Bayesian Inference Of Hidden Markov Item Response Theory Models For Responses And Response Times

In education and psychometrics,examinee response and response time are the key research objects of educational psychometrics.They provide important information in assessing subjects’ abilities and in analyzing test items.In educational test,examinees often show different answer states: solution behavior and rapid guessing behavior.Mixture hierarchical model can analyze the two states;but it does not consider the relationship between states of responses.For example,when subjects guess an item,they were more likely to guess the next item.Whether subjects with higher ability are more likely to show solution behavior.Based on these problems,this paper proposes a hidden Markov IRT model for responses and response times to solve the problem of state transition.In many test data,missing response data often appears.In most cases,the loss of response data is non-random.The subjects with low ability are more likely to miss the response.Deleting the missing response data will lead to biased parameter estimation results,which will seriously affect the statistical inference.This paper constructed a two-parameter Logistic model for Nonignorable missing of response data,described the correlation between the subject trait parameters in the deletion model and the ability parameters in the Hidden Markov Item Response Theory(IRT)model.Based on the above model,slice sampling algorithm,Gibbs sampling algorithm and Metropolis-Hastings algorithm are used to estimate parameters in the Bayesian framework.The convergence and stability of the algorithm under different sample sizes were examined through different simulation design,and the parameter fitting effect was evaluated,so as to analyze the changing process of examinee’s answer status.Finally,an example is given to verify the value of the proposed model in practice.