Using Response Times and Response Accuracy to Measure Fluency Within Cognitive Diagnosis Models

The recent "Every Student Succeed Act" encourages schools to use an innovative assessment to provide feedback about students' mastery level of grade-level content standards. Mastery of a skill requires the ability to complete the task with not only accuracy but also fluency. This paper offers a new sight on using both response times and response accuracy to measure fluency with cognitive diagnosis model framework. Defining fluency as the highest level of a categorical latent attribute, a polytomous response accuracy model and two forms of response time models are proposed to infer fluency jointly. A Bayesian estimation approach is developed to calibrate the newly proposed models. These models were applied to analyze data collected from a spatial rotation test. Results demonstrate that compared with the traditional CDM that using response accuracy only, the proposed joint models were able to reveal more information regarding test takers' spatial skills. A set of simulation studies were conducted to evaluate the accuracy of model estimation algorithm and illustrate the various degrees of model complexities.