Combining Nonparametric and Parametric Item Response Theory to Explore Data Quality: Illustrations and a Simulation Study

Researchers who use measurement models for evaluation purposes often select models with stringent requirements, such as Rasch models, which are parametric. Mokken Scale Analysis (MSA) offers a theory-driven nonparametric modeling approach that may be more appropriate for some measurement applications. Researchers have discussed using MSA as a preliminary procedure with which to evaluate data quality before applying a parametric model. However, the literature includes only a few examples in which researchers have integrated MSA techniques with parametric models throughout the analytic procedure. We consider a systematic approach for integrating results from nonparametric MSA techniques with parametric measurement models to evaluate measurement quality and construct scales with useful measurement properties. We use real-data illustrations and a simulation study to demonstrate and systematically explore our approach. We discuss implications for research and practice.