Modified Distribution-Free Goodness-of-Fit Test Statistic

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62–83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.     

On the multivariate asymptotic distribution of sequential Chi-square statistics

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-squaredifference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided.This research was carried out while the first author was Visiting Professor in the Department of Statistics in the University of South Africa, and was supported in part by a research grant (NSERC #67-4640) from the National Sciences and Engineering Council of Canada to the first author. The support of both of these organizations is acknowledged with gratitude.     

A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis

Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's (1988, 1994) mean scaling statistic were developed under the presumption of nonnormality in the factors and errors. This article finds new application to the case where factors and errors are normally distributed in the population but the skewness of the obtained test statistic is still high due to sampling error in the observed indicators. An extension of Satorra Bentler's statistic is proposed that not only scales the mean but also adjusts the degrees of freedom based on the skewness of the obtained test statistic in order to improve its robustness under small samples. A simple simulation study shows that this third moment adjusted statistic asymptotically performs on par with previously proposed methods and at a very small sample size offers superior Type I error rates under a properly specified model. Data from Mardia, Kent, and Bibby's (1980) study of students tested for their ability in 5 content areas that were either open or closed book were used to illustrate the real-world performance of this statistic.     

检验导出的等值新方法及其表现探讨

该文受Berkson将检验方法用于估计未知参数的启发,根据三个拟合优度统计量导出三种新的求取等值系数的方法,即:平方根等值方法(Square Root criterion,SQRTcrit)、对称相对熵等值方法(Symmetric Relative Entropy criterion,SREcrit)、加权等值方法(Weighted criterion,Wcrit),即Haebara准则的加权式。虽然在被检验的两个分布列很接近时,这三个多项拟合优度检验方法是渐近等价的,然而用它们求取等值系数时,Monte-Carlo模拟结果表明这三种新等值方法的行为表现存在差异。它们之间的差异和随机误差的大小有密切关系,即与项目参数估计的精度有关;还与等值系数A的范围有关。     

Normal Versus Noncentral Chi-square Asymptotics of Misspecified Models

In this article, we present a Bayesian spatial factor analysis model. We extend previous work on confirmatory factor analysis by including geographically distributed latent variables and accounting for heterogeneity and spatial autocorrelation. The simulation study shows excellent recovery of the model parameters and demonstrates the consequences of ignoring spatial dependence. Specifically, we find inefficiency in the estimates of the factor score means and bias and inefficiency in the estimates of the corresponding covariance matrix. We apply the model to Schwartz value priority data obtained from 5 European countries. We show that the Schwartz motivational types of values, such as Conformity, Tradition, Benevolence, and Hedonism, possess high spatial autocorrelation. We identify several spatial patterns—specifically, Conformity and Hedonism have a country-specific structure, Tradition has a North–South gradient that cuts across national borders, and Benevolence has South–North cross-national gradient. Finally, we show that conventional factor analysis may lead to a loss of valuable insights compared with the proposed approach.     

A normal approximation for testing the equality of two independent Chi-square variables

A simple normal approximation is supplied to test the equality of two independent Chi-square variables. The approximation appears to be valid for degrees of freedom as small as two. Thus no new table of critical values is needed. The standard unit normal distribution tables are sufficient.     

应用统计学方法认知经络本质

运用统计学方法考察了各经络上腧穴与所属脏腑的相关性,结果表明,各经络上腧穴与所属脏腑的总体相关性较差,且各经络问差异显著,这与传统经络理论不符,因此,提出经络只是一种分类系统的假设.放弃现有的经络理论系统,建立更加完善的腧穴分类体系与针灸临床指导理论将是针灸学发展的方向.     

