Locating the Extrema of Fungible Regression Weights

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of “fungible weights” (Waller, Psychometrica, in press) that yields identical SSE (sum of squared errors) and R ² values. When the R ² using the alternate weights is a fixed value, fungible weights (a _i ) that yield the maximum or minimum cosine with an OLS weight vector (b) are called “fungible extrema.” We describe two methods for locating fungible extrema and we report R code (R Development Core Team, 2007) for one of the methods. We then describe a new approach for populating a class of fungible weights that is derived from the geometry of alternate regression weights. Finally, we illustrate how fungible weights can be profitably used to gauge parameter sensitivity in linear models by locating the fungible extrema of a regression model of executive compensation (Horton & Guerard, Commun. Stat. Simul. Comput. 14:441–448, 1985).     

Correlation Weights in Multiple Regression

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights. We then derive the least squares weights (for any set of predictors) that yield the largest drop in R ² (the coefficient of determination) when switching to correlation weights. Our findings suggest that two characteristics of a model/data combination are especially important in determining the effectiveness of correlation weights: (1) the condition number of the predictor correlation matrix, R _xx , and (2) the orientation of the correlation weights to the latent vectors of R _xx .     

On the sensitivity of a composite to its weights

A method is presented for investigating two aspects of the sensitivity of a linear composite to the values of its weights.     

Regression among factor scores

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.     

The Geometry of Enhancement in Multiple Regression

In linear multiple regression, “enhancement” is said to occur when R ²=b′r>r′r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R _xx≠I, R _xx=E[xx′]=V Λ V′ (where V Λ V′ denotes the eigen decomposition of R _xx; λ ₁>λ ₂), the set B₁:={b_i:R²=b_i￠r_i=r_i￠r_i;0 < R² ￡ 1}\boldsymbol{B}_{1}:=\{\boldsymbol{b}_{i}:R^{2}=\boldsymbol{b}_{i}'\boldsymbol{r}_{i}=\boldsymbol{r}_{i}'\boldsymbol{r}_{i};0R² ￡ 1;R²l_p ￡ r_i￠r_i < R²}0p≥3 (and λ ₁>λ ₂>⋯>λ _p ), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B ₁ occurs at the intersection of two hyper-ellipsoids in ℝ ^p . Equations are provided for populating the sets B ₁ and B ₂ and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ _p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included in Appendices A and B.     

Regression estimation and post-stratification in factor analysis

Regression estimation and poststratification are methods used in survey sampling to estimate a population mean, when additional information is available for some auxiliary variables. The extension of these methods to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISREL framework.The author is grateful to the referees for their comments.     

Neuropsychological Aspects of Multiple Sclerosis

Since S. Rao's [Neuropsychology of Multiple Sclerosis: A Critical Review, A Journal of Clinical and Experimental Neuropsychology, Vol. 85, pp. 503–542] (1986) seminal review, considerable research has been undertaken on the neuropsychological consequences of multiple sclerosis. This review incorporates the research literature of the last decade in presenting an overview of the current state of our knowledge concerning the etiology, course, symptoms, assessment, consequences, and treatment of multiple sclerosis (MS). The concept of subcortical dementia is revisited in light of the most recent literature documenting the neuropsychological deficits in patients with MS. The view that cognitively heterogeneous patient groups may disguise more specific patterns of focal neuropsychological impairment is considered. A critical review of the recent literature is also presented, detailing the degree to which recent research has addressed the areas of research need identified by Rao in 1986. Given recent advances in our knowledge, the need for more attention to be directed toward the evaluation of rehabilitation and psychological intervention is highlighted.     

