A Mixture Response Time Process Model for Aberrant Behaviors and Item Nonresponses

Abstract

In high-stakes, large-scale, standardized tests with certain time limits, examinees are likely to engage in either one of the three types of behavior (e.g., van der Linden & Guo, 2008; Wang & Xu, 2015): solution behavior, rapid guessing behavior, and cheating behavior. Oftentimes examinees do not always solve all items due to various reasons such as time limit or test-taking strategy. Item nonresponses may happen due to intentionally omitting some items (omitted responses) or due to lack of time (not-reached responses). Both types are related to latent abilities and hence the missingness is nonignorable. In this article, we proposed an innovative mixture response time process model (1) to detect two most common aberrant behaviors: rapid guessing behavior and cheating behavior, and (2) to account for two types of item nonresponses: not-reached items and omitted items. The new model combines the two-stage approach of Wang et al. (2018) with Lu and Wang (2020) model. It also contains two steps: (1) a mixture response time process model is first fitted to the responses and response times data to distinguish normal and aberrant behaviors and to account for the missing data mechanism; and (2) a Bayesian residual index is used to further distinguish rapid guessing and cheating behaviors. Simulation results show that the two-stage method yields accurate item and person parameter estimates, as well as high detection of aberrant behaviors. A real data analysis was conducted to illustrate the potential application of the proposed method.