Differential ordering of objects and attributes

By reference to nominated attributes, a genus, being a population of objects of one specified kind, may be partitioned into species, being subpopulations of different kinds. A prototype is an object representative of its species within the genus. Using this framework, the paper describes how objects can be relatively differentiated with respect to attributes, and how attributes can be relatively differentiating with respect to objects. Methods and rationale for such differential ordering of objects and attributes are presented by example, formal development, and application.For a genus comprisingn species of object there is a subsetP ofn distinct prototypes. With respect tom nominated attributes, each object in has anm-element characterization. Together these determine ann ×m objects × attributes matrix, the rows of which are the characterizations of the prototypical objects. Over then species in , an associated relative frequency vector gives the distribution of objects (and of their characterizations). The matrix and vector associate the objects in with points in a metric space (P, ); and it is with respect to various sums of distances in this attribute space that one can differentially order objects and attributes.The definition of the distance function is generalized across kinds of difference, types of characterization, scale-types of measurement, Minkowskiindex 1, and any form of distribution of objects over species. Explanatory and taxonomic applications in psychology and other fields are discussed, with focus on classification, identification, recognition, and search. The Braille code and the identification of its characters provide illustration.An anticipation and some preliminary indications were given in Sutcliffe and Bristow (1966), Sutcliffe (1972, 1973), and Nowakowska (1975). Subsequently the ideas have been extended and their applications realized in a computer program which, in its development, has so far gone through many minor and three major revisions to its present form in Sutcliffe (1985). The foregoing provided the foundation for the empirical applications and for the presentation in this paper of the ideas in their general form. the research has been supported by funds from the University of Sydney Research Grant and from the Australian Research Grants Scheme. In the working out and exposition of the ideas I have very much benefited from constructive critical comment given by C. R. Latimer, J. B. Michell, G. Oliphant, and E. Seneta, and from the professional programming skills of Michael Wilson and David Shillito. I am grateful for the invitation and the facilities for writing extended during 1983 by Georges Noizet, Laboratoire de Psychologie Expérimentale, Université René Descartes, Paris V, and by Samuel Messick, Vice President for Research, E.T.S. Princeton, N.J. Finally, I acknowledge the improvements in presentation of this paper which have arisen from the editor's and reviewers' comments.     

Student-teacher concordance on dimensions of student social competence: A multitrait-multimethod analysis

Teacher and self-ratings of social competence were obtained for 669 (341 males, 328 females) grades 3–6 students using the Social Behavior Assessment—Revised (SBA-R) and a self-report scale consisting of the identical items reworded in first person. Factor analysis and multitrait-multimethod matrix analysis were used to validate construct interpretations. The previous four-factor structure of the SBA-R was not replicated. However, the three-factor structure that did emerge was better defined. Although student-teacher concordance was moderate for the Self-Control/Social Convention and Academic Responsibility factors, it was minimal for the Social Participation factor. Evidence of discriminant validity was weak. As with other studies using rating scales, method bias was in evidence. Sex differences were found in terms of variance explained by each factor and convergent validity. Discussion focuses on problems associated with construct validation in general and validation of school-related social competence in particular.     

A sequential cognitive diagnosis model for polytomous responses

This paper proposes a general polytomous cognitive diagnosis model for a special type of graded responses, where item categories are attained in a sequential manner, and associated with some attributes explicitly. To relate categories to attributes, a category‐level Q‐matrix is used. When the attribute and category association is specified a priori, the proposed model has the flexibility to allow different cognitive processes (e.g., conjunctive, disjunctive) to be modelled at different categories within a single item. This model can be extended for items where categories cannot be explicitly linked to attributes, and for items with unordered categories. The feasibility of the proposed model is examined using simulated data. The proposed model is illustrated using the data from the Trends in International Mathematics and Science Study 2007 assessment.     

Fungible Correlation Matrices: A Method for Generating Nonsingular,Singular, and Improper Correlation Matrices for Monte Carlo Research

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.     

改进的认知诊断模型项目功能差异检验方法——基于观察信息矩阵的Wald统计量

Hou,de la Torre和Nandakumar(2014)提出可以使用Wald统计量检验DIF,但其结果的一类错误率存在过度膨胀的问题。本研究中提出了一个使用观察信息矩阵进行计算的改进后的Wald统计量。结果表明:(1)使用观察信息矩阵计算的这一改进后的Wald统计量在DIF检验中具有良好的一类错误控制率,尤其是在项目具有较高区分能力的时候,解决了以往研究中一类错误率过度膨胀的问题。(2)随着样本量的增加以及DIF量的增大,使用观察信息矩阵计算Wald统计量的统计检验力也在增加。     

独体汉字的字形相似性研究

本文以速示呈现方式获得了一系列独体汉字和字符的混淆矩阵。用Luce（1963）的选择模型特混淆矩阵分解为对称的相似矩阵和反应倾向矢量。基于相似矩阵,以聚类分析和多维量表法探索了汉字和字符的视觉特征及其表征形式,为揭示汉字视觉特征的几何特性和潜在结构,在研究方法上作了有意义的偿试、此外,本研究的结果支持了作者（1995）关于在含“十”或“口”的独体汉字中,“十”与“口”是该类汉字的突出视觉特征的结论。     

Image and anti-image covariance matrices from a correlation matrix that may be singular

Following the work of Tucker, Cooper, and Meredith, image and anti-image covariance matrices from a correlation matrix that may be singular are derived.     

The rowwise correlation between two proximity matrices and the partial rowwise correlation

This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearman, and Kendall, three different rowwise test statistics and their normalized coefficients are discussed, and subsequently compared with their nonrowwise alternatives like Mantel'sZ. It is shown that the rowwise matrix correlation coefficient between two matricesX andY is the partial correlation between the entries ofX andY controlled for the nominal variable that has the row objects as categories. Given this fact, partial rowwise correlations (as well as multiple regression extensions in the case of Pearson's approach) can be easily developed.The author wishes to thank the Editor, two referees, Jan van Hooff, and Ruud Derix for their useful comments, and E. J. Dietz for a copy of the algorithm of the Mantel permutation test.     

A direct approach to individual differences scaling using increasingly complex transformations

A family of models for the representation and assessment of individual differences for multivariate data is embodied in a hierarchically organized and sequentially applied procedure called PINDIS. The two principal models used for directly fitting individual configurations to some common or hypothesized space are the dimensional salience and perspective models. By systematically increasing the complexity of transformations one can better determine the validities of the various models and assess the patterns and commonalities of individual differences. PINDIS sheds some new light on the interpretability and general applicability of the dimension weighting approach implemented by the commonly used INDSCAL procedure.     

Scaling a conditional proximity matrix to symmetry

Two least squares procedures for symmetrization of a conditional proximity matrix are derived. The solutions provide multiplicative constants for scaling the rows or columns of the matrix to maximize symmetry. It is suggested that the symmetrization is applicable for the elimination of bias effects like response bias, or constraints on the marginal frequencies imposed by the experimental design, as in confusion matrices.The application of the scaling procedure to a matrix of conditional probabilities was suggested by one of the referees, whose helpful comments are gratefully acknowledged.