Bayesian Tests For Aberrant Behavior Based On The Box-Cox Response Time Modeling

In recent years,with the widely application of computer technology and the rapid development of educational measurement theory,many standardized tests have replaced the traditional paper-and-pencil examination format,rely on computer-based testing(CBT).CBT has many advantages,it can not only provide feedback immediately,but also record response time of each subjects.Item response time is very important information resources deserved to study,it is closely connected with the speed of the subjects,test strategy,the difficulty of item and the property of the examination.This study focuses on how to use the response time to identify the aberrant behavior of the test-taker.There are different forms of aberrant behavior,for example,a test-taker answers a difficult question within a very short response time,we can guess the test-taker has preknowledge of the items.Another example if the test-taker displays short response times for the back part of the items,it may indicate the test-taker has run out of time.In this paper,we propose the Bayesian test method to identify the aberrant behavior.We improve the commonly used lognormal response time model,propose the Box-Cox response time model,and prove that the Box-Cox normal response time model is better.In the simulation study,the estimation of the model parameters adopted Markov chain Monte Carlo(MCMC)algorithm,put the estimated value of the parameters into the person-fit test statistics then determine whether flagged.Finally,the two models are compared by the data analysis of the type?error and the type ?error.