Modeling the response style in continuous bounded responses: Model development and validation

Existing models, such as the item response tree (IRTree), have been extensively developed to analyze response styles in Likert-scale data. However, less attention has been given to questionnaires employing continuous measurement formats. These continuous bounded response formats include the visual analogue scale (VAS), slider bars, and probability judgments. We propose a novel item response model framework that leverages a hierarchical structure and constructs pseudo-responses. This framework enables the flexible incorporation of content traits, extreme response style (ERS), and midpoint response style (MRS), while isolating the effect of response style from observed responses. An empirical study was conducted to validate the ability of the new model to assess ERS and MRS. The results demonstrated that the model achieves a superior fit to continuous bounded response data and provides effective estimates of ERS and MRS. Furthermore, a simulation study was conducted to test the recovery of model parameters in various situations. The results demonstrated that the Markov chain Monte Carlo method can accurately estimate model parameters. In general, the trait of interest and response styles estimated by the new models demonstrate robust validity, and our models successfully mitigate the adverse effects of response styles on observed responses.