The asymptotic posterior normality of the latent trait in an IRT model

It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-J-90-1940, 442-1548, National Science Foundation Mathematics Grant NSF-DMS-91-01436, and the National Center for Supercomputing Applications. We wish to thank Kumar Joag-dev and Zhiliang Ying for enlightening suggestions concerning the proof of the basic result.The authors wish to thank Kumar Joag-Dev, Brian Junker, Bert Green, Paul Holland, Robert Mislevy, and especially Zhiliang Ying for their useful comments and discussions.     

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.     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.     

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。     

An extension of the partial credit model with an application to the measurement of change

The partial credit model is considered under the assumption of a certain linear decomposition of the item × category parameters _ih into basic parameters _j. This model is referred to as the linear partial credit model. A conditional maximum likelihood algorithm for estimation of the j is presented, based on (a) recurrences for the combinatorial functions involved, and (b) using a quasi-Newton approach, the so-called Broyden-Fletcher-Goldfarb-Shanno (BFGS) method; (a) guarantees numerically stable results, (b) avoids the direct computation of the Hesse matrix, yet produces a sequence of certain positive definite matricesB _k ,k=1, 2, ..., converging to the asymptotic variance-covariance matrix of the . The practicality of these numerical methods is demonstrated both by means of simulations and of an empirical application to the measurement of treatment effects in patients with psychosomatic disorders.The authors thank one anonymous reviewer for his constructive comments. Moreover, they thankfully acknowledge financial support by the Österreichische Nationalbank (Austrian National Bank) under Grant No. 3720.     

Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. The number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping-rule validity. Equal and unequal population base rates were also considered. Both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space. The replication criterion, which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set, was superior as the degree of overlap in population distributions increased. Neither method performed adequately when overlap obliterated visually discernible density nodes.This research was supported in part by NIMH grant 5R01 MH 32457 14.     

解题策略的同质性和线性逻辑斯谛模型的拟合

为探讨线性逻辑斯谛模型（ＬＬＴＭ）的拟合条件及其和解题策略同质性之间的关系,让被试比较两个负整数指数幂的大小,发现全体被试的数据不能与拉希模型及ＬＬＴＭ相拟合。把被试按其解题策略分成不同策略组后,同一策略组被试的数据可以拟合于拉希模型,但对于ＬＬＴＭ,同一策略组的数据中部分项目的拟合较好,另外一些项目的拟合较差。这一结果表明,解题策略的同质性是ＬＬＴＭ拟合的必要条件,但还不是充分条件。     

系列范畴词表时序记忆和项目记忆研究

该项研究探讨系列范畴词表的时序长时记忆和项目长时记忆,实验设计的系列范畴词表将记忆项目分为词表内范畴相同项和词表间范畴相同项,时序记记测量方法是词表辨认,项目记忆测量方法是自由回忆。实验一发现：２分钟延缓测试词表内范畴相同项时序记忆和项目记忆优于词表间范畴相同项;６分钟以及１０分钟延缓测试时序记忆仍是词表内范畴相同项好。实验二发现：以范畴线索提取,两类项目记忆没有显著差异;以词表线索提取,两类项目     

How much woe when we go: A quantitative method for predicting culture shock

Culture shock is defined as the confusion and discomfort caused by the conflict in perceived motives and expected behaviors between the home culture and the foreign culture. Several quantitative and graphical methods employing techniques of cluster analysis and similarity mapping are offered for predicting the magnitude of culture shock between pairs of countries using data extracted from Hofstede's 1980–83 studies of national cultural values. Implications for business, politics, and personal stress management are discussed.     

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.