Testing for independence between pairs of autocorrelated binomial data sequences

A problem arises in analyzing the existence of interdependence between the behavioral sequences of two individuals: tests involving a statistic such as chi-square assume independent observations within each behavioral sequence, a condition which may not exist in actual practice. Using Monte Carlo simulations of binomial data sequences, we found that the use of a chi-square test frequently results in unacceptable Type I error rates when the data sequences are autocorrelated. We compared these results to those from two other methods designed specifically for testing for intersequence independence in the presence of intrasequence autocorrelation. The first method directly tests the intersequence correlation using an approximation of the variance of the intersequence correlation estimated from the sample autocorrelations. The second method uses tables of critical values of the intersequence correlation computed by Nakamuraet al. (J. Am. Stat. Assoc., 1976,71, 214–222). Although these methods were originally designed for normally distributed data, we found that both methods produced much better results than the uncorrected chi-square test when applied to binomial autocorrelated sequences. The superior method appears to be the variance approximation method, which resulted in Type I error rates that were generally less than or equal to 5% when the level of significance was set at .05.     

Higher-order approximations to the distributions of fit indexes under fixed alternatives in structural equation models

Higher-order approximations to the distributions of fit indexes for structural equation models under fixed alternative hypotheses are obtained in nonnormal samples as well as normal ones. The fit indexes include the normal-theory likelihood ratio chi-square statistic for a posited model, the corresponding statistic for the baseline model of uncorrelated observed variables, and various fit indexes as functions of these two statistics. The approximations are given by the Edgeworth expansions for the distributions of the fit indexes under arbitrary distributions. Numerical examples in normal and nonnormal samples with the asymptotic and simulated distributions of the fit indexes show the relative inappropriateness of the normal-theory approximation using noncentral chi-square distributions. A simulation for the confidence intervals of the fit indexes based on the normal-theory Studentized estimators under normality with a small sample size indicates an advantage for the approximation by the Cornish–Fisher expansion over those by the noncentral chi-square distribution and the asymptotic normality. The author is indebted to the reviewers for their comments and suggestions, which have led to the improvement of the previous versions of this paper. This work was partially supported by Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science, and Technology.     

Masking misfit in confirmatory factor analysis by increasing unique variances: a cautionary note on the usefulness of cutoff values of fit indices

Fit indices are widely used in order to test the model fit for structural equation models. In a highly influential study, Hu and Bentler (1999) showed that certain cutoff values for these indices could be derived, which, over time, has led to the reification of these suggested thresholds as "golden rules" for establishing the fit or other aspects of structural equation models. The current study shows how differences in unique variances influence the value of the global chi-square model test and the most commonly used fit indices: Root-mean-square error of approximation, standardized root-mean-square residual, and the comparative fit index. Using data simulation, the authors illustrate how the value of the chi-square test, the root-mean-square error of approximation, and the standardized root-mean-square residual are decreased when unique variances are increased although model misspecification is present. For a broader understanding of the phenomenon, the authors used different sample sizes, number of observed variables per factor, and types of misspecification. A theoretical explanation is provided, and implications for the application of structural equation modeling are discussed.     

Some small sample results for maximum likelihood estimation in multidimensional scaling

Some aspects of the small sample behavior of maximum likelihood estimates in multidimensional scaling are investigated by Monte Carlo. An investigation of Model M2 in the MULTISCALE program package shows that the chi-square test of dimensionality requires a correction of tabled chi-square values to be unbiased. A formula for this correction in the case of two dimensions is estimated. The power of the test of dimensionality is acceptable with as few as two replications for 15 stimuli and as few as five replications for 10 stimuli. The biases in the exponent and standard error estimates in this model are also investigated.The research reported here was supported by grant number APA 320 to the author by the National Science and Engineering Research Council of Canada.     

The EZ diffusion method: Too EZ?

