Stochastic ordering using the latent trait and the sum score in polytomous IRT models

In a restricted class of item response theory (IRT) models for polytomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait. MLR implies two stochastic ordering (SO) properties, denoted SOM and SOL, which are both weaker than MLR, but very useful for measurement with IRT models. Therefore, these SO properties are investigated for a broader class of IRT models for which the MLR property does not hold.In this study, first a taxonomy is given for nonparametric and parametric models for polytomous items based on the hierarchical relationship between the models. Next, it is investigated which models have the MLR property and which have the SO properties. It is shown that all models in the taxonomy possess the SOM property. However, counterexamples illustrate that many models do not, in general, possess the even more useful SOL property.Hemker's research was supported by the Netherlands Research Council, Grant 575-67-034. Junker's research was supported in part by the National Institutes of Health, Grant CA54852, and by the National Science Foundation, Grant DMS-94.04438.     

Residualanalysis in the polytomous rasch model

Residuals for check of model fit in the polytomous Rasch model are examined. Comparisons are made between using counts for all response pattern and using item totals for score groups for the construction of the residuals. Comparisons are also, for the residuals based on score group totals, made between using as basis the item totals, or using the estimated item parameters. The developed methods are illustrated by two examples, one from a psychiatric rating scale, one from a Danish Welfare Study.     

Essential independence and likelihood-based ability estimation for polytomous items

A definition ofessential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory ofessential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to change-of-scale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models (with or without ordered responses), anM-estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.This work was supported in part by Office of Naval Research Grant N00014-87-K-0277 and National Science Foundation Grant NSF-DMS-88-02556. The author is grateful to William F. Stout for many helpful comments, and to an anonymous reviewer for raising the questions addressed in section 2. A preliminary version of section 6 appeared in the author's Ph.D. thesis.     

A person-fit index for polytomous rasch models,latent class models,and their mixture generalizations

A normally distributed person-fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution IRT models for dichotomous and polytomous data.This article extends previous work on the null distribution of person-fit indices for the dichotomous Rasch model to a number of models for categorical data. A comparison of two different approaches to handle the skewness of the person-fit index distribution is included.Major parts of this paper were written while the first author worked at the Institute for Science Education, Kiel, Germany. Any opinions expressed in this paper are those of the authors and not necessarily of Educational Testing Service. The results presented in this paper were improved by valuable comments from J. Rost, K. Yamamoto, N.D. Verhelst, E. Bedrick and two anonymous reviewers.     

Multi‐Criteria Evaluation for Collaborative Circulating Farming with Collective Operations Between Arable and Cattle Farmers

Tokachi sub‐prefecture in Hokkaido is one of the most famous dairy and crop farming regions in Japan. It is known that Tokachi is faced with various difficult problems such as soil degradation, water contamination and unpleasant odours because of the excessive use of chemical fertilizers and inappropriate treatment of livestock excretion. In this paper, we focus on Shihoro town where agricultural outputs are relatively large in Tokachi, and propose collaborative circulating farming with collective operations between arable and cattle farmers. Under the assumption that the decision‐maker in this problem is a representative of a farming organization who hopes for sustainable agricultural development and values the intentions of local residents including arable and cattle farmers in this region, we employ multi‐attribute utility theory in order to evaluate multiple alternatives of the farming management problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Polytomous multilevel testlet models for testlet‐based assessments with complex sampling designs

A pplications of standard item response theory models assume local independence of items and persons. This paper presents polytomous multilevel testlet models for dual dependence due to item and person clustering in testlet‐based assessments with clustered samples. Simulation and survey data were analysed with a multilevel partial credit testlet model. This model was compared with three alternative models – a testlet partial credit model (PCM), multilevel PCM, and PCM – in terms of model parameter estimation. The results indicated that the deviance information criterion was the fit index that always correctly identified the true multilevel testlet model based on the quantified evidence in model selection, while the Akaike and Bayesian information criteria could not identify the true model. In general, the estimation model and the magnitude of item and person clustering impacted the estimation accuracy of ability parameters, while only the estimation model and the magnitude of item clustering affected the item parameter estimation accuracy. Furthermore, ignoring item clustering effects produced higher total errors in item parameter estimates but did not have much impact on the accuracy of ability parameter estimates, while ignoring person clustering effects yielded higher total errors in ability parameter estimates but did not have much effect on the accuracy of item parameter estimates. When both clustering effects were ignored in the PCM, item and ability parameter estimation accuracy was reduced.     

