Fuzzy Regression Analysis of fIRT-Tree-based data

Rating scales are common tools for gathering data in behavioral and social sciences. The selection of a response category is the result of a complex process involving cognitive, affective, and, contextual factors. As a result of the interplay among these factors, non- random and systematic components such as vagueness and imprecision can affect the final rating data. Unlike standard rating scales, fuzzy rating scales allow for the inclusion of respondents’ uncertainty in scaling outcomes. In this contribution we present fIRTree, a fuzzy-based formal representation for the imprecision associated to ratings data. This uses the compositional information measured using Item Response Theory trees (IRTrees), a psychometric model aim at representing individual’s pattern of responses by means of a latent tree structure. An application from behavioral and clinical context will be used in order to highlight the features of fIRTree and show how fuzzy ratings can be included in common statistical analyses, such as linear regression.