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In non-speeded educational testing, the goal is to give students a generous time limit so that their response accuracy only depends on their ability and will not be affected by the time limit. Traditional IRT models do not consider the students’ response time. In our study, we consider extensions of the speed-accuracy hierarchical IRT models with the effect of response time on accuracy and select the best-fitting model by the deviance information criterion. Bayesian Markov chain Monte Carlo algorithm is used for parameter estimation. The results of our empirical study show that it is not indispensable to add the effect of response time on the accuracy, thus the current time limit provides students sufficient ability to choose their working speed.