A psychometric modeling approach to fuzzy rating data

TL;DR

This paper introduces a novel psychometric model using Item Response Theory trees to better understand and interpret fuzziness and uncertainty in human rating data, improving upon standard rating scales.

Contribution

It proposes a new fuzzy scaling procedure based on IRTrees that models response fuzziness through overall response patterns rather than single items.

Findings

The model effectively captures decision uncertainty in fuzzy rating data.

Simulation and empirical results demonstrate improved modeling of fuzziness.

The approach offers a consistent interpretation of rating imprecision.

Abstract

Modeling fuzziness and imprecision in human rating data is a crucial problem in many research areas, including applied statistics, behavioral, social, and health sciences. Because of the interplay between cognitive, affective, and contextual factors, the process of answering survey questions is a complex task, which can barely be captured by standard (crisp) rating responses. Fuzzy rating scales have progressively been adopted to overcome some of the limitations of standard rating scales, including their inability to disentangle decision uncertainty from individual responses. The aim of this article is to provide a novel fuzzy scaling procedure which uses Item Response Theory trees (IRTrees) as a psychometric model for the stage-wise latent response process. In so doing, fuzziness of rating data is modeled using the overall rater's pattern of responses instead of being computed using a single-item based approach. This offers a consistent system for interpreting fuzziness in terms of individual-based decision uncertainty. A simulation study and two empirical applications are adopted to assess the characteristics of the proposed model and provide converging results about its effectiveness in modeling fuzziness and imprecision in rating data.