A Beta Mixture Model for Careless Respondent Detection in Visual Analogue Scale Data

Visual Analogue scales (VASs) are increasingly popular in psychological, social, and medical research. However, VASs can also be more demanding for respondents, potentially leading to quicker disengagement and a higher risk of careless responding. Existing mixture modeling approaches for careless response detection have so far only been available for Likert-type and unbounded continuous data but have not been tailored to VAS data. This study introduces and evaluates a model-based approach specifically designed to detect and account for careless respondents in VAS data. We integrate existing measurement models for VASs with mixture item response theory models for identifying and modeling careless responding. Simulation results show that the proposed model effectively detects careless responding and recovers key parameters. We illustrate the model's potential for identifying and accounting for careless responding using real data from both VASs and Likert scales. First, we show how the model can be used to compare careless responding across different scale types, revealing a higher proportion of careless respondents in VAS compared to Likert scale data. Second, we demonstrate that item parameters from the proposed model exhibit improved psychometric properties compared to those from a model that ignores careless responding. These findings underscore the model's potential to enhance data quality by identifying and addressing careless responding.