A class of multidimensional IRT models for testing unidimensionality and clustering items

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a likelihood ratio statistic between two nested models in this class. For this aim, we also derive an asymptotically equivalent Wald test statistic which is faster to compute. Moreover, we propose a hierarchical clustering algorithm which can be used, when the dimensionality of the latent structure is completely unknown, for dividing items into groups referred to different latent traits. The approach is illustrated through a simulation study and an application to a dataset collected within the National Assessment of Educational Progress, 1996. The author would like to thank the Editor, an Associate Editor and three anonymous referees for stimulating comments. I also thank L. Scaccia, F. Pennoni and M. Lupparelli for having done part of the simulations.     

初中词汇理解能力量表的编制

应用项目反应理论为初中各年级编制了词汇理解能力的测验,其中包含了１４３个多项选择的词汇项目,经过反复预测和大规模的正式测试,证关了这三个测验的量表拟全于２ＰＬ模型,项目特征曲线拟合度良好的项目占全体项目数９０％以上,能力的一维性也得以确认,经等值化后,各年级的区分度均值分别为０．６１（初一）,０．５９（初二）,０．５５（初三）难度均值分别为－１．６１,－１．３０,－０．５６。     

关系研究的新取向：社会网络分析

社会网络分析（Social Network Analysis, SNA）是用社会实体之间的关系来描述、解释和预测社会现象的一种研究取向。SNA提供了深入探究社会环境特征及其对个体心理发展影响的一种方法。本文基于SNA的发展历程,依次介绍了中心性分析、小团体分析、位置分析、QAP以及统计模型法。SNA在社会学研究中得到了较多应用,近年来在心理学研究中开始受到重视。     

An alternative two stage least squares (2SLS) estimator for latent variable equations

The Maximum-likelihood estimator dominates the estimation of general structural equation models. Noniterative, equation-by-equation estimators for factor analysis have received some attention, but little has been done on such estimators for latent variable equations. I propose an alternative 2SLS estimator of the parameters in LISREL type models and contrast it with the existing ones. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and is estimable with standard statistical software. Diagnostics for evaluating instrumental variables are described. An empirical example illustrates the estimator. I gratefully acknowledge support for this research from the Sociology Program of the National Science Foundation (SES-9121564) and the Center for Advanced Study in the Behavioral Sciences, Stanford, California. This paper was presented at the Interdisciplinary Consortium for Statistical Applications at Indiana University at Bloomington (March 2, 1994) and at the RMD Conference on Causal Modeling at Purdue University, West Lafayette, Indiana (March 3-5, 1994).     

On the robustness of maximum likelihood scaling for violations of the error model

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Data sets generated according to the lognormal, the normal, and the rectangular distribution were analysed with the log-normal error model in Ramsay's MULTISCALE program package. The results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. In a comparison among several dimensionality tests, the corrected version of thex ² test, as proposed by Ramsay, yielded the best results, and turned out to be quite robust against violations of the error model.     

The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective

It is demonstrated in this paper that two major tests for 2 × 2 talbes are highly related from a Bayesian perspective. Although it is well-known that Fisher's exact and Pearson's chi-square tests are asymptotically equivalent, the present analysis shows that a formal similarity also exists in small samples. The key assumption that leads to the resemblance is the presence of a continuous parameter measuring association. In particular, it is shown that Pearson's probability can be obtained by integrating a two-moment approximation to the posterior distribution of the log-odds ratio. Furthermore, Pearson's chi-square test gave an excellent approximation to the actual Bayes probability in all 2×2 tables examined, except for those with extremely disproportionate marginal frequencies.     

Children's perceptions of major positive and negative events and factors in single-parent families

A study was designed to tap children's perceptions of the divorce situation as opposed to adults' perceptions of the child's response to the parental divorce. Subjects were 75 boys and 75 girls from mother- and father-headed families. Using an individual structured interview procedure children were encouraged to reconstruct both positive and negative dimensions of their interactions with the custodial parent. Through factor analyses of the contents of interviews four negative and two positive factors involving 20 specific items were identified in the children's perceptual data. Subsequently, chi-square analyses were done to compare differences in girls' and boys' perceptions between and across father- and mother-headed families. Results are discussed in terms of their relationship with the existing literature and their clinical and educational relevance to children, single parents and professionals.     

Contiguity and contingency in instrumental conditioning

There have been several attempts to construct molar theories of conditioning on the empirical basis that response-reinforcement contingency is important in determining conditioning. Such theories claim to explain behavior in terms of molar level processes which transcend the molecular level and, therefore, are not reducible to molecular processes or their interaction. These molar theories are critically examined and found to be seriously flawed because they fail to account for the effects of delaying reinforcement (degree of contiguity). Observed molar level relations, such as the matching law, do not require a molar theory, but may be more usefully considered as a product of molecular processes.     

A note on the "word-order problem" in agrammatism

This brief note has two parts. First, it presents an analysis of the ability of English agrammatic patients to assign the thematic roles of agent, instrument, theme, and locative to noun phrases in active and passive sentences and prepositional phrases. Data regarding this ability have been presented by Schwartz, Saffran, and Marin (Brain and Language, 10, 149-262 (1980) regarding comprehension, and by Saffran, Schwartz, and Marin (Brain and Language, 10, 263-280 (1980) regarding production. These authors claim their data show that English agrammatic aphasics do not map "word order" onto thematic information. However, a very simple set of principles accounts for all their results, including results which are discrepant in their treatment, but requires that English agrammatics assign thematic roles to NPs in part by virtue of the position of an NP in a sentence or a phrase. In the second part of this note, several issues raised by this re-analysis are briefly discussed.