A Multidimensional Continuous Response Model for Measuring Unipolar Traits

Unipolar constructs are encountered in a variety of non-cognitive measurement scenarios that include clinical and forensic assessments, symptoms checklists, addictive behaviors, and irrational beliefs among others. Furthermore, Item Response Theory (IRT) models intended for fitting and scoring measures of unipolar constructs, particularly Log-Logistic models, are fully developed at present, but they are limited to unidimensional structures. This paper proposes a novel multidimensional log-logistic IRT model intended for double-bounded continuous response items that measure unipolar constructs. The chosen response format is a natural application, and is increasingly used, in the scenarios for which the model is intended. The proposed model is remarkably simple, has interesting properties and, at the structural level can be fitted by using linearizing transformations. Multidimensional item location and discrimination indices are developed, and procedures for fitting the model, scoring the respondents, and assessing conditional and marginal accuracy (including information curves) are proposed. Everything that is proposed has been implemented in fully available R program. The functioning of the model is illustrated by using an empirical example with the data of 371 undergraduate students who answered the Depression and Anxiety subscales of the Brief Symptom Inventory 18 and also the Rosenberg Self-Esteem Scale. The results show the usefulness of the new model to adequately interpret unipolar variables, particularly in terms of the conditional reliability of trait estimates and external validity.