Modeling response granularity with mixture models: A case of severity ratings in child maltreatment

Heaping, where responses are concentrated in round numbers, such as 5 or 10, is one of the response behaviors observed in surveys. The heaping phenomenon in subjective quantities may be explained by response granularity, which expresses the uncertainty of subjective quantities. We conducted an exploratory study using mixture models with a response granularity assumption, and used the severity ratings of child maltreatment measured by slider scales with numerical feedback as a case of heaped subjective quantity (14,401 records from 487 respondents). The results of the model comparison showed that it was reasonable to assume a response granularity for severity ratings. We classified the respondents into five groups based on the uncertainty of response granularity because individual differences were observed. This study proposes the usefulness of an approach that utilizes mixture models to examine individual response granularity.