Approximate confidence intervals for a robust scale parameter

A recent paper by Wainer and Thissen has renewed the interest in Gini's mean difference,G, by pointing out its robust characteristics. This note presents distribution-free asymptotic confidence intervals for its population value,γ, in the one sample case and for the difference Δ=(γ ₁?γ ₂) in the two sample situations. Both procedures are based on a technique of jackknifingU-statistics developed by Arvesen.     

On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation

In the context ofconditional maximum likelihood (CML) estimation, confidence intervals can be interpreted in three different ways, depending on the sampling distribution under which these confidence intervals contain the true parameter value with a certain probability. These sampling distributions are (a) the distribution of the data given theincidental parameters, (b) the marginal distribution of the data (i.e., with the incidental parameters integrated out), and (c) the conditional distribution of the data given the sufficient statistics for the incidental parameters. Results on the asymptotic distribution of CML estimates under sampling scheme (c) can be used to construct asymptotic confidence intervals using only the CML estimates. This is not possible for the results on the asymptotic distribution under sampling schemes (a) and (b). However, it is shown that theconditional asymptotic confidence intervals are also valid under the other two sampling schemes. I am indebted to Theo Eggen, Norman Verhelst and one of Psychometrika's reviewers for their helpful comments.     

Goodness-of-fit and confidence intervals of approximate models

If the model for the data are strictly speaking incorrect, then how can one test whether the model fits? Standard goodness-of-fit (GOF) tests rely on strictly correct or incorrect models. But in practice the correct model is not assumed to be available. It would still be of interest to determine how good or how bad the approximation is. But how can this be achieved? If it is determined that a model is a good approximation and hence a good explanation of the data, how can reliable confidence intervals be constructed? In this paper, an attempt is made to answer the above questions. Several GOF tests and methods of constructing confidence intervals are evaluated both in a simulation and with real data from the internet-based daily news memory test.     

The statistical recommendations of the American Psychological Association Publication Manual: Effect sizes,confidence intervals,and meta‐analysis

Estimation based on effect sizes, confidence intervals, and meta‐analysis usually provides a more informative analysis of empirical results than does statistical significance testing, which has long been the conventional choice in psychology. The sixth edition of the American Psychological Association Publication Manual now recommends that psychologists should, wherever possible, use estimation and base their interpretation of research results on point and interval estimates. We outline the Manual's recommendations and suggest how they can be put into practice: adopt an estimation framework, starting with the formulation of research aims as ‘How much?’ or ‘To what extent?’ questions. Calculate from your data effect size estimates and confidence intervals to answer those questions, then interpret. Wherever appropriate, use meta‐analysis to integrate evidence over studies. The Manual's recommendations can assist psychologists improve they way they do their statistics and help build a more quantitative and cumulative discipline.     

On reliving theWanderjahr: The many voyages of theBeagle

This is a study of constancy and change in the development of one adult's system of beliefs and way of thought. It compares two documents, two versions of Charles Darwin's account of the voyage of theBeagle, one written at an early stage in the development of his evolutionary thought, the other much later but still long before he wrote theOrigin of the Species. The second version was produced 7 years after Darwin developed the theory of evolution through natural selection. Although no explicit reference is made to that theory, both versions exhibit a style of thought and a pattern of beliefs that remained very stable throughout. Examination of the documents reveals 13 major themes: relation between food supply and population; struggle; extinction; the superfecundity of nature; the tangled bank; selection; variation and divergence; the law of the succession of types; biogeography; strange contrivances, maladaptations, and rudimentary organs; human imperfections and perfectibility; the transformation of creation; and psychology. The study concludes with a discussion of the relation between private thought and public discourse, and the bearing of this relationship on exchanges between Charles Darwin and Alfred Russel Wallace.     

On the Dao in the Commentary of the Book of Change

The existence of the Dao 道 (the Way), according to the Yizhuan 易传 (the Commentary), is something intangible. The connotation of the Dao is the law of change caused by the interaction between yin and yang. The main functions of the Dao are “to change” and “to generate”. The intangible refers to the law of change caused by the interaction between yin and yang, and the law is expressed by the divinatory symbolic system (卦爻符号, the trigrams or hexagrams). It is through the unique permutation of yin and yang lines of a trigram or hexagram that the law of change is explained as a universal model uniting celestial, terrestrial and human laws. The symbolic system is used to express the universal nature of continual generation of life. __________ Translated from Zhongguo Zhexue Shi 中国哲学史 (History of Chinese Philosophy), 2005(4) by Yun Yufen     

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.     

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.     

On the Proof Theory of the Modal mu-Calculus

We study the proof-theoretic relationship between two deductive systems for the modal mu-calculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on non-well-founded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely often along every branch. The main contribution of our paper is a translation from proofs in the first system to proofs in the second system. Completeness of the second system then follows from completeness of the first, and a new proof of the finite model property also follows as a corollary. Presented by Heinrich Wansing     

Fisher transformations for correlations corrected for selection and missing data

The validity of a test is often estimated in a nonrandom sample of selected individuals. To accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction. Unfortunately, this corrected correlation cannot be transformed using Fisher'sZ transformation, and asymptotic tests of hypotheses based on small or moderate samples are not accurate. We developed a Fisherr toZ transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on the predictor (the missing data were MAR); and (b) the criterion was missing at random, not due to selection (the missing data were MCAR). The twoZ transformations were evaluated in a computer simulation. The transformations were accurate, and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations.     

