A note on monotone polygons fitted to bivariate data

The monotone regression function of Kruskal and the rank image function of Guttman and Lingoes were fitted to bivariate normal samples and their statistical properties contrasted.This paper was written while the author was a Visiting Professor in the Department of Psychology, University College, London.     

THE USE AND UTILITY OF THE MONOTONE CRITERION IN MULTIDIMENSIONAL SCALING

The monotone criterion as a multidimensional scaling technique is theoret- ically and empirically evaluated using the algorithms of Kruskal (MDSCAL) and Guttman-Lingoes (SSA-1). Geometric configurations are used to test the recovery capabaty and other aspects of MDSCAL and SSA-1. In addition to theoretical shortcomings, the monotone criterion permits results which do not correspond to the shape of the input data. Because of its deficiencies, alterna- tive goodness-of-fit criteria are suggested in preference to the monotone criterion.     

A simple method for pairwise monotone regression

A simple method of monotone regression is described based on the principle of minimizing pairwise departures from monotonicity.     

The Influence of Close Ties on Depression: Does Network Religiosity Matter?

Despite a growing body of the literature on how features of social networks influence well-being, we know little of how the religiosity of social networks matter. This study addresses three types of religious social network ties and their association with mental health: same (non)-religious ties, religious discussion ties, and ties offering prayers on an individual's behalf. Using ego-centric network data from the 2006 Portraits of American Life Study (N = 2,223), multivariate regression results suggest that a greater number of ties that discuss religion and pray for the respondent are detrimental to the mental health of those of a low religious salience. Taken together, this study demonstrates that religious dimensions of social networks exact an important influence on mental health and highlights the importance of identifying specific features of religion among core network ties.     

Positive and negative social ties among older adults: Measurement models and the prediction of psychological distress and well-being

The factor structure of positive and negative social ties was studied among 246 older adults who were either recently physically disabled, recently conjugally bereaved, or matched controls. Covariance structure analyses were carried out on a network measure to determine whether positive and negative social ties represent independent domains of social experience, and to assess the degree to which their structure is invariant across groups undergoing major loss transitions. Positive and negative social ties were found to be independent and there was substantial similarity in their factor structure across the three groups. Hierarchical regression analyses revealed that, whereas positive social ties were related to psychological well-being, negative social ties were predictive of both psychological well-being and distress. These results demonstrate the importance of assessing both positive and negative ties in explaining the psychological adjustment of older adults.     

Some boundary conditions for a monotone analysis of symmetric matrices

This paper gives a rigorous and greatly simplified proof of Guttman's theorem for the least upper-bound dimensionality of arbitrary real symmetric matricesS, where the points embedded in a real Euclidean space subtend distances which are strictly monotone with the off-diagonal elements ofS. A comparable and more easily proven theorem for the vector model is also introduced. At mostn-2 dimensions are required to reproduce the order information for both the distance and vector models and this is true for any choice of real indices, whether they define a metric space or not. If ties exist in the matrices to be analyzed, then greatest lower bounds are specifiable when degenerate solutions are to be avoided. These theorems have relevance to current developments in nonmetric techniques for the monotone analysis of data matrices.This research in nonmetric methods is supported in part by a grant from the National Science Foundation (GS-929 & -2850).The very helpful comments and encouragement of Louis Guttman and J. Douglas Carroll are greatly appreciated. Finally, to that unknown, but not unsung, reviewer who helped in the clarification of the argument, I express my thanks.     

Monotone regression: Continuity and differentiability properties

Least-squares monotone regression has received considerable discussion and use. Consider the residual sum of squaresQ obtained from the least-squares monotone regression ofy _i onx _i . TreatingQ as a function of they _i , we prove that the gradient Q exists and is continuous everywhere, and is given by a simple formula. (We also discuss the gradient ofd=Q ^1/2.) These facts, which can be questioned (Louis Guttman, private communication), are important for the iterative numerical solution of models, such as some kinds of multidimensional scaling, in which monotone regression occurs as a subsidiary element, so that they _i and hence indirectlyQ are functions of other variables.     

Robust decision making in a nonlinear world

The authors propose a general modeling framework called the general monotone model (GeMM), which allows one to model psychological phenomena that manifest as nonlinear relations in behavior data without the need for making (overly) precise assumptions about functional form. Using both simulated and real data, the authors illustrate that GeMM performs as well as or better than standard statistical approaches (including ordinary least squares, robust, and Bayesian regression) in terms of power and predictive accuracy when the functional relations are strictly linear but outperforms these approaches under conditions in which the functional relations are monotone but nonlinear. Finally, the authors recast their framework within the context of contemporary models of behavioral decision making, including the lens model and the take-the-best heuristic, and use GeMM to highlight several important issues within the judgment and decision-making literature.     

