of the assembly of individualized computer-based assessments (CBAs). Response time constraints are probabilistic in nature. Stochastic programming was compared to three existing strategies for dealing with probabilistic constraints. Stochastic programming proved to be a very suitable strategy for solving test assembly problems with mixture response time models. Using stochastic programming, computer-based tests could be assembled in such a way that response time information could be used to the fullest extent.