When can we trust theF-approximation of the box-test?

Consider a multivariate context withp variates andk independent samples, each of sizen. To test equality of thek population covariance matrices, the likelihood ratio test is commonly employed. Box'sF-approximation to the null distribution of the test statistic can be used to computep-values, if sample sizes are not too small. It is suggested to regard theF-approximation as accurate if the sample sizesn are greater than or equal to 1+0.0613p ²+2.7265p-1.4182p ^0.5+0.235p ^1.4* In (k), for 5p30,k20.This research was supported by the Deutsche Forschungsgemeinschaft through Ste 405/2-1.     

Logit models and logistic regressions for social networks: III. Valued relations

This paper generalizes thep* model for dichotomous social network data (Wasserman & Pattison, 1996) to the polytomous case. The generalization is achieved by transforming valued social networks into three-way binary arrays. This data transformation requires a modification of the Hammersley-Clifford theorem that underpins thep* class of models. We demonstrate that, provided that certain (non-observed) data patterns are excluded from consideration, a suitable version of the theorem can be developed. We also show that the approach amounts to a model for multiple logits derived from a pseudo-likelihood function. Estimation within this model is analogous to the separate fitting of multinomial baseline logits, except that the Hammersley-Clifford theorem requires the equating of certain parameters across logits. The paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples.This research was supported by grants from the Australian Research Council, the National Science Foundation (#SBR96-30754), and the National Institute of Health (#PHS-1RO1-39829-01).     

On the Logic of β-pregroups

In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups (first introduced by Lambek [18] in 1999) enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit (locally) the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non-expanding rules must always proceed non-contracting ones in order the derivation to be minimal (normalization theorem). We also propose a sequent system for this calculus and prove the cut elimination theorem for it. As an illustration we show how to use β-pregroups for linguistical applications. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Back to the basics: Rethinking partial correlation network methodology

The Gaussian graphical model (GGM) is an increasingly popular technique used in psychology to characterize relationships among observed variables. These relationships are represented as elements in the precision matrix. Standardizing the precision matrix and reversing the sign yields corresponding partial correlations that imply pairwise dependencies in which the effects of all other variables have been controlled for. The graphical lasso (glasso) has emerged as the default estimation method, which uses ℓ₁-based regularization. The glasso was developed and optimized for high-dimensional settings where the number of variables (p) exceeds the number of observations (n), which is uncommon in psychological applications. Here we propose to go ‘back to the basics’, wherein the precision matrix is first estimated with non-regularized maximum likelihood and then Fisher Z transformed confidence intervals are used to determine non-zero relationships. We first show the exact correspondence between the confidence level and specificity, which is due to 1 minus specificity denoting the false positive rate (i.e., α). With simulations in low-dimensional settings (p ≪ n), we then demonstrate superior performance compared to the glasso for detecting the non-zero effects. Further, our results indicate that the glasso is inconsistent for the purpose of model selection and does not control the false discovery rate, whereas the proposed method converges on the true model and directly controls error rates. We end by discussing implications for estimating GGMs in psychology.     

Network models for social influence processes

This paper generalizes thep* class of models for social network data to predict individual-level attributes from network ties. Thep* model for social networks permits the modeling of social relationships in terms of particular local relational or network configurations. In this paper we present methods for modeling attribute measures in terms of network ties, and so constructp* models for the patterns of social influence within a network. Attribute variables are included in a directed dependence graph and the Hammersley-Clifford theorem is employed to derive probability models whose parameters can be estimated using maximum pseudo-likelihood. The models are compared to existing network effects models. They can be interpreted in terms of public or private social influence phenomena within groups. The models are illustrated by an empirical example involving a training course, with trainees' reactions to aspects of the course found to relate to those of their network partners.This research was supported by grants from the Australian Research Council. The authors would like to acknowledge the help of Stanley Wasserman, Janice Langan-Fox and Larry Hubert, and would like to thank four anonymous reviewers for their helpful comments. Earlier versions of this article were presented at the North American Conference of the Psychometric Society, Lawrence, Kansas, June, 1999, and at the Australasian Mathematical Psychology Conference, Brisbane, Australia, December 1999.     

