基于等级反应模型的多水平多侧面评分者模型

国内外考试改革和大型测评实践越来越强调主观题的作用,则评分者信度研究又重新成为一个备受关注的议题。研究在Wang和Liu（2007）的广义多水平侧面模型基础上,提出并探讨了等级反应多水平侧面模型。结果表明：在评分者固定效应和随机效应两种实验条件下,各偏差值的均值与标准差均较小,说明模型在当前实验条件下,各参数估计值的返真性和稳健性均较好,可以检测出评分者效应,由此,后续可进一步加入评分者效应的影响因素,使其发展为可同时检测评分者效应及其影响因素的完整模型。     

Optimal correction for guessing in multiple-choice tests

Subjects’ decisions in multiple-choice tests are an interesting domain for the analysis of decision making under uncertainty. When the test is graded using a rule that penalizes wrong answers, each item can be viewed as a lottery where a rational examinee would choose whether to omit (sure reward) or answer (take the lottery) depending on risk aversion and level of knowledge. We formalize students as heterogeneous decision makers with different risk attitudes and levels of knowledge. Building on IRT, we compute the optimal penalty given students’ optimal behavior and the trade-off between bias and measurement error. Although MCQ examinations are frequently used, there is no consensus as to whether a penalty for wrong answers should be used or not. For example, examinations for medical licensing in some countries include MCQ sections with penalty while in others there is no penalty for wrong answers. We contribute to this discussion with a formal analysis of the effects of penalties; our simulations indicate that the optimal penalty is relatively high for perfectly rational students but also when they are not fully rational: even though penalty discriminates against risk averse students, this effect is small compared with the measurement error that it prevents.     

项目反应理论多级记分模型参数估计的实现

项目反应理论中参数估计程序的实现,一直是研究现代测量理论的学者们关注的问题。该研究从理论上探讨了多级模型参数估计的实现途径,并模拟了5批不同数量及分布情形的项目及被试参数,生成相应的原始得分矩阵,对自编程序及国际流行的相关程序进行了严格的比较校验,验证结果证明本程序具有精确、稳定的性能,并且发现被试量太少将影响参数估计的精确性及稳定性     

A gauss-newton algorithm for exploratory factor analysis

It is shown that the scoring algorithm for maximum likelihood estimation in exploratory factor analysis can be developed in a way that is many times more efficient than a direct development based on information matrices and score vectors. The algorithm offers a simple alternative to current algorithms and when used in one-step mode provides the simplest and fastest method presently available for moving from consistent to efficient estimates. Perhaps of greater importance is its potential for extension to the confirmatory model. The algorithm is developed as a Gauss-Newton algorithm to facilitate its application to generalized least squares and to maximum likelihood estimation.This research was supported by NSF Grant MCS-8301587.     

概化理论在作文评分中的应用研究

概化理论是现代心理测量理论之一,该文简要地介绍了该理论的基本思想并用此理论对作文评分的误差控制问题进行了应用性探讨。研究中请６位评分员对２０名学生每人三种文体的作文用分项评分法进行评定。然后用ＧＥＮＯＶＡ软件的估计了作文评分中的评分员效应和题目效应,并对各种误差构成进行了分析比较。结果表明：在作文评分中,评分员勺最大,题目效应不明显。同时还发现,不同文体对评分误差有重要影响。论文文的评分误差最大,     

Iterated revision and minimal change of conditional beliefs

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a virtual manner, using uniterated revision.     

Generalized bilinear models

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family of models that includes many existing models, as well as suggest other potentially useful ones. This approach both unifies and extends models for two-way arrays, including the ability to treat response and explanatory variables differently in the models, and the incorporation of external information about the variables directly into the analysis. A unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature. A three-step procedure is proposed to analyze data sets by generalized bilinear models. Two data sets of different nature are analyzed.     

Principal component analysis of three-mode data by means of alternating least squares algorithms

A new method to estimate the parameters of Tucker's three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.     

Sufficient statistics and latent trait models

For questionnaires with two answer categories, it has been proven in complete generality that if a minimal sufficient statistic exists for the individual parameter and if it is the same statistic for all values of the item parameters, then the raw score (or the number of correct answers) is the minimal sufficient statistic. It follows that the model must by of the Rasch type with logistic item characteristic curves and equal item-discriminating powers.This paper extends these results to multiple choice questionnaires. It is shown that the minimal sufficient statistic for the individual parameter is a function of the so-called score vector. It is also shown that the so-called equidistant scoring is the only scoring of a questionnaire that allows for a real valued sufficient statistic that is independent of the item parameters, if a certain ordering property for the sufficient statistic holds.