Improving the Crossing-SIBTEST Statistic for Detecting Non-uniform DIF

This paper demonstrates that, after applying a simple modification to Li and Stout’s (Psychometrika 61(4):647–677, 1996) CSIBTEST statistic, an improved variant of the statistic could be realized. It is shown that this modified version of CSIBTEST has a more direct association with the SIBTEST statistic presented by Shealy and Stout (Psychometrika 58(2):159–194, 1993). In particular, the asymptotic sampling distributions and general interpretation of the effect size estimates are the same for SIBTEST and the new CSIBTEST. Given the more natural connection to SIBTEST, it is shown that Li and Stout’s hypothesis testing approach is insufficient for CSIBTEST; thus, an improved hypothesis testing procedure is required. Based on the presented arguments, a new chi-squared-based hypothesis testing approach is proposed for the modified CSIBTEST statistic. Positive results from a modest Monte Carlo simulation study strongly suggest the original CSIBTEST procedure and randomization hypothesis testing approach should be replaced by the modified statistic and hypothesis testing method.     

Use of the Jackknife Statistic to Evaluate Result Replicability

Result replicability has often been confused with significance testing because of a misinformed view that statistical significance evaluates result importance and result replicability. Several alternatives, of which the jackknife statistic is one, provide researchers with the tools for estimating result replicability. In the present study, an available data set from A. L. Edwards (1985, p. 57) is used to illustrate the use of the jackknife statistic to assess the replicability of multiple regression results in a concrete fashion. The jackknifed coefficients are computed to assess the stability of beta weights and the multiple R ² value. Confidence intervals and t statistics are also calculated to facilitate the interpretation of these jackknifed coefficients.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

数字差异和概率差异对比率偏差的影响

比率偏差是一种常见的决策偏差,指的是当小概率事件以不同比率形式呈现时,人们倾向于认为以较小数字呈现的事件更不可能发生.本文采用问卷调查方式,在两个研究中分别探讨了数字差异和概率差异对比率偏差的影响,结果发现：（1）比率偏差的产生具有跨情境的一致性和稳健性;（2）等概率条件下比率偏差的发生率不随两个比率间的数字差异的增大而增大;（3）不等概率条件下比率偏差程度不随两个比率间概率差异的改变而改变.     

农村健康保障制度与反贫困

从我国农村健康保障现实出发,认为建立农村健康保障制度是反贫困的迫切要求和重要组成部分,并提出了一些政策建议,如树立公共健康投资理念、政府职能转变与市场机制结合等.     

Cognitive self-instruction for the control of impulsive classroom behavior: Ensuring the treatment package

The practical utility of cognitive self-instruction training in facilitating the work habits and academic performance of impulsive first-graders was assessed in the context of the regular classroom. The training paradigm was modified and environmental conditions were arranged to facilitate the transfer of the cognitive self-instruction strategy to the classroom. Following training, there were no significant increases in on-task behavior or in academic performance within the context of a group design. On the basis of this and other studies, a drastic revision of the cognitive self-instruction paradigm seems indicated. Not only must training become broader based, but models must be developed that take into account the requisite cognitive processes for task completion as well as the cognitive abilities of the youngsters to whom training is addressed. In general, the incorporation of information from the developmental and cognitive process literature would appear to facilitate the development of more effective training models.     

Moral Responsibility: The Difference of Strawson,and the Difference it Should Make

P.F. Strawson’s work on moral responsibility is well-known. However, an important implication of the landmark “Freedom and Resentment” has gone unnoticed. Specifically, a natural development of Strawson’s position is that we should understand being morally responsible as having externalistically construed pragmatic criteria, not individualistically construed psychological ones. This runs counter to the contemporary ways of studying moral responsibility. I show the deficiencies of such contemporary work in relation to Strawson by critically examining the positions of John Martin Fischer and Mark Ravizza, R. Jay Wallace, and Philip Pettit for problems due to individualistic assumptions.Thanks to an audience at Carleton University for helpful discussion.     

Dilemmas of Difference

SUMMARY

This paper outlines a particular conceptual framework or working tool which individuals, couples and couples therapists have found useful in exploring the meaning of love and separateness, increasing the opportunities for love in couples relationships and reducing the potential for war in the intimacy zone. Three categories of difference between partners are outlined as an example both of specific couples therapy work in the microcosm, and of the relationships of nations in the macrocosm.