Culturally adapted CBT (CA-CBT) for Latino women with treatment-resistant PTSD: a pilot study comparing CA-CBT to applied muscle relaxation

We examined the therapeutic efficacy of a culturally adapted form of CBT (CA-CBT) for PTSD as compared to applied muscle relaxation (AMR) for female Latino patients with treatment-resistant PTSD. Participants were randomized to receive either CA-CBT (n = 12) or AMR (n = 12), and were assessed before treatment, after treatment, and at a 12-week follow-up. The treatments were manualized and delivered in the form of group therapy across 14 weekly sessions. Assessments included a measure of PTSD, anxiety, culturally relevant idioms of distress (nervios and ataque de nervios), and emotion regulation ability. Patients receiving CA-CBT improved significantly more than in the AMR condition. Effect size estimates showed very large reductions in PTSD symptoms from pretreatment to posttreatment in the CA-CBT group (Cohen’s d = 2.6) but only modest improvements in the AMR group (0.8). These results suggest that CA-CBT can be beneficial for previously treatment-resistant PTSD in Latino women.     

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.     

A central limit theorem for families of stochastic processes indexed by a small average step size parameter,and some applications to learning models

Let > 0 be a measure of the average step size of a stochastic process {p _n ⁽⁾ } _n=1 ⁽⁾. Conditions are given under whichp _n ⁽⁾ is approximately normally distributed whenn is large and is small. This result is applied to a number of learning models where is a learning rate parameter andp _n ⁽⁾ is the probability that the subject makes a certain response on thenth experimental trial. Both linear and stimulus sampling models are considered.     

All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■ⁿ⁺¹_F p → ⁿ_F p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete.     

Greater arousal and less attentiveness to face/voice stimuli by neonates of depressed mothers on the Brazelton Neonatal Behavioral Assessment Scale

Neonates born to depressed (n = 44) versus non-depressed (n = 43) mothers were compared on individual items of the Brazelton Neonatal Behavioral Assessment Scale (NBAS). The neonates of depressed mothers received lower scores on orienting to the live face/voice stimulus and on the alertness items, suggesting they were less attentive. They also scored less optimally on the cuddliness and hand-to-mouth activity items, suggesting they were more aroused. These data lend support to the model that infants of depressed mothers are more aroused and less attentive.     

中国哲学与文化之根——"象"与"象思维"引论

To grasp the truth in traditional Chinese classics, we need to uncover the long obscured “xiang” 象 (image) thinking, which has long been overshadowed by Occidentalism. “xiang thinking” is the most fundamental thought of human beings. The logic of linguistics all comes from “xiang thinking”. Through conceptual thinking, people can understand Western classics on metaphysics, yet they may not completely understand the various schools of Chinese classics. The difference between Chinese and Western ways of thinking originated in the difference of the basic views developed in the “Axial period”. Since Aristotle, Western metaphysical ideas have all been manifested in substantiality, objectivity, and being ready-made, whereas Chinese Taiji, Dao, Xin-xing, and Zen were manifested in the non-substantiality, non-objectivity, and non-ready-made-ness of a dynamic whole. To grasp substance, rational and logical thinking such as definition, judgment, and reasoning is necessary. On the other hand, to grasp Taiji, Dao, etc., which is a dynamic whole or non-substances, “xiang thinking”, which is related to perception and rich in poetic association, is essential. History has taught us a lesson, i.e., when we opened the window to logical thought, we closed that of “xiang thinking”. We should remember the words of Xu Guangqi, i.e., “To mingle harmoniously and understand thoroughly so as to excel”. Translated by Zhang Lin from Hebei xuekan 河北学刊 (Hebei Academic Journal), 2007, (5): 21–25     

Optimal Partitioning of a Data Set Based on the p-Median Model

Although the K-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The p-median model is an especially well-studied clustering problem that requires the selection of p objects to serve as cluster centers. The objective is to choose the cluster centers such that the sum of the Euclidean distances (or some other dissimilarity measure) of objects assigned to each center is minimized. Using 12 data sets from the literature, we demonstrate that a three-stage procedure consisting of a greedy heuristic, Lagrangian relaxation, and a branch-and-bound algorithm can produce globally optimal solutions for p-median problems of nontrivial size (several hundred objects, five or more variables, and up to 10 clusters). We also report the results of an application of the p-median model to an empirical data set from the telecommunications industry.     

Two alternative models of health behaviour and recovery from activity limitations due to acute injury: A prospective study

Cognitions influence recovery from activity limitations. In this study we aimed to independently test, compare and combine the common sense self-regulation model (CS-SRM) and social cognitive theory (SCT) in predicting recovery from activity limitations due to acute injury. Measures were gathered at two time points 5–6 weeks apart. The sample consisted of 146 university students (Mean age: 21.86, SD: 4.83, 62% female) with a heterogeneous range of injuries that limited their participation in physical activity. The dependent variable was recovery from activity limitations (Physical Functioning?–?Short Form-36). The predictor variables were measured using the Brief Illness Perception Questionnaire and SCT items designed according to theoretical recommendations. Time-line (TL) and self-efficacy (SE) were significant predictors of recovery in a multivariate analysis, controlling for reported pain at Time 1. A combined model including the best predictors from both models, TL (β = ?0.25, p < 0.05, R ² change = 0.17, p < 0.01) and SE (β =0.31, p < 0.05, R ² change = 0.05, p < 0.05), accounted for a significant amount of the variance in recovery from activity limitations. A combination of key variables from both models may be particularly useful for understanding the cognitive factors that influence recovery from activity limitations.     

