The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.     

分时距认知特点的研究

本研究探讨了分时距估计的认知特点,检验了SS模型、PT模型和CS模型的预测效度,结果表明：分时距估计主要是在信息提取阶段采用分段推算策略对时间信息进行重建的过程,变化／分割和注意分配对分时距估计有显著影响;SS模型的预测效度最低,PT、CS模型的预测效度较高。     

小学儿童对习俗时间的周期性特点的认知

本研究探讨了小学儿童对习俗时间周期性特点的认知发展．实验任务是让被试判断两个给定日期之间的时间距离是正向接近还是反向接近。结果表明:儿童对习俗时间的周期性特点的认知成绩随年龄增长而不断提高;随着两个日期之间距离的增大,反应时不断增加,正确率不断降低,在两个日期相互接近的方向发生改变的边界处,反应时最长,正确率最低,表现出显著的“距离效应”和“边界效应”;儿童可以利用数字系统进行判断,他们的认知加工策略包括计数、数字运算和凭借习俗时间的空间表象进行模拟加工等等。     

Separability of item and person parameters in response time models

This paper discusses two forms of separability of item and person parameters in the context of response time (RT) models. The first is separate sufficiency: the existence of sufficient statistics for the item (person) parameters that do not depend on the person (item) parameters. The second is ranking independence: the likelihood of the item (person) ranking with respect to RTs does not depend on the person (item) parameters. For each form a theorem stating sufficient conditions, is proved. The two forms of separability are shown to include several (special cases of) models from psychometric and biometric literature. Ranking independence imposes no restrictions on the general distribution form, but on its parametrization. An estimation procedure based upon ranks and pseudolikelihood theory is discussed, as well as the relation of ranking independence to the concept of double monotonicity.I am indebted to Wim van der Linden for bringing Thissen's (1983) paper to my notice, and to Martijn Berger, Frans Tan, and the anonymous reviewers for their constructive comments on earlier drafts of this paper.     

Exploring the set-theoretical structure of objects by additive trees

Arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects are shown to generate identical sets of set-symmetric distances. The set-symmetric distances for these feature arrangements can be represented by path lengths in an additive linear tree. Imperfect versions of these feature arrangements are proposed, which also are indistinguishable by the set-symmetric distance model. The distances for the imperfect versions can be represented by path lengths in an additive imperfectly linear tree. When dissimilarities are defined by the more general contrast model and a constant may be added to proximity data, then for both the perfect and imperfect arrangements an additive tree analysis obtains a perfect fit with an imperfectly linear tree. However, in the case of the contrast model also the distinction between the perfect and imperfect arrangements disappears in that also for the perfect arrangements the resulting tree need no longer be linear.The author is grateful to Mathieu Koppen for detailed comments on an earlier version of this article.     

运用规则空间模型识别解题中的认知错误

运用规则空间模型识别学生解题中的认知错误,该模型将认知心理学,项目反应理论和数据库的代数理论相结合,将被试的二值反应模式映射为笛卡尔乘积空间的一组序偶,然后计算被试和错误规则在该空间的代表性位置之间的马氏距离,并通过贝叶斯决策准则划分被试的错误类型,根据６４４名中学生对３０个数学题目的反应,识别出其中８６％的学生可以被划分人１８种认知错误类型中。     

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.     

Some neglected problems in IRT

The paper addresses three neglected questions from IRT. In section 1, the properties of the “measurement” of ability or trait parameters and item difficulty parameters in the Rasch model are discussed. It is shown that the solution to this problem is rather complex and depends both on general assumptions about properties of the item response functions and on assumptions about the available item universe. Section 2 deals with the measurement of individual change or “modifiability” based on a Rasch test. A conditional likelihood approach is presented that yields (a) an ML estimator of modifiability for given item parameters, (b) allows one to test hypotheses about change by means of a Clopper-Pearson confidence interval for the modifiability parameter, or (c) to estimate modifiability jointly with the item parameters. Uniqueness results for all three methods are also presented. In section 3, the Mantel-Haenszel method for detecting DIF is discussed under a novel perspective: What is the most general framework within which the Mantel-Haenszel method correctly detects DIF of a studied item? The answer is that this is a 2PL model where, however, all discrimination parameters are known and the studied item has the same discrimination in both populations. Since these requirements would hardly be satisfied in practical applications, the case of constant discrimination parameters, that is, the Rasch model, is the only realistic framework. A simple Pearsonx ² test for DIF of one studied item is proposed as an alternative to the Mantel-Haenszel test; moreover, this test is generalized to the case of two items simultaneously studied for DIF.     

Social integration and social support in a life crisis: Effects of macrosocial change in east Germany

This process evaluation study examined what variables moderate and mediate treatment effects on days in stable housing and client satisfaction for homeless mentally ill clients. In general, demographic characteristics did not moderate either outcome variable. Housing contacts, entitlement contacts, mental health contacts, and supportive services were significant mediators of the treatment effect on days in stable housing. Program contacts, mental health contacts, and supportive services were significant mediators of client satisfaction. The authors thank the National Institute of Mental Health for their financial support (MH43248, MH42357) for this project, Dorothy Gano for word processing and editorial assistance, and Gitry Heydebrand, Melissa Dannelet, Betty Tempelhoff, Ruth Smith, and Laeeq Ahmad for assisting in the interviews of clients. We are also appreciative of the cooperation given to us by the staffs of Malcolm Bliss Mental Health Center, St. Patrick's Center, the Community Advocacy and Support Alliance Program, and the St. Louisemergency shelters. Finally, we thank all of the participants in this study; we hope that their homelessness has now ended. (The conclusions presented in this paper are the sole responsibility of the authors and do not necessarily reflect official National Institute for Mental Health policy.)