A mixture model for responses and response times with a higher‐order ability structure to detect rapid guessing behaviour

Jing Lü · Chun Wang · Jiwei Zhang · Jian Tao

39 citations0/0 files storedBritish Journal of Mathematical and Statistical Psychology

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Psychometric Methodologies and Testing Statistical Methods and Bayesian Inference Bayesian Methods and Mixture Models

Abstract

Many educational and psychological assessments focus on multidimensional latent traits that often have a hierarchical structure to provide both overall-level information and fine-grained diagnostic information. A test will usually have either separate time limits for each subtest or an overall time limit for administrative convenience and test fairness. In order to complete the items within the allocated time, examinees frequently adopt different test-taking behaviours during the test, such as solution behaviour and rapid guessing behaviour. In this paper we propose a new mixture model for responses and response times with a hierarchical ability structure, which incorporates auxiliary information from other subtests and the correlation structure of the abilities to detect rapid guessing behaviour. A Markov chain Monte Carlo method is proposed for model estimation. Simulation studies reveal that all model parameters could be recovered well, and the parameter estimates had smaller absolute bias and mean squared error than the mixture unidimensional item response theory (UIRT) model. Moreover, the true positive rate of detecting rapid guessing behaviour is also higher than when using the mixture UIRT model separately for each subscale, whereas the false detection rate is much lower than the mixture UIRT model. The deviance information criterion and the logarithm of the pseudo-marginal likelihood are employed to evaluate the model fit. Finally, a real data analysis is presented to demonstrate the practical value of the proposed model.

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References

2004Higher-Order Latent Trait Models for Cognitive Diagnosis 2005Response Time Effort: A New Measure of Examinee Motivation in Computer-Based Tests 2007A Hierarchical Framework for Modeling Speed and Accuracy on Test Items 1999A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models 2010Bayesian Item Response Modeling 1992Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling 1992A Didactic Explanation of Item Bias, Item Impact, and Item Validity From a Multidimensional Perspective 2006A Lognormal Model for Response Times on Test Items

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