Some critical observations of the test information function as a measure of local accuracy in ability estimation

The test information function serves important roles in latent trait models and in their applications. Among others, it has been used as the measure of accuracy in ability estimation. A question arises, however, if the test information function is accurate enough for all meaningful levels of ability relative to the test, especially when the number of test items is relatively small (e.g., less than 50). In the present paper, using the constant information model and constant amounts of test information for a finite interval of ability, simulated data were produced for eight different levels of ability and for twenty different numbers of test items ranging between 10 and 200. Analyses of these data suggest that it is desirable to consider some modification of the test information function when it is used as the measure of accuracy in ability estimation.     

Catholic missions in China: failure to form native clergy

The success and failure of Christianity in China was tied to the missionaries’ ability to accommodate to Chinese culture and the powers that ruled over this vast nation. A number of reasons have been put forward regarding the failure of Christian missions in China. Inability to adapt to native norms, ignorance of Chinese language, association with Western imperialism, rivalries among various religious orders, congregations and missionary societies, and the reluctance to establish a Chinese ecclesiastical hierarchy all contributed to hindering the propagation of the gospel. This paper argues that the main reason for their failure was the refusal of European clergy to hand over the leadership of the church to the Chinese, in spite of Rome’s edicts to establish an indigenous ecclesiastical hierarchy. With local clergy in charge, the issue of language and cultural adaptation would have been resolved. Unfortunately, the native clergy were looked down upon by their Western counterparts, who were mostly motivated by national and institutional interests rather than pastoral concern for the local people. The appointment of the first Chinese bishop, Gregorio Lopéz (Luo Wenzao), was more a political move than a pastoral need.     

A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.     

多感官线索整合的理论模型

日常生活中,人脑能联合来自不同感官通道的线索对外部世界中的物体和事件进行感知。这些感官通道采用不同的参照系来表征物体的特征和位置;而且各种线索的可靠性也不恒定,根据环境而改变。但是人脑依然能够有效地整合这些线索,对物体和事件进行正确的感知。在以往研究的基础上,总结评述了多感官线索整合的几种理论模型及其验证结果,其中重点介绍了近年来引起广泛关注的贝叶斯统计优化模型。未来的研究应结合虚拟现实技术和脑成像技术对多感官线索整合进行探讨。     

做会后悔还是不做会后悔?——自我调节模式对不作为惯性的影响

从消费者的不作为惯性反应差异出发,探讨运动模式和评估模式的消费者在错过第一次合意机会、面对第二次次优机会时购买可能性的差异及原因。通过3个研究发现,相比评估模式的消费者而言,运动模式的消费者具有更高的二次购买可能性。在自我调节模式影响次优购买可能性的过程中,预期后悔起到重要的中介作用。此外,研究还发现,当第二次次优机会中提供了与第一次机会中的产品类似但不同的替代产品时,运动模式和评估模式消费者之间的购买可能性差异消失了。     

Interval estimation of gamma for an<Emphasis Type="Italic">R</Emphasis>×<Emphasis Type="Italic">S</Emphasis> table

When the underlying responses are on an ordinal scale, gamma is one of the most frequently used indices to measure the strength of association between two ordered variables. However, except for a brief mention on the use of the traditional interval estimator based on Wald's statistic, discussion of interval estimation of the gamma is limited. Because it is well known that an interval estimator using Wald's statistic is generally not likely to perform well especially when the sample size is small, the goal of this paper is to find ways to improve the finite-sample performance of this estimator. This paper develops five asymptotic interval estimators of the gamma by employing various methods that are commonly used to improve the normal approximation of the maximum likelihood estimator (MLE). Using Monte Carlo simulation, this paper notes that the coverage probability of the interval estimator using Wald's statistic can be much less than the desired confidence level, especially when the underlying gamma is large. Further, except for the extreme case, in which the underlying gamma is large and the sample size is small, the interval estimator using a logarithmic transformation together with a monotonic function proposed here not only performs well with respect to the coverage probability, but is also more efficient than all the other estimators considered here. Finally, this paper notes that applying an ad hoc adjustment procedure—whenever any observed frequency equals 0, we add 0.5 to all cells in calculation of the cell proportions—can substantially improve the traditional interval estimator. This paper includes two examples to illustrate the practical use of interval estimators considered here.The authors wish to thank the Associate Editor and the two referees for many valuable comments and suggestions to improve the contents and clarity of this paper. The authors also want to thank Dr. C. D. Lin for his graphic assistance.     

EM algorithms for ML factor analysis

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least squares regression operations; the largest matrix inversion required is for aq ×q symmetric matrix whereq is the matrix of factors. The example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other; such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.