Generalized concordance

Based on a simple nonparametric procedure for comparing two proximity matrices, a measure of concordance is introduced that is appropriate whenK independent proximity matrices are available. In addition to the development of a general concept of concordance and specific techniques for its evaluation within and between the subsets of a partition of theK matrices, several methods are also suggested for comparing and/or for fitting a particular structure to the given data. Finally, brief indications are provided as to how the well-known notion of concordance forK rank orders can be included within the more general framework.Partial support for this research was supplied by the National Science Foundation through SOC-77-28227.     

Combinatorial data analysis: Association and partial association

A combinatorial data analysis strategy is reviewed that is designed to compare two arbitrary measures of proximity defined between the objects from some set. Based on a particular cross-product definition of correspondence between these two numerically specified notions of proximity (typically represented in the form of matrices), extensions are then pursued to indices of partial association that relate the observed pattern of correspondence between the first two proximity measures to a third. The attendant issues of index normalization and significance testing are discussed; the latter is approached through a simple randomization model implemented either through a Monte Carlo procedure or distributional approximations based on the first three moments. Applications of the original comparison strategy and its extensions to partial association may be developed for a variety of methodological and substantive tasks. Besides rank correlation, we emphasize the topics of spatial autocorrelation for one variable and spatial association between two and mention the connection to the usual randomization approach for one-way analysis-of-variance.     

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.     

On kristof's test for a linear relation between true scores of two measures

The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. We show that several previously proposed ad hoc tests are in fact likelihood ratio tests. The cases when the linear relation is specified and when it is unspecified are both discussed.This work was done while the author was at Purdue University Under Air Force Grant AFOSR-72-2350B.     

Testing Variance Components in Linear Mixed Modeling Using Permutation

Abstract

Inference of variance components in linear mixed modeling (LMM) provides evidence of heterogeneity between individuals or clusters. When only nonnegative variances are allowed, there is a boundary (i.e., 0) in the variances’ parameter space, and regular inference statistical procedures for such a parameter could be problematic. The goal of this article is to introduce a practically feasible permutation method to make inferences about variance components while considering the boundary issue in LMM. The permutation tests with different settings (i.e., constrained vs. unconstrained estimation, specific vs. generalized test, different ways of calculating p values, and different ways of permutation) were examined with both normal data and non-normal data. In addition, the permutation tests were compared to likelihood ratio (LR) tests with a mixture of chi-squared distributions as the reference distribution. We found that the unconstrained permutation test with the one-sided p-value approach performed better than the other permutation tests and is a useful alternative when the LR tests are not applicable. An R function is provided to facilitate the implementation of the permutation tests, and a real data example is used to illustrate the application. We hope our results will help researchers choose appropriate tests when testing variance components in LMM.     

Asymptotic clarifications,generalizations, and concerns regarding an extended class of matched pairs tests based on powers of ranks

Recent studies pertaining to an extended class of matched pairs tests based on powers of ranks are discussed. Previous questions regarding the asymptotic properties for this class of tests are clarified and a generalization of this class is described. This generalization raises a previously unanticipated concern about whether or not the analytic comparisons resulting from these tests correspond with an intuitive notion of what is being compared.     

The comparison of interdependent correlations between optimal linear composites

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.This research was supported in part by an operating grant (#67-4640) to the first author from the National Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the helpful comments and encouragement of Alexander Shapiro, Stanley Nash, and Ingram Olkin.     

Statistical inference based on ranks

This paper develops a unified approach, based on ranks, to the statistical analysis of data arising from complex experimental designs. In this way we answer a major objection to the use of rank procedures as a major methodology in data analysis. We show that the rank procedures, including testing, estimation and multiple comparisons, are generated in a natural way from a robust measure of scale. The rank methods closely parallel the familiar methods of least squares, so that estimates and tests have natural interpretations.This research was supported in part by grant MCS76-07292 from the National Science Foundation.     

