Bayesian Joint Modeling of Response Times with Dynamic Latent Ability in Educational Testing

In educational testing, inferences of ability have been mainly based on item responses, while the time taken to complete an item is often ignored. To better infer the ability, a new class of state space models, which conjointly model response time with time series of dichotomous responses, is developed. Simulations for the proposed models demonstrate that the biases of ability estimation are reduced as well as the precisions of ability estimation are improved. An empirical study is conducted using EdSphere datasets, where the two competing relationships (i.e., monotone and inverted U-shape) for the distance between ability and difficulty are investigated in modeling response times. The results of model comparison support that the inverted U-shape relationship better captures the behaviors and psychology of examinees in exams for EdSphere datasets.