Assessing Dimensionality by Maximizing H Coefficient–Based Objective Functions

Abstract

Mokken scale analysis can be used for scaling under nonparametric item response theory models. The results may, however, not reflect the underlying dimensionality of data. Various features of Mokken scale analysis-the H coefficient, Mokken scale conditions, and algorithms-may explain this result. In this article, three new H-based objective functions with slight reformulations of Mokken scale analysis in the unidimensional and multidimensional cases are introduced. Deterministic and stochastic nonhierarchical clustering algorithms reduced the probability of obtaining suboptimal solutions. A simulation study investigated whether these methods can determine the dimensionality structure of data sets that vary with respect to item discrimination, item difficulty, number of items per trait, and numbers of observations per test. Furthermore, it was investigated whether deterministic and stochastic algorithms can generate approximately global optimal solutions. The method based on the average within-scale H i combined with a stochastic nonhierarchical clustering algorithm was the most successful in dimensionality assessment.

Exploratory Mokken Scale Analysis as a Dimensionality Assessment Tool

“…In particular, those studies revealed that MSA does not function well in conditions in which the traits correlate (Mroch & Bolt, 2006; van Abswoude et al, 2004), or in which the items load on more than one trait (van Abswoude et al, 2004). Although those test conditions are the rule rather than the exception in empirical practice (van Abswoude, Vermunt, & Hemker, 2007), after publication of these articles, numerous researchers have still used MSA as a dimensionality assessment tool (e.g., Bech, Fava, Trivedi, Wisniewski, & Rush, 2011; Chen, Tseng, Hu, & Koh, 2010; Doyle, Conroy, McGee, & Delaney, 2010; Emons et al, 2010; Koster et al, 2009; Meijer et al, 2011; Ordoñez, Ponsoda, Abad, & Romero, 2009; Roorda, Houwink, Smits, Molenaar, & Geurts, 2011; Sousa et al, 2010). Furthermore, MSA is still recommended to assess unidimensionality (Sijtsma et al, 2011).…”