Test theory without an answer key

A general model is presented for homogeneous, dichotomous items when the answer key is not known a priori. The model is structurally related to the two-class latent structure model with the roles of respondents and items interchanged. For very small sets of respondents, iterative maximum likelihood estimates of the parameters can be obtained by existing methods. For other situations, new estimation methods are developed and assessed with Monte Carlo data. The answer key can be accurately reconstructed with relatively small sets of respondents. The model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of.This research was supported by NSF Grant No. SES-8320173 to the authors. We gratefully acknowledge comments and suggestions from John Boyd, Tarow Indow, and Kathy Maher as well as the editor and several anonymous referees.     

颜色知觉恒常理论的回顾

本文对早期颜色恒常理论、系数理论、计算理论和 Octant模型作了简要回顾 ,并结合已有的研究成果进行评述。对影响颜色恒常性机制的主要因素进行了探讨。强调了知觉经验、记忆、认知决策等高级意识活动对颜色恒常知觉的作用 ,并尝试性地提出了描述颜色恒常知觉过程的一般参照框架。     

Every Finitely Reducible Logic has the Finite Model Property with Respect to the Class of ♦-Formulae

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators.     

Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at theM-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.This research was supported by a Hong Kong UCG Earmarked Grant, CUHK 4026/97H. We are greatly indebted to D.E. Morisky and J.A. Stein for the use of their AIDS data in our example. We also thank the Editor, two anonymous reviewers, W.Y. Poon and H.T. Zhu for constructive suggestions and comments in improving the paper. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.     

A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Forgiveness, personality and gratitude

Recent evidence indicates that personality plays a role in the study of forgiveness, but the literature has been limited. This study sought to determine whether gratitude accounted for a significant portion of the variance beyond that of personality in the study of dispositional forgiveness (enduring resentment, sensitivity to circumstances, and overall propensity to forgive). One hundred and fifty-two Portuguese college students (51% females and 49% males, mean = 21.10 years) participated in the study. The results confirmed that personality, particularly agreeableness and neuroticism correlate with enduring resentment and overall tendency to forgive. Additionally, results using multiple regression models indicated that gratitude explained a significant amount of variance of overall propensity to forgive.     

Constructing the exact significance level for a person fit statistic

This paper uses an extension of the network algorithm originally introduced by Mehta and Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. By assuming that item difficulties are known, the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score. A simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less.     

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.     

Bayesian parameter estimation in the Expectancy Valence model of the Iowa gambling task

The purpose of the popular Iowa gambling task is to study decision making deficits in clinical populations by mimicking real-life decision making in an experimental context. Busemeyer and Stout [Busemeyer, J. R., & Stout, J. C. (2002). A contribution of cognitive decision models to clinical assessment: Decomposing performance on the Bechara gambling task. Psychological Assessment, 14, 253-262] proposed an “Expectancy Valence” reinforcement learning model that estimates three latent components which are assumed to jointly determine choice behavior in the Iowa gambling task: weighing of wins versus losses, memory for past payoffs, and response consistency. In this article we explore the statistical properties of the Expectancy Valence model. We first demonstrate the difficulty of applying the model on the level of a single participant, we then propose and implement a Bayesian hierarchical estimation procedure to coherently combine information from different participants, and we finally apply the Bayesian estimation procedure to data from an experiment designed to provide a test of specific influence.