Browsing by Author "Van den Wollenberg, Arnold L."

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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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    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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    Robustness of marginal maximum likelihood estimation in the Rasch model
    (1990) Zwinderman, Aeilko H.; Van den Wollenberg, Arnold L.
    Simulation studies examined the effect of misspecification of the latent ability (θ) distribution on the accuracy and efficiency of marginal maximum likelihood (MML) item parameter estimates and on MML statistics to test sufficiency and conditional independence. Results were compared to the conditional maximum likelihood (CML) approach. Results showed that if θ is assumed to be normally distributed when its distribution is actually skewed, MML estimators lose accuracy and efficiency when compared to CML estimators. The effects are not large, though they increase as the skewness of the number-correct score distribution increases. However, statistics to test the sufficiency and conditional independence assumptions of the Rasch model in the MML approach are very sensitive to misspecification of the θ distribution. Index terms: ability distribution, conditional likelihood, efficiency, goodness of fit, marginal likelihood, Rasch model, robustness.
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    A simple and effective method to test the dimensionality axiom of the Rasch model.
    (1982) Van den Wollenberg, Arnold L.
    A simple method is introduced to test the dimensionality axiom in the Rasch model. The method consists of a suitable partitioning of the data set. This partitioning is based on the responses to some of the items being investigated. The items used for this purpose are called the external criterion items. data are presented indicating the effectiveness of the method in instances where the traditional test procedures fail.