The diffusion model (Ratcliff, 1978) for fast two-choice decisions has been successful in a number of domains. Wagenmakers, van der Maas, and Grasman (2007) proposed a new method for fitting the model to data (“EZ”) that is simpler than the standard chisquare method (Ratcliff & Tuerlinckx, 2002). For an experimental condition, EZ can estimate parameter values for the main components of processing using only correct response times (RTs), their variance, and accuracy, not error RTs or the shapes of RT distributions. Wagenmakers et al. suggested that EZ produces accurate parameter estimates in cases in which the chi-square method would fail-specifically, experimental conditions with small numbers of observations or with accuracy near ceiling. In this article, I counter these claims and discuss EZ’s limitations. Unlike the chi-square method, EZ is extremely sensitive to outlier RTs and is usually less efficient in recovering parameter values, and it can lead to errors in interpretation when the data do not meet its assumptions, when the number of observations in an experimental condition is small, or when accuracy in an experimental condition is high. The conclusion is that EZ can be useful in the exploration of parameter spaces, but it should not be used for meaningful estimates of parameter values or for assessing whether or not a model fits data.     

Simultaneous nonlinear prediction

A previous article was concerned with simultaneous linear prediction [1]. There one was given a set of predictor tests or items and one predicted a set of predictands (also tests or items, or perhaps criteria.) We proposed asimultaneous prediction which was a certain weighted sum of the predictors. In the present article the constraint that the prediction be a weighted sum is relaxed. We seek a general function of the predictors which will maximize the quantity chosen for measuring prediction efficiency. This quantity is the same as the one used in linear prediction and we justify this approach by showing it is the appropriate one when there is only one predictand. In order to solve the problem we restrict consideration to a vector of predictors having only a finite number of possible values, i.e., it possesses discrete probability distribution weights. This can be applied in the case of dichotomous items for instance. It may also be used in continuous distributions as an approximation, by first dividing the original range of values into a finite number of intervals. Then one attributes to the interval the weight corresponding to the probability mass it underlies in the original distribution.This work was initiated at Stanford University under contract 2-10-065 with U. S. Office of Education and was partly revised at the Université de Montréal.I wish to express my gratitude to Professor Herbert Solomon, Stanford University, for his unfailing assistance at all stages of my work and specially for bringing to my attention the problem of nonlinear prediction in the present context.     

A non-parametric test of correlation using rank orders within subgroups

Kendall's rank order test for association between two variables is generalized to the case where the total sample is made up of several subgroups and the data on one or both variables consist of the rank order within each subgroup. The test involves no assumptions concerning scales of measurement, shapes of distributions, or relative level of excellence or amount of variability of the different subgroups. Two empirical examples indicate that the normal approximation to the exact test of significance can be considered adequate for most practical situations. Special consideration is given to the case of tied ranks. If ties occur in but one variable within any given subgroup, only a slight modification in procedure is needed. Extensive ties in both variables within subgroups lead to difficulties in determining the appropriate correction for continuity.     

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.     

Single subject incomplete designs for nonmetric multidimensional scaling

Monte Carlo procedures were used to investigate the properties of a nonmetric multidimensional scaling algorithm when used to scale an incomplete matrix of dissimilarities. Various recommendations for users who wish to scale incomplete matrices are made: (a) recovery was found to be satisfactory provided that the “degrees of freedom” ratio exceeded 3.5, irrespective of error level; (b) cyclic designs were found to provide best recovery, although random patterns of deletion performed almost as well; and (c) strongly locally connected designs, specifically overlapping cliques, were generally inferior. These conclusions are based on 837 scaling solutions and are applicable to stimulus sets containing more than 30 objects.     

On the ranking problem

Observed rankings of objects can be treated as arising from a time dependent probability process. Under such circumstances, associations observed are an indication of the character of this underlying process. In the particular example treated in some detail here, a quantity related to Kendall's tau is found to have an important role and its properties are examined.     

The validity of the successive intervals method of psychometric scaling

The degree to which scale values computed by the method of successive intervals diverge from theoretically true values is seen to be due to three types of error: error due to inequalities in variances of the distributions from which the scale values are computed, error due to non-normality of the distributions, and sampling error. The contribution of each type of error to the total error is evaluated; the latter is seen to be surprisingly small under appropriate conditions. Certain aspects of the formal methodology underlying scaling procedures are also briefly considered.This paper reports research undertaken in cooperation with the Quartermaster Food and Container Institute for the Armed Forces, and has been assigned number 475 in the series of papers approved for publication. The views or conclusions contained in this report are those of the authors. They are not to be construed as necessarily reflecting the views or indorsement of the Department of Defense.     