Regression in Autistic Spectrum Disorders

A significant proportion of children diagnosed with Autistic Spectrum Disorder experience a developmental regression characterized by a loss of previously-acquired skills. This may involve a loss of speech or social responsitivity, but often entails both. This paper critically reviews the phenomena of regression in autistic spectrum disorders, highlighting the characteristics of regression, age of onset, temporal course, and long-term outcome. Important considerations for diagnosis are discussed and multiple etiological factors currently hypothesized to underlie the phenomenon are reviewed. It is argued that regressive autistic spectrum disorders can be conceptualized on a spectrum with other regressive disorders that may share common pathophysiological features. The implications of this viewpoint are discussed.     

A Latent Transition Model With Logistic Regression

Latent transition models increasingly include covariates that predict prevalence of latent classes at a given time or transition rates among classes over time. In many situations, the covariate of interest may be latent. This paper describes an approach for handling both manifest and latent covariates in a latent transition model. A Bayesian approach via Markov chain Monte Carlo (MCMC) is employed in order to achieve more robust estimates. A case example illustrating the model is provided using data on academic beliefs and achievement in a low-income sample of adolescents in the United States. This research was partially supported by the National Institute on Drug Abuse Grant 1-R03-DA021639. This research was partially supported by the National Institute on Drug Abuse Grant 1-P50-DA10075, The Methodology Center, The Pennsylvania State University. This research was partially supported by the National Institute of Mental Health funds as part of the Studying Diverse Lives research support program at the Henry A. Murray Research Archive, Institute for Quantitative Science, Harvard University.     

视觉搜索中多目标追踪的研究

在视觉信息的选择加工过程中 ,只有很少信息能够通过注意系统得到进一步的认知加工 ,其中视觉搜索起着十分重要的作用。本研究基于动态视觉信息注意追踪的研究 ,采用 3× 2× 2的实验设计 ,从如下三方面对注意追踪的规律进行了探讨 :(1)分心物数量 (1,5和 9)的变化对多目标注意追踪的影响 ;(2 )目标的显著性 (特征变化和特征不变 )对多目标注意追踪的影响 ;(3)目标运动形式 (目标随机运动和目标运动形式不变 )对多目标注意追踪的影响。研究结果表明 :(1)分心物数量的增加对目标的注意识别没有抑制作用 ;(2 )特征变化目标的注意识别速度显著高于特征不变的目标 ;(3)运动形式不变的目标较运动形式变化目标的注意识别速度快。     

北京大学生多元自尊的解析

该研究试图考察北京大学生的整体自尊、多元自尊的特点,探讨整体自尊的结构,考察它与抑郁等消极情绪的关系。研究采用华人多元自尊量表、华人整体自尊量表,在北京地区18所高校中,随机选取300名大学生施测。结果显示:1)多元自尊存在性别差异和年级差异;2)在北京大学生的多元自尊中,个人独立与能力自尊、人际关系与人缘自尊以及家世背景与经济自尊是自尊结构中的主要维度,能够有效预测整体自尊;3)整体自尊与焦虑、抑郁、以及消极情绪的强度与频率都存在显著的负相关。     

The asymptotic distribution of commonality components

Commonality components have been defined as a method of partitioning squared multiple correlations. In this paper, the asymptotic joint distribution of all 2 ^k – 1 squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. In particular, the asymptotic joint distribution of commonality components are derived as a special case. Simultaneous and nonsimultaneous asymptotic confidence intervals for commonality components can be obtained from this distribution.This work was supported in part by the Spencer Foundation and the National Science Foundation.The authors are grateful to Bryna Siegel-Gorlick for her help in obtaining the data used in Example 4.3, and to the referees for their comments and suggestions.     

Unstable Interaction in Multiple Criteria Decision Problems

In this paper, we present a decision‐aid method with interacting criteria. The fuzzy measures used to aggregate the criteria depend on the considered alternatives. Pairwise comparisons on the importance of criteria and some levels of veto (or favor) degrees, specified by the decision maker, are taken into consideration. For each alternative, we search for the fuzzy measure that makes it the best. The orness degrees of the resulting fuzzy measures are compared and the alternative associated with the minimum orness degree is selected. Copyright © 2014 John Wiley & Sons, Ltd.     

