Browsing by Author "Meijer, Rob R."

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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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    The influence of the presence of deviant item score patterns on the power of a person-fit statistic
    (1996) Meijer, Rob R.
    Studies investigating the power of person-fit statistics often assume that the item parameters that are used to calculate the statistics are estimated in a sample without misfitting item score patterns. However, in practical test applications calibration samples likely will contain such patterns. In the present study, the influence of the type and the number of misfitting patterns in the calibration sample on the detection rate of the ZU3 statistic was investigated by means of simulated data. An increase in the number of misfitting simulees resulted in a decrease in the power of ZU3. Furthermore, the type of misfit and the test length influenced the power of ZU3. The use of an iterative procedure to remove the misfitting patterns from the dataset was investigated. Results suggested that this method can be used to improve the power of ZU3. Index terms: aberrance detection, appropriateness measurement, nonparametric item response theory, person fit, person-fit statistic ZU3.
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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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    The number of Guttman errors as a simple and powerful person-fit statistic
    (1994) Meijer, Rob R.
    A number of studies have examined the power of several statistics that can be used to detect examinees with unexpected (nonfitting) item score patterns, or to determine person fit. This study compared the power of the U3 statistic with the power of one of the simplest person-fit statistics, the sum of the number of Guttman errors. In most cases studied, (a weighted version of) the latter statistic performed as well as the U3 statistic. Counting the number of Guttman errors seems to be a useful and simple alternative to more complex statistics for determining person fit. Index terms: aberrance detection, appropriateness measurement, Guttman errors, nonparametric item response theory, person fit.
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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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    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.