Looking a Hundred Years Back: Remarks on the Concept of "Wishing" in Psychoanalysis

While the concepts of "wish" and "wish fulfillment" have indeed remained central since the start of classical psychoanalysis, they are only weakly anchored both in theory and practice. It has become common today for psychoanalysts to use the term "to wish" in the sense of "to want" or "to intend." As a first step, it will be emphasized that "wish" should not be constructed along the lines of "intention." An examination of the relationship of "wish" to "wish fulfillment" is then followed by an evaluation of its practical significance for psychoanalysis and for our understanding of mental life in a general sense. Turning to an example dream sequence, we will arrive at the psychoanalytic core of the issue: the assumption of hidden, non-obvious, non-recognizable wish fulfillment scenarios. At this point in the discussion, a method of access will be sketched out - the dramaturgical approach - that, although it makes use of the idea of free association, does so in a manner that diverges from Freud's original recommendation.     

Internal multidimensional unfolding about a single-ideal—A probabilistic solution

A solution is presented for an internal multidimensional unfolding problem in which all the judgments of a rectangular proximity matrix are a function of a single-ideal object. The solution is obtained by showing that when real and ideal objects are represented by normal distributions in a multidimensional Euclidean space, a vector of distances among a single-ideal and multiple real objects follows a multivariate quadratic form in normal variables distribution. An approximation to the vector's probability density function (PDF) is developed which allows maximum likelihood (ML) solutions to be estimated. Under dependent sampling, the likelihood function contains information about the parametric distances among real object pairs, permitting the estimation of single-ideal solutions and leading to more robust multiple-ideal solutions. Tests for single- vs. multiple-ideal solutions and dependent vs. independent sampling are given. Properties of the proposed model and parameter recovery are explored. Empirical illustrations are also provided.     

The distinction between needs and wishes: implications for psychoanalytic theory and technique.

After a comprehensive survey of the literature is presented and some caveats entered, this paper delineates the concept of a psychological "need," noting that it bears a complex relation to the concept of a "wish." Need is universal, wish experience-bound. A need, unlike a wish, is not subject to repression. In addition, although a wish can be replaced by another wish, a need cannot be replaced by another need. Whereas the frustration of a wish causes dynamic shifts, the frustration of a need leads to structural disintegration. Needs and wishes can be in harmony or in opposition. The paper also identifies six basic psychological needs, which would seem to be ubiquitous, though the degree to which they are overt and the ways in which they are met vary across cultures. Their gratification seems necessary for healthy psychic development to occur, for relationships to survive, and for psychoanalytic work to take hold and to continue optimally. These needs are (1) the need for one's physical needs to be deemed legitimate; (2) the need for identity, recognition, and affirmation; (3) the need for interpersonal and intrapsychic boundaries; (4) the need for understanding the causes of events; (5) the need for optimal emotional availability of a love object; and (6) the need for a resilient responsiveness by one's love objects under special circumstances. Ordinarily these needs are met during the course of treatment with no deliberate effort by the analyst. In the treatment of some patients, however, they require more direct attention. A number of clinical vignettes are presented to elucidate these ideas.     

BORGES, IMMORTALITY AND THE CIRCULAR RUINS

The author explores ideas surrounding immortality and death focusing on the interplay between their development in two stories by Borges ('The circular ruins' and 'The immortal') and their manifestation in a patient. With the help of Borges's stories, the author addresses the desperate necessity experienced by some individuals to search for immortality. This is not just an expression of the universal wish to live forever but, at a deeper level, arises from the impossibility of bearing the mental pain of experiencing ordinary human vulnerability and loss - death being the ultimate expression of such vulnerability. It is suggested that the relentless pursuit of immortality in such individuals expresses an omnipotent phantasy of ridding the self of the emotional pain and fear that arises through being alive. It leads to a denial of the emotional significance of passage of time, of separation and sexual differences. In actuality, the individual's state of not feeling approximates to a complete loss of human identity and emotional death, with no place for any meaningful others. The individual him/herself becomes a 'mere image', living in a delusional world peopled by him/herself and his/ her projections, and ending up trapped inside the circular ruins he/she has generated. The horror experienced at the stark awareness of the individual's emotional death and the wish to re-establish contact with the good internal objects that have been attacked sets in motion the long process of searching for the recovery of a sense of temporality (that would still include the wish for immortality) and, with it, a sense of identity.     