Statistical Significance Levels of Nonparametric Tests Biased by Heterogeneous Variances of Treatment Groups

The statistical significance levels of the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test are substantially biased by heterogeneous variances of treatment groups—even when sample sizes are equal. Under these conditions, the Type I error probabilities of the nonparametric tests, performed at the .01, .05, and .10 significance levels, increase by as much as 40%-50% in many cases and sometimes as much as 300%. The bias increases systematically as the ratio of standard deviations of treatment groups increases and remains fairly constant for various sample sizes. There is no indication that Type I error probabilities approach the significance level asymptotically as sample size increases.     

Evaluating the conformity of sociometric measurements

The problem of comparing two sociometric matrices, as originally discussed by Katz and Powell in the early 1950's, is reconsidered and generalized using a different inference model. In particular, the proposed indices of conformity are justified by a regression argument similar to the one used by Somers in presenting his well-known measures of asymmetric ordinal association. A permutation distribution and an associated significance test are developed for the specific hypothesis of no conformity reinterpreted as a random matching of the rows and (simultaneously) the columns of one sociometric matrix to the rows and columns of a second. The approximate significance tests that are presented and illustrated with a simple numerical example are based on the first two moments of the permutation distribution, or alternatively, on a random sample from the complete distribution.Partial support for the research of the first author was provided by the National Science Foundation through SOC 75-07860. Equal authorship is implied. The work was done when the first author was at the University of Wisconsin.     

A monte carlo study of thirty internal criterion measures for cluster analysis

A Monte Carlo evaluation of thirty internal criterion measures for cluster analysis was conducted. Artificial data sets were constructed with clusters which exhibited the properties of internal cohesion and external isolation. The data sets were analyzed by four hierarchical clustering methods. The resulting values of the internal criteria were compared with two external criterion indices which determined the degree of recovery of correct cluster structure by the algorithms. The results indicated that a subset of internal criterion measures could be identified which appear to be valid indices of correct cluster recovery. Indices from this subset could form the basis of a permutation test for the existence of cluster structure or a clustering algorithm.     

Gender differences in the determinants of the willingness to accept an international assignment

Multinational organisations experience difficulties in finding managers willing to accept international assignments. This study has therefore focused on factors that can predict males' and females' willingness to accept international assignments, or to follow their partners on international assignments. Hypotheses were formulated based on the Rational Choice/Human Capital Theory, the Family Power Theory, the Life Role Salience Theory, and the Psychological Contract Theory. Data were collected using a written questionnaire from 178 male and 122 female employees of a large Anglo-Dutch company. Results using regression analyses showed that male candidates were more willing to accept an overseas assignment and more willing to follow their partners than female ones. Further, the rational choice and family power theories were best able to explain male candidates' willingness, whereas females' willingness was better predicted using variables from the life role salience and psychological contract theories. However, in terms of willingness to follow their partner, all the sets of variables are significant predictors for men, whereas, for women, only rational choice and family power variables explain a significant amount of the variance. The results are discussed in terms of theory and organisational practice.     

On the large sample distributions of modified sample biserial correlation coefficients

The asymptotic distributions of Brogden's and Lord's modified sample biserial correlation coefficients are derived. The asymptotic variances of these estimators are evaluated for bivariate normal populations and compared to the asymptotic variance of the maximum likelihood estimator.The author would like to thank the referees for several suggestions which improved the presentation of the paper.     

Testing the significance of the successive components in redundancy analysis

In this paper we study the interrelationships between two sets of data measured on the same subjects via redundancy analysis. We consider redundancy analysis from an inferential point of view. Under the hypothesis of multinormality, tests of significance are obtained for each successive redundancy component so that only the significant factors are retained for prediction purposes. An example illustrates the method. The authors would like to thank the Editor and the referees for their helpful comments. This research has been partly financed by NSERC (Canada).     

