A Multilevel Testlet Joint Model of Responses and Response Time

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In approaches to joint response and response time (RT) modeling there is an assumption of conditional independence of the responses and the RTs. Further, in IRT modeling of the responses, there is the assumption that the items and the persons have local independence, respectively. In practice, violations of the local item independence results from the bundling of items into testlets. Violation of the person independence are encountered in complex examinee sampling situations.

A multilevel testlet joint responses and RT model is proposed and evaluated in this study that accounts for the dual local item and person dependence due to testlets and complex sampling. A simulation study is performed to investigate parameter recovery for the proposed model and provide comparison to models that do not model dual local dependencies. In addition to the simulation study, a study using empirical data is also conducted to evaluate relative model fit indices.

Generally, results determined by statistical analyses and inspection of graphs developed from descriptive statistics supported the need to model local item dependency and local person dependency. Parameter recovery outcome measures in the simulation study showed interaction of factors included with the model factor when the comparison models were included. When deviance model fit criterion was applied the proposed model was selected as the best-fitting model. For the Bayesian model fit index DIC the proposed model was not selected as best-fitting in for either the simulation or the empirical data analyses. Limitations of the study and opportunities to refine joint response and RT modeling of this dual dependency were elaborated.