Abstract
Item response tree (IRTree) approaches have received increasing attention in the response style literature due to their capability to partial out response style latent traits from content-related latent traits by considering separate decisions for agreement and level of agreement. Additionally, it has shown that the functioning of the intensity of agreement decision may depend upon the agreement decision with an item, so that the item parameters and person parameters may differ by direction of agreement; when the parameters across direction are the same, this is called directional invariance. Furthermore, for non-cognitive psychological constructs, it has been argued that the response process may be best described as following an unfolding process. In this study, a family of IRTree models to handle unfolding responses with the agreement decision following the hyperbolic cosine model and the intensity of agreement decision following a graded response model is investigated. This model family also allows for investigation of item- and person-level directional invariance. A simulation study is conducted to evaluate parameter recovery; model parameters are estimated with a fully Bayesian approach using JAGS (Just Another Gibbs Sampler). The proposed modeling scheme is demonstrated with two data examples with multiple model comparisons allowing for varying levels of directional invariance and unfolding versus dominance processes. An approach to visualizing the final model item response functioning is also developed. The article closes with a short discussion about the results.