Modeling Unfolding Response Data Within the Structural Equation Modeling Framework

Dominance and unfolding response processes describe two ways in which individuals may respond to rating scale items. The dominance process assumes a monotonic relationship between a latent trait and the probability of endorsement and is typically modeled using a linear factor model within structural equation modeling (SEM). In contrast, the unfolding process assumes single-peaked response functions, with endorsement most likely when item and person locations are close on the latent continuum. Fitting unfolding models usually requires specialized software, which limits their integration with SEM. In this article, we proposed the ordered categorical response unfolding model (OCRUM), which can be estimated in Mplus. We illustrated its use with two empirical datasets and found that item and person locations were comparable to those obtained from the generalized graded unfolding model (GGUM). We also conducted Monte Carlo simulations to examine parameter recovery under varying sample sizes, test lengths, and response formats. Finally, we demonstrated that OCRUM can serve as the measurement component of a general structural equation model, enabling dominance and unfolding response processes to be represented within a single SEM framework.