The Research Of Item Response Models Based On Response Times

The times taken by subjects on items (response times, RTs) can be a valuable sourceof information on persons and items. However, for a long times, this information sourcecan not be used. The reason is that the recording of RTs is difficult in a conventionalpaper-and-pencil test. With the introduction of computer-based testing, the recording ofRTs on test items has become straightforward. Therefore, how to make full use of theinformation contained in RTs is a popular research issue in the educational and psycho-logical measurement nowadays. An important prerequisite for the use of informationprovided by data is to propose an appropriate statistical model for their distribution. Sofar, a lot of different models for RTs have been developed. However, there are someissues on the current models needed to further research. To solve these problems, thereare three item response theory (IRT) models that incorporates RT are developed in thispaper.We present a general framework for modeling response variable and RT variableon Likert–type personality items. The model framework consists of two submodels: onedescribes the item response data, and the other describes the RT data. The theoretical ba-sis for modeling is the generalized distance–difficulty hypothesis. Use of the frameworkis illustrated by employing the generalized partial credit model (GPCM) for responsesand a a log–normal model for RTs. Then, we propose using a two-stage procedure to es-timate the parameters in the model. Furthermore, a simulation study shows that this newmodel improves the accuracy of estimating the latent trait levels with the ancillary infor-mation contained in RTs. Finally, our approach is empirically studied by an empiricalexample in personality measurementsCurrent modeling of response times on test items has been strongly influenced bythe RTs research in experimental psychology. Some models measure speed by the ac-tual time spent on the item. Also, some models seem to be unclear as to the level ofparametrization they represent. As a matter of fact, these ideas are inappropriate for RTs on test items. Therefore, we develop a local joint model for item response variable andRT variable, and show how to estimate all of the parameters using a Gibbs samplingalgorithm. This model is able to have the flexibility to explain the local dependency be-tween speed and accuracy. We propose using the deviance information criterion (DIC)to investigate the value of this model. Then, we conducted two simulation studies toexplore the performance of the proposed Gibbs sampling scheme and the accuracy ofDIC. Finally, the joint model is empirically assessed in a rigorous way by an empiricalexample.The log–normal distribution has been a convenient choice in response time mod-elling on test items, and it has good results in terms of model fit. However, the log-transformed RTs of some test do not always satisfy the normality assumption. For in-stance, the RTs data from the Medical College Admission Test (MCAT). To solve thisproblem, we use the skew–normal distribution instead of the normal distribution to de-velop a log–skew–normal response times model. This model is more flexible. Becausethe skew normal distribution is more general than the normal distribution, an it containsthe normal density as a special case. Then, based on an efficient data augmentationscheme, a hybrid Markov chain Monte Carlo (MCMC) methods applied to this model isproposed. Finally, the results from a simulation studie and a real-data example are givento illustrate the excellence of the more general approach for modelling RTs.