The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.     

Integration of disparity and velocity information for haptic and perceptual judgments of object depth

Do reach-to-grasp (prehension) movements require a metric representation of three-dimensional (3D) layouts and objects? We propose a model relying only on direct sensory information to account for the planning and execution of prehension movements in the absence of haptic feedback and when the hand is not visible. In the present investigation, we isolate relative motion and binocular disparity information from other depth cues and we study their efficacy for reach-to-grasp movements and visual judgments. We show that (i) the amplitude of the grasp increases when relative motion is added to binocular disparity information, even if depth from disparity information is already veridical, and (ii) similar distortions of derived depth are found for haptic tasks and perceptual judgments. With a quantitative test, we demonstrate that our results are consistent with the Intrinsic Constraint model and do not require 3D metric inferences (Domini, Caudek, & Tassinari, 2006). By contrast, the linear cue integration model (Landy, Maloney, Johnston, & Young, 1995) cannot explain the present results, even if the flatness cues are taken into account.     

Kripke Incomplete Logics Containing KTB

It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □² p → □³ p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □⁵ p → □⁶ p). Presented by Michael Zakharyaschev     

Psychological Empowerment Among Urban Youth: Measurement Model and Associations with Youth Outcomes

Empowerment‐based strategies have become widely used method to address health inequities and promote social change. Few researchers, however, have tested theoretical models of empowerment, including multidimensional, higher‐order models. We test empirically a multidimensional, higher‐order model of psychological empowerment (PE), guided by Zimmerman's conceptual framework including three components of PE: intrapersonal, interactional, and behavioral. We also investigate if PE is associated with positive and negative outcomes among youth. The sample included 367 middle school youth aged 11–16 (M = 12.71; SD = 0.91); 60% female, 32% (n = 117) white youth, 46% (n = 170) African‐American youth, and 22% (n = 80) identifying as mixed race, Asian‐American, Latino, Native American, or other ethnic/racial group; schools reported 61–75% free/reduced lunch students. Our results indicated that each of the latent factors for the three PE components demonstrate a good fit with the data. Our results also indicated that these components loaded on to a higher‐order PE factor (X² = 32.68; df: 22; p = .07; RMSEA: 0.04; 95% CI: .00, .06; CFI: 0.99). We found that the second‐order PE factor was negatively associated with aggressive behavior and positively associated with prosocial engagement. Our results suggest that empowerment‐focused programs would benefit from incorporating components addressing how youth think about themselves in relation to their social contexts (intrapersonal), understanding social and material resources needed to achieve specific goals (interactional), and actions taken to influence outcomes (behavioral). Our results also suggest that integrating the three components and promoting PE may help increase likelihood of positive behaviors (e.g., prosocial involvement); we did not find an association between PE and aggressive behavior. Implications and future directions for empowerment research are discussed.     

Dimensionality of stress experiences: Factorial structure of the Perceived Stress Questionnaire (PSQ) in a population‐based Swedish sample

We investigated the factorial structure of the Perceived Stress Questionnaire (PSQ‐recent; Levenstein, Prantera, Varvo et al., 1993) in a large (N = 1516; 35–95 years) population‐based Swedish sample (Nilsson, Adolfsson, Bäckman et al., 2004; Nilsson, Bäckman, Erngrund et al., 1997). Exploratory principal components analysis (PCA) was conducted on a first, randomly drawn subsample (n = 506). Next, the model based on the PCA was tested in a second sample (n = 505). Finally, a third sample (n = 505) was used to cross‐validate the model. Five components were extracted in the PCA (eigenvalue > 1) and labeled “Demands,” “Worries/Tension,” “Lack of joy,” “Conflict,” and “Fatigue,” respectively. Twenty‐one out of the 30 original PSQ items were retained in a confirmatory factor analysis (CFA) model that included the five (first‐order) factors and, additionally, a general (second‐order) stress factor, not considered in prior models. The model showed reasonable goodness of fit [χ²(184) = 511.2, p < 0.001; CFI = 0.904; RMSEA = 0.059; and SRMR = 0.063]. Multigroup confirmatory factor analyses supported the validity of the established model. The results are discussed in relation to prior investigations of the factorial structure of the PSQ.