Browsing by Author "Jansen, Paul G. W."

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    Consistency of Rasch model parameter estimation: A simulation study
    (1988) Van den Wollenberg, Arnold L.; Wierda, Folkert W.; Jansen, Paul G. W.
    It is shown in this paper that the unconditional or simultaneous maximum likelihood estimation procedure for the one-parameter logistic model gives rise to biased estimators. This bias cannot be removed by a correction factor (K - 1)/K (where K is the number of items), contrary to the contention of several authors. The bias is dependent not only on the number of items, but also on the distribution of the item parameters, which makes correcting for bias practically impossible. Furthermore, it is shown that the minimum chi-square estimation procedure, as introduced by Fischer, results in unbiased estimates. In addition, this method is computationally fast, so that it seems to be a good alternative for CML estimation when the latter method meets practical impediments. Index terms: Maximum likelihood estimation, conditional; Maximum likelihood estimation, unconditional; Minimum chi-square estimation; One-parameter logistic model; Rasch model.
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    Correcting unconditional parameter estimates in the Rasch model for inconsistency
    (1988) Jansen, Paul G. W.; Van den Wollenberg, Arnold L.; Folkert W., Folkert W.
    Results of simulation studies indicate that the unconditional maximum likelihood method is commonly regarded as an appropriate substitute for the theoretically superior conditional method for estimating the parameters of the Rasch model. To this end, the unconditional estimates are "corrected" by a factor (K - 1)/K, where is the number of items. In this paper, the simulation study of Wright and Douglas (1977b), which seemed to corroborate this correction term, is critically discussed. It appears to contain a puzzling assumption, and to rest on inadequate logic. Accordingly, there is a need for new simulation studies on the validity of the correction term (K − 1)/K for unconditional maximum likelihood estimation in the Rasch model. Index terms: Item response theory, item parameter estimation; Item response theory, one-parameter logistic model; Maximum likelihood estimation, unconditional; One-parameter logistic model; Rasch model.
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    The Mokken scale: A critical discussion
    (1986) Roskam, Edward E.; Van den Wollenberg, Arnold L.; Jansen, Paul G. W.
    The Mokken scale is critically discussed. It is argued that Loevinger’s H, adapted by Mokken and advocated as a coefficient of scalability, is sensitive to properties of the item set which are extraneous to Mokken’s requirement of holomorphy of item response curves. Therefore, when defined in terms of H, the Mokken scale is ambiguous. It is furthermore argued that item-selection free statistical inferences concerning the latent person order appear to be insufficiently based on double monotony alone, and that the Rasch model is the only item response model fulfilling this requirement. Finally, it is contended that the Mokken scale is an unfruitful compromise between the requirements of a Guttman scale and the requirements of classical test theory.
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    Relationships between the Thurstone, Coombs, and Rasch approaches to item scaling
    (1984) Jansen, Paul G. W.
    Andrich (1978) derived a formal equivalency between Thurstone’s Case V specialization of the law of comparative judgment for paired comparisons, with a logistic function substituted for the normal, and the Rasch model for direct responses. The equivalency was corroborated by a specific substantial-psychological interpretation of the Rasch binary item response probability. Studying the relationships between the Thurstone and Rasch models from another perspective than Andrich’s, namely, from a data-theoretical point of view, it appears that the equivalency is based on an implicit assumption with respect to the subject population. This assumption (1) is rather restrictive, and therefore its empirical validity seems to be low, and (2) seems to contradict the substantial reasoning corroborating the Thurstone-Rasch equivalency. It is argued that the Thurstone model cannot be considered the sample-independent pair comparison counterpart of the Rasch model. An alternative pair comparison equivalent of the Rasch model is tentatively proposed. Finally, the theoretical and practical implications of Andrich’s and of the present study are discussed.