An automated item selection procedure for selecting
unidimensional scales of polytomous items from multidimensional
datasets is developed for use in the context
of the Mokken item response theory model of monotone
homogeneity (Mokken & Lewis, 1982). The selection
procedure is directly based on the selection procedure
proposed by Mokken (1971, p. 187) and relies heavily
on the scalability coefficient H (Loevinger, 1948;
Molenaar, 1991). New theoretical results relating the
latent model structure to H are provided. The item selection
procedure requires selection of a lower bound
for H. A simulation study determined ranges of H for
which the unidimensional item sets were retrieved from
multidimensional datasets. If multidimensionality is
suspected in an empirical dataset, well-chosen lower
bound values can be used effectively to detect the unidimensional
scales. Index terms: item response theory,
Mokken model, multidimensional item banks, nonparametric
item response models, scalability coefficient H,
test construction, unidimensional scales.
Hemker, Bas T.; Sijtsma, Klaas; Molenaar, Ivo W..
Selection of unidimensional scales from a multidimensional item bank in the polytomous Mokken IRT model.
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