关于多发性骨髓瘤的诊断

多发性骨髓瘤是浆细胞克隆性增生的恶性肿瘤,起病隐匿,临床表现复杂多样,且无特异性,诊断上依赖实验室检查。临床上对该病足够的认识,正确诊断尤为重要。在诊断中,科学地应用哲学思维,有助于减少误诊和漏诊。     

童年中期儿童社会能力与学业成就的交叉滞后研究

本研究采用同伴提名法、问卷法,对武汉市一所小学3、4、5、6年级儿童进行6个月的追踪调查。采用交叉时序滞后设计,考察了同伴关系4个特征水平(群体水平、双向关系水平、人际互动水平和个体特征水平)的变量与学业成就的相互预测关系。结果表明,在控制了前测学业成就后,前测的社会喜好、积极友谊质量、社交领导行为可以分别正向预测后测的学业成就,而前测的攻击行为可以负向预测后期的学业成就;在控制了前测的社交自我知觉后,学业成就可以正向预测后期的社交自我知觉。     

Isolating and Examining Sources of Suppression and Multicollinearity in Multiple Linear Regression

The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic strategy to isolate, examine, and remove suppression effects has been offered. In this article such an approach, rooted in confirmatory factor analysis theory and employing matrix algebra, is developed. Suppression is viewed as the result of criterion-irrelevant variance operating among predictors. Decomposition of predictor variables into criterion-relevant and criterion-irrelevant components using structural equation modeling permits derivation of regression weights with the effects of criterion-irrelevant variance omitted. Three examples with data from applied research are used to illustrate the approach: the first assesses child and parent characteristics to explain why some parents of children with obsessive-compulsive disorder accommodate their child's compulsions more so than do others, the second examines various dimensions of personal health to explain individual differences in global quality of life among patients following heart surgery, and the third deals with quantifying the relative importance of various aptitudes for explaining academic performance in a sample of nursing students. The approach is offered as an analytic tool for investigators interested in understanding predictor-criterion relationships when complex patterns of intercorrelation among predictors are present and is shown to augment dominance analysis.     

Original and cumulative prospect theory: a discussion of empirical differences

This paper discusses differences between prospect theory and cumulative prospect theory. It shows that cumulative prospect theory is not merely a formal correction of some theoretical problems in prospect theory, but it also gives different predictions. Some experiments by Lola Lopes are re-analyzed, and are demonstrated to favor cumulative prospect theory over prospect theory. It turns out that the mathematical form of cumulative prospect theory is well suited for modeling the psychological phenomenon of diminishing sensitivity. © 1997 John Wiley & Sons, Ltd.     

Retributivism and Multiple Offending

This article addresses the question of how multiple offenders – that is, offenders who have committed more than one crime before they are apprehended – should be punished from a retributivist point of view. Two theories are evaluated, both defending the view that there should be a bulk discount for multiple offending. According to the first theory, a bulk discount follows from the idea of a punishment ceiling for types of crimes and the principle of parsimony in punishing. According to the second, the discount follows from a certain view on mercy. However, it is argued that both theories suffer from theoretical flaws and that they are also insufficient in practical terms. That is, they fail to provide a basis for the making of decisions about how multiple-offence cases should be dealt with by the criminal justice system.     

The Detection and Interpretation of Interaction Effects Between Continuous Variables in Multiple Regression

issues in the detection and interpretation of interaction effects between quantitative variables in multiple regression analysis are discussed. Recent articles by Cronbach (1987) and Dunlap and Kemery (1987) suggested the use of two transformations to reduce "problems" of multicollinearity. These transformations are discussed in the context of the conditional nature of multiple regression with product terms. It is argued that although additive transformations do not affect the overall test of statistical interaction, they do affect the interpretational value of regression coefficients. Factors other than multicollinearity that may account for failures to observe interaction effects are noted.