Conditions for rasch-dichotomizability of the unidimensional polytomous rasch model

Jansen and Roskam (1986) discussed the compatibility of the unidimensional polytomous Rasch model with dichotomization of the response continuum. They derived a rather strict condition in which dichotomization of multicategory data that fit the unidimensional polytomous Rasch model, results in dichotomous data which fit the dichotomous Research model with effectively the same subject parameter. In this paper a more general dichotomization condition is derived for the polytomous Rasch model, which appears less restrictive, but upholds that the intrinsic logic of the unidimensional polytomous Rasch model defies dichotomization in general. The robustness of dichotomous analysis investigated in a simulation study. It shows a close relation with the two-parameters (Birnbaum) model. Theoretical and methodological implications are discussed.The authors are indebted to H. Müller (personal communication, August 1986), for giving an example which pointed toward the core equation in this paper. The authors also acknowledge the critical comments of Th. Bezambinder and P. Wakker, and of Psychometrika's reviewers to an earlier version of this paper.     

Loglinear multidimensional IRT models for polytomously scored items

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.Hank Kelderman is currently affiliated with Vrije Universiteit, Amsterdam.We thank Linda Vodegel-Matzen of the Division of Developmental Psychology of the University of Amsterdam for making available the data used in the example in this article.     

THE EXISTENCE OF GOD AND THE CREATION OF THE UNIVERSE

Abstract. Kant argues that any argument for a transcendent God presupposes the logically flawed ontological argument. The teleological argument cannot satisfy the demands of reason for a complete explanation of the meaning and purpose of our universe without support from the cosmological argument. I avoid the assumption of a perfect being, and hence the ontological argument, in my version of the cosmological argument. The necessary being can be identified with the creator of the universe by adding analogical mental relations. The creation of the universe is then shown to reflect modern scientific cosmology as well as stories and metaphors in the Eastern and Western religious traditions and to resolve the problem of evil.     

低卷入情境中品牌远延伸的成功机制

品牌延伸是近年营销学界的一个研究热点。多数实证研究表明,母品牌认知、母品牌好感、延伸类别与母品牌类别之间的拟合度以及母品牌特定联想对品牌延伸评价有重要的影响作用。然而,已有理论在解释跨类别的远距离延伸的成功机制上比较乏力。本研究采用实证方法对这一点进行了补充。考虑到初始延伸评价所处的低卷入情境,概念层级较高的品牌相关变量在品牌远延伸评价中有重要的影响作用,本研究对三个品牌相关变量：品牌类别固着度、品牌抽象性与功能性特点、品牌声誉的主效应采用三个控制实验进行了测查。实验结果表明,较小的类别固着度,较高的品牌抽象性特点,以及较高的品牌声誉是品牌远延伸获得成功的机制保证。     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

基于项目节点的多级评分模型的统一

多级评分项目由于可以提供更多关于被试的信息而被广泛的使用。本文首先通过引用一个多级评分的数学试题, 给出了项目节点这一概念。假设被试在项目节点上的正确反应概率为二参数逻辑斯蒂模型之下, 本文通过分析三种不同类型的多级评分项目, 得出了三个评分模型, 其中一个和等级反应模型在形式上是一样的。鉴于我国目前考试测量所使用的多级评分项目的形式, 可以运用本文所述的项目节点的方法将项目评分模型统一提出。     

Paradoxes in Double Extension Set Theories

Three systems of double extension set theory have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs.     

Stochastic Ordering Of the Latent Trait by the Sum Score Under Various Polytomous IRT Models

The sum score is often used to order respondents on the latent trait measured by the test. Therefore, it is desirable that under the chosen model the sum score stochastically orders the latent trait. It is known that unlike dichotomous item response theory (IRT) models, most polytomous IRT models do not imply stochastic ordering. It is unknown, however, (1) whether stochastic ordering is often or rarely violated and (2) whether violations yield a serious problem for practical data analysis. These are the central issues of this paper. First, some unanswered questions that pertain to polytomous IRT models implying stochastic ordering were investigated. Second, simulation studies were conducted to evaluate stochastic ordering in practical situations. It was found that for most polytomous IRT models that do not imply stochastic ordering, the sum score can be used safely to order respondents on the latent trait.The author would like to thank Klaas Sijtsma for commenting on earlier drafts of this paper.