A Family of Cognitive Diagnosis Models for Continuous Bounded Responses

Continuous bounded responses in psychometrics usually come from the visual analog scale (VAS). The VAS is a rating scale measurement tool that requires respondents to report their agreement with items by tracing a mark somewhere on a fixed-length continuous horizontal segment with ends that are generally labeled “0% disagreement” to “100% agreement” (or other possible labeling) using continuous data. In recent years, the VAS has gradually appeared in medical, educational, and psychological research, such as research on pain, worry, rumination, anxiety, risk perception, and even personality trait measurement. However, there are very few cognitive diagnosis models (CDMs) in cognitive diagnostic assessment that can analyze such continuous bounded data from VAS-type scale. In this study, we propose a family of CDMs for the continuous bounded data in VAS-type scale and provide model selection methods for practice. Three simulation studies were used to examine parameter recovery, the impact of model misspecification on parameter recovery, and the effectiveness of the model selection method. Moreover, real data are used as an illustration to demonstrate the application and effectiveness of the proposed models.