一种多级评分的广义认知诊断模型

认知诊断是近些年教育测量研究中的热点,大多数的认知诊断模型仅适用于0～1评分的情况.本文提出一种有多个潜变量多个滑动参数的多级评分认知诊断模型——GP-D1NA,只要由评分标准和知识状态能确定理想反应模式,就可以利用此方法进行认知诊断分析.在该方法中,我们给出项目滑动矩阵的概念,将被试的观测得分均看成由某个理想得分的滑动,并采用EM算法估计滑动矩阵.在模拟研究中,采用每掌握一个属性得1分的评分标准,结果表明线性型、收敛型、发散型、无结构型和独立型五种属性层级结构均有较高的判准率.     

Influence analysis of structural equation models with polytomous variables

The estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures. However, sensitivity or influence analysis of the model is not well studied. We demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables; and we develop appropriate procedures based on the local influence approach of Cook (1986). The proposed procedures are computationally efficient, the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model. We consider the influence of an individual cell frequency with respect to three cases: when all parameters in an unstructured model are of interest, when the unstructured polychoric correlations are of interest, and when the structural parameters are of interest. We also consider the sensitivity of the parameters estimates. Two examples based on real data are presented for illustration.The work described in this paper was partially supported by a Chinese University of Hong Kong Postdoctoral Fellows Scheme and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC Ref. No. CUHK4186/98P). We are indebted to P.M. Bentler and M.D. Newcomb for providing the data set, Michael Leung for his assistance, and the Editor and the referees for some very valuable comments.     

An experimental analysis of decision channeling by restrictive information display

This study focuses on the effect of restrictive information display on decision performance. Specifically the study examines whether two‐channeled and one non‐channeled computerized information display systems result in significant differences in decision accuracy. The two‐channeled information display systems are designed to encourage two general information processing patterns commonly observed in the experimental literature examining multi‐alternative, multi‐attribute choice decisions: information processing by alternative and information processing by attribute. An information display program was developed which used restrictive information display to operationalize the channeled versus non‐channeled manipulation. Channeling was implemented either by displaying information only by alternative or by displaying information only by attribute. The task was an operations scheduling problem that subjects completed under three levels of time pressure. The results indicate statistically significant effects on decision accuracy for both the type of information display and time pressure manipulations. The highest decision accuracy was observed when information was displayed by alternative and when subjects were under highest levels of time pressure. Copyright © 2002 John Wiley & Sons, Ltd.     

多级属性Q矩阵的验证与估计

多级属性是将诊断测验中传统的二值(即两种水平, 通常定义为0和1)属性定义为多值(多个水平可以为0, 1, …), 它不但可以描述学生对于知识属性是否掌握, 而且可以描述学生在属性上的掌握程度, 这样使得诊断测验能提供给被试更丰富的知识掌握详情。本文将适用于二级属性Q矩阵的统计量(S统计量)拓展到多级属性下的Q矩阵验证和估计, 在两种常见的条件下, 设计了两种估计算法：联合估计算法和在线估计算法。模拟实验结果表明：联合估计算法适用于对专家界定的初始Q矩阵进行验证, 当初始Q矩阵中包含较少的错误时, 通过联合估计算法有很大可能恢复正确的Q矩阵; 在线估计算法适用于对“新项目”进行属性向量和项目参数的在线标定, 基于一定数量的“基础项目”, 在线估计算法对于新项目的估计也能达到较满意的成功率。实证数据分析则进一步展示了该方法的使用。