Modeling Response Styles in Cross-Classified Data Using a Cross-Classified Multidimensional Nominal Response Model

In this study, we introduced a cross-classified multidimensional nominal response model (CC-MNRM) to account for various response styles (RS) in the presence of cross-classified data. The proposed model allows slopes to vary across items and can explore impacts of observed covariates on latent constructs. We applied a recently developed variant of the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm to address the computational challenge of estimating the proposed model. To demonstrate our new approach, we analyzed empirical student evaluation of teaching (SET) data collected from a large public university with three models: a CC-MNRM with RS, a CC-MNRM with no RS, and a multilevel MNRM with RS. Results indicated that the three models led to different inferences regarding the observed covariates. Additionally, in the example, ignoring/incorporating RS led to changes in student substantive scores, while the instructor substantive scores were less impacted. Misspecifying the cross-classified data structure resulted in apparent changes on instructor scores. To further evaluate the proposed modeling approach, we conducted a preliminary simulation study and observed good parameter and score recovery. We concluded this study with discussions of limitations and future research directions.