Departure from normal assumptions: A promise for future psychometrics with substantive mathematical modeling

Normal assumptions have been used in many psychometric methods, to the extent that most researchers do not even question their adequacy. With the rapid advancement of computer technologies in recent years, psychometrics has extended its territory to include intensive cognitive diagnosis, etcetera, and substantive mathematical modeling ha become essential. As a natural consequence, it is time to consider departure from normal assumptions seriously. As examples of models which are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale.     

The Ambiguity of Covariation: A Conceptual Note

Three dimensions of propositions, the factual, the epistemic and the modal, and their relationships, are described. The five factor model of personality is based on correlations between ordinary language items. The terms of this language are fuzzy and context-dependent in meaning, and, therefore, unsuitable for epistemic/modal analysis. Hence, one cannot decide to what extent FFM is a priori versus empirical. Only a scientific language, with explicitly stated primitives, axioms, and definitions will permit such a decision.     

智慧技能的一般教学模型与实验验证

该文给出了智慧技能的一般教学模型 ,将智慧技能的教学分为两个主要阶段 :陈述性编码阶段、程序性编码阶段。为验证此模型在教学实践中的可行性 ,在课堂教学情境中进行了模拟实验。选取同一所学校初二年级的四个班学生共 2 2 2人 ,随机安排四个班分别接受“欧姆定律”四种教案的教学 :发现式新教案、发现式旧教案、接受式新教案、接受式旧教案 ,随后进行迁移能力测验 ,结果表明采用新教案组织教学 ,即按上述模型控制好影响智慧技能的一些关键因素 ,将更利于学生获取智慧技能。     

A nonspatial methodology for the analysis of two-way proximity data incorporating the distance-density hypothesis

This paper presents a nonspatial operationalization of the Krumhansl (1978, 1982) distancedensity model of similarity. This model assumes that the similarity between two objectsi andj is a function of both the interpoint distance betweeni andj and the density of other stimulus points in the regions surroundingi andj. We review this conceptual model and associated empirical evidence for such a specification. A nonspatial, tree-fitting methodology is described which is sufficiently flexible to fit a number of competing hypotheses of similarity formation. A sequential, unconstrained minimization algorithm is technically presented together with various program options. Three applications are provided which demonstrate the flexibility of the methodology. Finally, extensions to spatial models, three-way analyses, and hybrid models are discussed.     

The Dutch Identity: A new tool for the study of item response models

The Dutch Identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (a) to suggest how item response models behave for large numbers of items—they are approximate submodels of second-order loglinear models for 2 ^J tables; (b) to suggest new ways to assess the dimensionality of the latent trait—principle components analysis of matrices composed of second-order interactions from loglinear models; (c) to give insight into the structure of latent class models; and (d) to illuminate the problem of identifying the IRFs and the latent trait distribution from sample data.This research was supported in part by contract number N00014-87-K-0730 from the Cognitive Science Program of the Office of Naval Research. I realized the usefulness of the identity in Theorem 1 while lecturing in the Netherlands during October, 1986. Because this was in no small part due to the stimulating psychometric atmosphere there, I call the result the Dutch Identity.     

SCIENTISM, INTERPRETATION, AND CRITICISM

Abstract. What is the relationship between natural science, social science, and religion? The dominant paradigm in contemporary social science is scientism, the attempt to apply the methods of natural science to the study of society. However, scientism is problematic: it rests on a conception of natural science that cannot be sustained. Natural scientific understanding emerges from an instrumental and objectifying relation to the world; it is oriented toward control and manipulation of the physical world. Social-scientific understanding, by contrast, must begin with a practical and meaningful relation to the world: it is oriented toward the mediation of values and objective possibilities in the social world. Social science is therefore a form of practical reason based on objective claims. But while social-scientific understanding starts with interpretation, its possibilities by no means end there. In particular, by developing abstract and objectified models of society as a system, social science opens existing social organization to critical reflection. Religion, by contrast, is a form of speculative reason about ultimate values, based on subjective claims of religious experience. Social science nevertheless shares with religion an orientation toward values and concern with the “good life.”     

Unbiased estimators of ability parameters,of their variance,and of their parallel-forms reliability

Given known item parameters, unbiased estimators are derived i) for an examinee's ability parameter and for his proportion-correct true score, ii) for the variances of and across examinees in the group tested, and iii) for the parallel-forms reliability of the maximum likelihood estimator .This work was supported in part by contract N00014-80-C-0402, project designation NR 150-453 between the Office of Naval Research and Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Characterizing the manifest probabilities of latent trait models

The problem of characterizing the manifest probabilities of a latent trait model is considered. The item characteristic curve is transformed to the item passing-odds curve and a corresponding transformation is made on the distribution of ability. This results in a useful expression for the manifest probabilities of any latent trait model. The result is then applied to give a characterization of the Rasch model as a log-linear model for a 2 ^J -contingency table. Partial results are also obtained for other models. The question of the identifiability of “guessing” parameters is also discussed. The research reported here is collaborative in every respect and the order of authorship is alphabetical. Dr. Cressie was a Visiting Research Scientist at ETS during the Fall of 1980. His current address is: School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park SA, 5042, AUSTRALIA. The preparation of this paper was supported, in part, by the Program Statistics Research Project in the Research Statistics Group at ETS.     

Maximum likelihood estimation of item response parameters when some responses are omitted

A theoretical model is given for dealing with omitted responses. Two special cases are investigated.This work was supported in part by contract N00014-80-C-0402, project designation NR 150-453 between the Office of Naval Research and Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.