A nonmetric variety of linear factor analysis

The numbers in each column of ann ×m matrix of multivariate data are interpreted as giving the measured values of alln of the objects studied on one ofm different variables. Except for random error, the rank order of the numbers in such a column is assumed to be determined by a linear rule of combination of latent quantities characterizing each row object with respect to a small number of underlying factors. An approximation to the linear structure assumed to underlie the ordinal properties of the data is obtained by iterative adjustment to minimize an index of over-all departure from monotonicity. The method is “nonmetric” in that the obtained structure in invariant under monotone transformations of the data within each column. Except in certain degenerate cases, the structure is nevertheless determined essentially up to an affine transformation. Tests show (a) that, when the assumed monotone relationships are strictly linear, the recovered structure tends closely to approximate that obtained by standard (metric) factor analysis but (b) that, when these relationships are severely nonlinear, the nonmetric method avoids the inherent tendency of the metric method to yield additional, spurious factors. From the practical standpoint, however, the usefulness of the nonmetric method is limited by its greater computational cost, vulnerability to degeneracy, and sensitivity to error variance.     

Gifts,talismans and tokens in analysis: symbolic enactments or sinister acts?

Analysis is nuanced with many non-verbal cues and interactions. This is vividly illustrated when gifts are presented to the analyst. Their physical presence transcends the symbolic frame of analysis because, although their meaning may be metaphorical, their presence is real. Unlike other material objects and pictures, the gift may seem to invite the analyst to receive it personally. It may apparently demand some form of action. A gift may be consciously given as a token, or it may be magically invested as a talisman. On the surface, it might appear to be an expression of love; it may be a communication of a wish for acceptance; but it may have more 'sinister', unconscious intent. It may embody the wish to expel unwanted affect, ward off evil or control the analyst. Therefore disposal, that is the resolution and settling of the object, is significant. The case with which this paper is illustrated traces the meaning of a series of gifts in a single analysis. It is hoped that this will enhance a wider understanding of this common analytic phenomenon.     

年幼儿童的尺寸匹配误差现象

近十年来,尺寸匹配误差作为年幼儿童生活中的一种常见的尺寸误用现象逐渐受到了一些研究者的关注。现有研究主要集中在尺寸匹配误差的特点、出现频率和产生原因等方面。抑制控制的失败、神经通路的协调失败、“计划-控制”模型和“感觉-行动”模型、功能性推理偏好以及身体意识发展的不成熟等观点能够对某些类型的尺寸匹配误差现象做出解释。未来的研究应从进一步深入探讨尺寸匹配误差与假装的区别、完善研究方法以及跨文化研究的开展几方面进行。     

Individual distributions under ordinal measurement

For ordinal measurement the concept of an individual propensity distribution is developed. For any given individual the mean of this distribution is his true score, for which estimation procedures are discussed. Two measures of individual dispersion are considered and their distributions derived in the null case. These measures are shown to be counterparts at the individual level of Kendall's tau and Spearman's rho. Estimation of the two dispersion measures from sample data is investigated, and the relation of these estimates to the variance of the individual propensity distribution is derived.     

Fear and its vicissitudes

Abstract

The USA has been a changed society since 9/11: the Zeitgeist either has a background of low-level angst, or when an attack occurs or a threat is sounded, the fear peaks and comes to the foreground for a time. Perhaps nothing demonstrates the degree to which fear permeates contemporary culture more than the continual presence of the measures the USA takes to be safe: airport security, the Patriot Act, the mining of formerly private information by the government, to name but a few. Can we account for the pervasive nature of fear solely by the devastating and deadly attacks 15 years ago, unspeakably horrifying though they were? This paper will explore this omnipresent fear in contemporary American culture from a psychoanalytic perspective, and in so doing hopes to shed light on the nature of that fear, why it is so persistent despite 15 years without any sequels, and what the consequences of that fear are for the American way of life. The discussion will be rounded out by linking this pervasive fear to the violence that is endemic to our age.