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

Authors

Affiliations

Stefanie A. Wind

The University of Alabama

Benjamin Lugu

University of Arkansas

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.