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.     

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     

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.     

Sensitivity of a linear composite of predictor items to differential item weighting

Many authors have demonstrated for idealized item configurations that equal item weights are often virtually as good for a particular predictive purpose as the item weights that are theoretically optimal. What has not been heretofore clear, however, is what happens to the similarity between weighted and unweighted composites of the same items when the item configuration's variance structure is complex.     

Weakly parallel tests in latent trait theory with some criticisms of classical test theory

A new concept of weakly parallel tests, in contrast to strongly parallel tests in latent trait theory, is proposed. Some criticisms of the fundamental concepts in classical test theory, such as the reliability of a test and the standard error of estimation, are given.     

Two-step weighted least squares factor analysis of dichotomized variables

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure.