Browsing by Author "Sijtsma, Klaas"

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    Influence of Test and Person Characteristics on Nonparametric Appropriateness Measurement
    (1994) Meijer, Rob R.; Molenaar, lvo W.; Sijtsma, Klaas
    Appropriateness measurement in nonparametric item response theory modeling is affected by the reliability of the items, the test length, the type of aberrant response behavior, and the percentage of aberrant persons in the group. The percentage of simulees defined a priori as aberrant responders that were detected increased when the mean item reliability, the test length, and the ratio of aberrant to nonaberrant simulees in the group increased. Also, simulees "cheating" on the most difficult items in a test were more easily detected than those "guessing" on all items. Results were less stable across replications as item reliability or test length decreased. Results suggest that relatively short tests of at least 17 items can be used for person-fit analysis if the items are sufficiently reliable. Index terms: aberrance detection, appropriateness measurement, nonparametric item response theory, person-fit, person-fit statistic U3.
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    A method for investigating the intersection of item response functions in Mokken's nonparametric IRT model
    (1992) Sijtsma, Klaas; Meijer, Rob R.
    For a set of k items having nonintersecting item response functions (IRFs), the H coefficient (Loevinger, 1948; Mokken, 1971) applied to a transposed persons by items binary matrix Hт has a non-negative value. Based on this result, a method is proposed for using Hт to investigate whether a set of IRFs intersect. Results from a monte carlo study support the proposed use of Hт. These results support the use of Hт as an extension to Mokken’s nonparametric item response theory approach. Index terms: double monotonicity, Hт coefficient, intersection of item response functions, item response theory, Mokken models, nonparametric models.
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    Rejoinder to "The Mokken scale: A critical discussion."
    (1986) Mokken, Robert J.; Lewis, Charles; Sijtsma, Klaas
    The nonparametric approach to constructing and evaluating tests based on binary items proposed by Mokken has been criticized by Roskam, van den Wollenberg, and Jansen. It is contended that their arguments misrepresent the objectives of this approach, that their criticisms of the role of the H coefficient in the procedures are irrelevant or erroneous, and that they fail to distinguish the inherent requirements (and limitations) of general nonparametric models and procedures from those of parametric ones. It is concluded that Mokken’s procedures provide a useful tool for researchers in the social sciences who wish to construct and evaluate tests for measuring theoretically meaningful latent traits while avoiding the strong parametric assumptions of traditional item response theory.
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    Reliability estimation for single dichotomous items based on Mokken's IRT model
    (1995) Meijer, Rob R.; Sijtsma, Klaas; Molenaar, Ivo W.
    Item reliability is of special interest for Mokken’s nonparametric item response theory, and is useful for the evaluation of item quality in nonparametric test construction research. It is also of interest for nonparametric person-fit analysis. Three methods for the estimation of the reliability of single dichotomous items are discussed. All methods are based on the assumptions of nondecreasing and nonintersecting item response functions. Based on analytical and monte carlo studies, it is concluded that one method is superior to the other two, because it has a smaller bias and a smaller sampling variance. This method also demonstrated some robustness under violation of the condition of nonintersecting item response functions. Index terms: item reliability, item response theory, Mokken model, nonparametric item response models, test construction.
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    Selection of unidimensional scales from a multidimensional item bank in the polytomous Mokken IRT model
    (1995) Hemker, Bas T.; Sijtsma, Klaas; Molenaar, Ivo W.
    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.
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    Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT
    (1990) Meijer, Rob R.; Sijtsma, Klaas; Smid, Nico G.
    The Mokken model of monotone homogeneity, the Mokken model of double monotonicity, and the Rasch model are theoretically and empirically compared. These models are compared with respect to restrictiveness to empirical test data, properties of the scale, and accuracy of measurement. Application of goodness-of-fit procedures to empirical data largely confirmed the expected order of the models according to restrictiveness: Almost all items were in concordance with the model of monotone homogeneity, and fewer items complied with the model of double monotonicity and the Rasch model. The model of monotone homogeneity was found to be a suitable alternative to more restrictive models for basic testing applications; more sophisticated applications, such as equating and adaptive testing, appear to require the use of parametric models. Index terms: goodness-of-fit, item response theory, measurement properties, Mokken model, Rasch model.