An ordinal coefficient of relational agreement for multiple judges

In a recent article, Fagot proposed a generalized family of coefficients of relational agreement for multiple judges, focusing on the concept of empirically meaningful relationships. In this paper an ordinal coefficient of relational agreement, based on ranking data, is presented as a special case of the generalized family. It is shown that the proposed ordinal coefficient encompasses other ordinal coefficients, such as the Kendall coefficient of concordance, the average Spearman rank-order coefficient, and intraclass correlation based on ranks. It is also shown that the Kendall coefficient of concordance, corrected for chance agreement, is equivalent to the ordinal coefficient proposed in this paper.     

Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions

Multiple regression quadratic assignment procedures (MRQAP) tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among n objects. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors. We present a new permutation method (called “double semi-partialing”, or DSP) that complements the family of extant approaches to MRQAP tests. We assess the statistical bias (type I error rate) and statistical power of the set of five methods, including DSP, across a variety of conditions of network autocorrelation, of spuriousness (size of confounder effect), and of skewness in the data. These conditions are explored across three assumed data distributions: normal, gamma, and negative binomial. We find that the Freedman–Lane method and the DSP method are the most robust against a wide array of these conditions. We also find that all five methods perform better if the test statistic is pivotal. Finally, we find limitations of usefulness for MRQAP tests: All tests degrade under simultaneous conditions of extreme skewness and high spuriousness for gamma and negative binomial distributions. Special thanks go to Cajo Ter Braak, Philip Hans Franses, Patrick Houweling, Pierre Legendre, three anonymous reviewers, the associate editor, and the editor for comments.     

心理测量本身及其在应用中的问题

从三个维度对心理测量进行了探讨：由理论基础上的缺陷所导致的局限性、在应用中所带来的问题以及由于运用统计相关分析所带来的弊端。最后对克服这些局限性的其它方法做简单介绍。     

浅析心理统计学教学设计中的统计意识

本文从教学设计的视角对下列两方面进行了理性的分析：(1)心理实验设计与心理统计课程的教学应逐步整合起来;(2)由于学科的特殊性,必须对统计再认识。     

An investigation of the partial-assignment completion effect on students' assignment choice behavior

This study was designed to investigate the partial assignment completion effect. Seventh-grade students were given a math assignment. After working for 5 min, they were interrupted and their partially completed assignments were collected. About 20 min later, students were given their partially completed assignment and a new, control assignment that contained the same number of equivalent problems that were incomplete on their partially completed assignment. Students were told that they would have to complete an assignment but could choose which assignment they completed. Significantly more students chose their partially completed assignment. Theoretical and applied implications and directions for future research are discussed.     

Repeated challenge studies: A comparison of union-intersection testing with linear modeling

Challenge studies are often implemented for assessing whether a subject is sensitive to a certain agent or allergen. In particular, researchers test groups of subjects to determine if there really exists a causal relationship between some agent of interest and a response. To answer such a question, we need to detect the presence of the phenomenon in just one individual. Typically, however, there are a large number of unknown risk factors associated with the response and a potentially small population prevalence. Hence, standard statistical techniques, by averaging the treatment effect across the group, may miss a significant response of a single individual and lead to inconclusive results. We develop an alternative approach based on union-intersection testing that will allow a practitioner to correctly examine observations on an individual apart from the other subjects and test the hypothesis of interest: Does the phenomenon exist in the population? More specifically, we show how this technique adjusts for the multiple number of tests encountered when analyzing data for each individual subject separately. Furthermore, we demonstrate power calculations for the determination of sample size prior to performing the study. The performance of the union-intersection approach in comparison to linear models and semiparametric techniques is considered through sample size calculations and simulations. The union-intersection testing methodology out performs the Kolmogorov tests. However, the nested linear model performs as well if not better than the union-intersection tests. To illustrate the ideas presented in the paper, we provide an application in which we analyze psychological data collected by way of a challenge study design.