Dissecting the clock: understanding the mechanisms of timing across tasks and temporal intervals

Currently, it is unclear what model of timing best describes temporal processing across millisecond and second timescales in tasks with different response requirements. In the present set of experiments, we assessed whether the popular dedicated scalar model of timing accounts for performance across a restricted timescale surrounding the 1-second duration for different tasks. The first two experiments evaluate whether temporal variability scales proportionally with the timed duration within temporal reproduction. The third experiment compares timing across millisecond and second timescales using temporal reproduction and discrimination tasks designed with parallel structures. The data exhibit violations of the assumptions of a single scalar timekeeper across millisecond and second timescales within temporal reproduction; these violations are less apparent for temporal discrimination. The finding of differences across tasks suggests that task demands influence the mechanisms that are engaged for keeping time.     

On the need for negative local item dependence

While negative local item dependence (LID) has been discussed in numerous articles, its occurrence and effects often go unrecognized. This is due in part to confusion over what unidimensional latent trait is being utilized in evaluating the LID of multidimensional testing data. This article addresses this confusion by using an appropriately chosen latent variable to condition on. It then provides a proof that negative LID must occur when unidimensional ability estimates (such as number right score) are obtained from data which follow a very general class of multidimensional item response theory models. The importance of specifying what unidimensional latent trait is used, and its effect on the sign of the LIDs are shown to have implications in regard to a variety of foundational theoretical arguments, to the simulation of LID data sets, and to the use of testlet scoring for removing LID.This paper is based in part on a chapter in the first author's doctoral dissertation, written at the University of Illinois at Urbana-Champaign under the supervision of William Stout. Part of this research has been presented at the annual meeting of the National Council on Measurement in Education, San Diego, California, April 14–16, 1998.The research of the first author was partially supported by a Harold Gulliksen Psychometric fellowship through Educational Testing Service and by a Research and Productive Scholarship award from the University of South Carolina.     

Association coefficients of identity and proportionality for metric scales

Zegers' (1986) chance-corrected coefficients of association are derived by alternative methods. A different definition of chance correction is used. It is shown that our correction and that of Zegers are identical for large samples. Three possible assumptions for the derivation of metric coefficients are examined. The first, variable reflection, formulated by Zegers and ten Berge (1985), leads to coefficients that require chance-correction. Two other assumptions, zero covariance and covariance reflection, are proposed and it is shown that the latter two assumptions lead directly to coefficients of identity and proportionality that do not require chance correction (i.e., are identical to the Zegers, 1986, corrected coefficients).We are indebted to Robyn M. Dawes, Carnegie-Mellon University, for stimulating our interest in this project, and for helpful suggestions.     

On modal μ-calculus with explicit interpolants

This paper deals with the extension of Kozen's μ-calculus with the so-called “existential bisimulation quantifier”. By using this quantifier one can express the uniform interpolant of any formula of the μ-calculus. In this work we provide an explicit form for the uniform interpolant of a disjunctive formula and see that it belongs to the same level of the fixpoint alternation hierarchy of the μ-calculus than the original formula. We show that this result cannot be generalized to the whole logic, because the closure of the third level of the hierarchy under the existential bisimulation quantifier is the whole μ-calculus. However, we prove that the first two levels of the hierarchy are closed. We also provide the μ-logic extended with the bisimulation quantifier with a complete calculus.     

Concurrent Validity Studies of the Facial Discrimination Task

We examined the concurrent validity properties of the Facial Discrimination Task (FDT), an instrument for the assessment of facial emotion recognition by comparing it with the widely used Pictures of Facial Affect (PFA). In Study 1, 100 adults with heterogeneous psychiatric diagnoses were administered items of the FDT Emotion Task, the FDT Age Task, and PFA. In Study 2, 25 normally developing preschool children were instructed to label happy, sad, or neutral facial expressions from the FDT and the PFA. Despite methodological differences between the two studies, very similar and high correlations were found between the FDT and the PFA overall correct scores (r = .79 and r = .77, respectively). The data suggest that the FDT and the PFA measure similar competencies in preschoolers and in adults with psychiatric disorders. This finding is important because it establishes the concurrent validity of the FDT in child and adult populations.     

Validating Clusters with the Lower Bound for Sum-of-Squares Error

Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum-of-squares error criterion in K-means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on the observed sum-of-squares error as compared to the minimum sum-of-squares error. The author was partially supported by the Office of Naval Research Grant #N00014-06-0106.     

Old Foundations for the Logic of Agency and Action

The paper presents an infinite hierarchy of sound and complete axiomatic systems for Two-Dimensional Modal Tense Logic with Historical Necessity, Agents and Acts. A main novelty of these logics is their capacity to represent formally (i) basic action-sentences asserting that such and such an act is performed/omitted by an agent, as well as (ii) causative action-sentences asserting that by performing/omitting a certain act, an agent causes that such and such a state-of-affairs is realized (e.g. comes about/ceases/remains/remains absent). We illustrate how the formal machinery of our systems can be used to reconstruct a number of interesting ideas in the Logic of Agency and Action that have been proposed by authors like von Wright, von Kutschera, Belnap and Segerberg.     

《恒先》义释——思想史视野下的一种解读

Hengxian, one of the bamboo books of the Chu State during the Warring States Period that is kept in the Shanghai Museum, was collected by the museum in 1994, and is an important piece of literature that discusses cosmic issues prior to Huainanzi. Based on Li Ling’s work on the text, as well as hermeneutic work by some other scholars, this essay represents another attempt to determine the words and meanings of the Hengxian, with a focus on its cosmological commentary. Translated by Huang Deyuan from Xi’an Jianzhu Keji Daxue Xuebao 西安建筑科技大学学报 (Journal of Xi’an University of Arch & Tech), 2007, (1): 1–8