Correspondence analysis of incomplete contingency tables

Correspondence analysis can be described as a technique which decomposes the departure from independence in a two-way contingency table. In this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi-independence model. This form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended, for example, in case of missing data or structural zeros. It is shown that Nora's reconstitution of order zero, a procedure well-known in the French literature, is formally identical to our correspondence analysis of incomplete tables. Therefore, reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi-independence model. Furthermore, correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis.     

Statistics as psychometrics

In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.1980 Psychometric Society presidential address.I am indebted to Paul Slovic and David Libby for valuable consultation on the issues discussed in this paper and to Nancy Turner and Laura Novick for assistance in preparation.Research reported herein was supported under contract number N00014-77-C-0428 from the Office of Naval Research to The University of Iowa, Melvin R. Novick, principal investigator. Opinions expressed herein reflect those of the author and not those of sponsoring agencies.     

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.     

Imitative violence in the real world: A reanalysis of homicide rates following championship prize fights

Recently, Phillips [Am Soc Rev, 1983; 48:560–568] reported that the homicide rate increases on the third day after heavyweight championship prize fights. The present paper reports a reanalysis of Phillips's data using more sophisticated statistical techniques and examining several theoretically important variables not discussed by Phillips or his critics. Using a conservative analysis strategy, our results suggest that the increases in homicides reported by Phillips were not a methodological artifact as suggested by Baron and Reiss [Am Soc Rev 1985; 50:347–363, 372–376]. The homicide increases only occur on the first weekend or holiday after prize fights that receive the greatest publicity.     

Social network analysis: A methodological introduction

Social network analysis is a large and growing body of research on the measurement and analysis of relational structure. Here, we review the fundamental concepts of network analysis, as well as a range of methods currently used in the field. Issues pertaining to data collection, analysis of single networks, network comparison, and analysis of individual-level covariates are discussed, and a number of suggestions are made for avoiding common pitfalls in the application of network methods to substantive questions.     

基于多传感器数据的航空管制员情境意识的计算

航空管制人员保持良好的情境意识是确保空中交通以安全、高效方式运行的必要条件。如果在管制员工作过程中, 能准确监测其情境意识状态, 并在情境意识丧失前给予及时告警, 那么将会极大地提高管制绩效和减少空中两机相撞的概率。目前, 国外评价管制员情境意识的方法虽然不少, 但这些方法基本都是诊断性质和回溯性质的, 无法对管制员的情境意识进行监测或预警。管制员的情境意识受个体差异、任务等多种因素的影响, 同时, 其也可以由某些指标来表征, 如某些作业绩效指标和生理指标。为了能够实现对航空管制员情境意识的准确监控及告警, 拟通过雷达管制模拟实验、心理测量、专家评定等方法采集多传感器数据, 分别建立基于表征指标和基于影响变量的情境意识计算模型, 并比较其预测性能。该研究结果可为管制员情境意识的实时监测提供支持。     

IRT框架下追踪数据的测量不变性分析——————以4至5岁儿童认知能力测验为例

本研究以4岁~5岁儿童认知能力测验为例,在IRT框架下探讨了如何进行追踪数据的测量不变性分析。分析模型采用项目间多维项目反应理论模型(between-item MIRT model)和项目内（within-item MIRT model）多维two-tier model,被试为来自全国的882名48个月的儿童,工具为自编4岁~5岁儿童认知能力测验。经测验水平 分析和项目水平分析,结果表明：(1)本文对追踪数据的测量不变性分析方法合理有效; (2)该测验在两个时间点上满足部分测量不变性要求,测验的潜在结构稳定; (3)“方位题”的区分度和难度参数都发生变化,另有4题难度参数出现浮动; (4)儿童在4岁~5岁期间认知能力总体呈快速发展趋势,能力增长显著。     

Asymptotic biases in exploratory factor analysis and structural equation modeling

Formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the Wishart maximum likelihood estimation for normally and nonnormally distributed variables. When multivariate normality is satisfied, considerable simplification is obtained for the models of unstandardized variables. Formulas for the models of standardized variables are also provided. Numerical examples with Monte Carlo simulations in factor analysis show the accuracy of the formulas and suggest the asymptotic robustness of the asymptotic biases with normality assumption against nonnormal data. Some relationships between the asymptotic biases and other asymptotic values are discussed.The author is indebted to the editor and anonymous reviewers for their comments, corrections, and suggestions on this paper, and to Yutaka Kano for discussion on biases.     

Prior distributions on symmetric groups

Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the Binary Tree, is developed on the symmetric group. The attractive features of the class are: it provides a closed-form solution to the posterior distribution; and a simple way to interpret the parameters of the prior distribution. The advantages of the proposed method are illustrated by comparing it to metric-based models using data analyzed by other researchers in this context.This revised article was published online in August 2005 with the PDF paginated correctly.