Variation in Respondent Speed and its Implications: Evidence from an Adaptive Testing Scenario

Bayesian hierarchical response time modelling-A tutorial

Response time modelling is developing rapidly in the field of psychometrics, and its use is growing in psychology. In most applications, component models for response times are modelled jointly with component models for responses, thereby stabilizing estimation of item response theory model parameters and enabling research on a variety of novel substantive research questions. Bayesian estimation techniques facilitate estimation of response time models. Implementations of these models in standard statistical software, however, are still sparse. In this accessible tutorial, we discuss one of the most common response time models-the lognormal response time model-embedded in the hierarchical framework by van der Linden (2007). We provide detailed guidance on how to specify and estimate this model in a Bayesian hierarchical context. One of the strengths of the presented model is its flexibility, which makes it possible to adapt and extend the model according to researchers' needs and hypotheses on response behaviour. We illustrate this based on three recent model extensions: (a) application to non-cognitive data incorporating the distance-difficulty hypothesis, (b) modelling conditional dependencies between response times and responses, and (c) identifying differences in response behaviour via mixture modelling. This tutorial aims to provide a better understanding of the use and utility of response time models, showcases how these models can easily be adapted and extended, and contributes to a growing need for these models to answer novel substantive research questions in both non-cognitive and cognitive contexts.

Investigating the Effect of Differential Rapid Guessing on Population Invariance in Equating

Score equating is an essential tool in improving the fairness of test score interpretations when employing multiple test forms. To ensure that the equating functions used to connect scores from one form to another are valid, they must be invariant across different populations of examinees. Given that equating is used in many low-stakes testing programs, examinees' test-taking effort should be considered carefully when evaluating population invariance in equating, particularly as the occurrence of rapid guessing (RG) has been found to differ across subgroups. To this end, the current study investigated whether differential RG rates between subgroups can lead to incorrect inferences concerning population invariance in test equating. A simulation was built to generate data for two examinee subgroups (one more motivated than the other) administered two alternative forms of multiple-choice items. The rate of RG and ability characteristics of rapid guessers were manipulated. Results showed that as RG responses increased, false positive and false negative inferences of equating invariance were respectively observed at the lower and upper ends of the observed score scale. This result was supported by an empirical analysis of an international assessment. These findings suggest that RG should be investigated and documented prior to test equating, especially in low-stakes assessment contexts. A failure to do so may lead to incorrect inferences concerning fairness in equating.