Multidimensional item response theory models for testlet-based doubly bounded data

A testlet-based visual analogue scale (VAS) is a doubly bounded scaling approach (e.g., from 0% to 100% or from 0 to 1) composed of multiple adjectives, nouns, or sentences (statements/items) within testlets for measuring individuals' attitudes, opinions, or career interests. While testlet-based VASs have many advantages over Likert scales, such as reducing response style effects, the development of proper statistical models for analyzing testlet-based VAS data lags behind. This paper proposes a novel beta copula model and a competing logit-normal model based on the item response theory framework, assessed by Bayesian parameter estimation, model comparison, and goodness-of-fit statistics. An empirical career interest dataset based on a testlet-based VAS design was analyzed using the proposed models. Simulation studies were conducted to assess the two models' parameter recovery. The results show that the beta copula model had superior fit in the empirical data analysis, and also exhibited good parameter recovery in the simulation studies, suggesting that it is a promising statistical approach to testlet-based doubly bounded responses.