Social Support and the Religious Dimensions of Close Ties

Despite the influence of social support on physical and mental health, few studies have examined why some close ties are more supportive than others. Though religion provides a rich context for social interaction and a meaningful social identity, it has received little attention in the social support literature. A growing literature on religion and health offers insight into how religion affects social support processes. Using dyadic network data derived from the nationally representative 2006 Portraits of American Life Study, I examine how the religious dimensions of close, nonhousehold ties relate to provision of social support. Results from logistic regression analyses indicate that (controlling for a range of other social tie characteristics) same‐faith ties are significantly more likely to be sources of help “in times of need,” while religious discussion is a strong predictor of receiving both help and advice. The effect of religious homophily is strongest for evangelical Protestants and African‐American Protestants. My findings underscore the need for social support researchers to consider the role of religion in shaping support processes in close relationships.     

Simple and multiple P‐splines regression with shape constraints

In many research areas, especially within social and behavioural sciences, the relationship between predictor and criterion variables is often assumed to have a particular shape, such as monotone, single‐peaked or U‐shaped. Such assumptions can be transformed into (local or global) constraints on the sign of the nth‐order derivative of the functional form. To check for such assumptions, we present a non‐parametric regression method, P‐splines regression, with additional asymmetric discrete penalties enforcing the constraints. We show that the corresponding loss function is convex and present a Newton–Raphson algorithm to optimize. Constrained P‐splines are illustrated with an application on monotonicity‐constrained regression with both one and two predictor variables, using data from research on the cognitive development of children.     

RESILIENCE IN LOW-INCOME, EMPLOYED, AFRICAN AMERICAN WOMEN

This study focuses on resilience in poor women and asks the question: In the face of a lifetime of adversity, stress, and poverty, what are the factors that enable some poor women to lead positive and productive lives? Fifty low-income, urban, African American women were interviewed, and factors that contribute to their resilience were explored. Specifically, we examined the influence of supportive and problematic social ties, downward social comparison, and self-efficacy on resilience, as measured by scales designed to assess well-being. In addition, the participants' perceptions of factors that contribute to their resilience were elicited. The women in the sample were between the ages of 19 and 54, were employed at least 20 hours per week, and had at least one child below the age of 13 at home. Multiple regression analyses revealed that problematic social ties and downward social comparison together predicted over 48% of the variance in resilience.     

A longitudinal study of the moderating effects of social capital on the relationships between changes in human capital and ikigai among Japanese older adults

Ikigai, one of the indices of well‐being, tends to decline with age because resources relating to ikigai decline. However, there are individual differences in this decline. This study tested for maintenance of ikigai among Japanese elderly, using a longitudinal study investigating the moderating role of social capital on the effects of changes in human capital on ikigai. We conducted a panel survey targeting 1,068 people (M age = 73.01 years) in 2013, and 686 people in 2017. The variables were ikigai, changes in human capital (self‐rated financial status, physical health) and social capital (social networks, trust in others), educational level, and control variables. Multiple regression analyses revealed the interaction effects of changes in physical health and changes in social networks (strong ties, weak ties) on follow‐up ikigai. Post hoc analyses indicated that declines in physical health predicted declines in ikigai among those whose social networks (strong ties and weak ties) had declined in the 4‐year study, but these relationships were not significant among those whose social networks had increased. The results suggest that older adults can weaken the adverse effect of a decline in human capital on ikigai by maintaining or increasing social networks.     

Positive Monotone Modal Logic

Studia Logica - Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and . We axiomatise positive monotone modal...     

Nonmetric multidimensional scaling with clustering of subjects

A new nonmetric multidimensional scaling method is devised to analyze three-way data concerning inter-stimulus similarities obtained from many subjects. It is assumed that subjects are classified into a small number of clusters and that the stimulus configuration is specific to each cluster. Under this assumption, the classification of subjects and the scaling used to derive the configurations for clusters are simultaneously performed using an alternating least-squares algorithm. The monotone regression of ordinal similarity data, the scaling of stimuli and the K -means clustering of subjects are iterated in the algorithm. The method is assessed using a simulation and its practical use is illustrated with the analysis of real data. Finally, some extensions are considered.     

An analysis of generative representation systems

Three ideas are basic to generative theory: (a) Subjects are assumed to attend to the relations among stimuli, extracting the transformations relating pairs of stimuli; (b) the set of abstracted transformations is decomposed or reduced to an elementary set of generators; (c) subjects use the elementary generators as the basis for judging similarity. The purpose of this paper is to illustrate these ideas with an experiment in which subjects were asked to rate the similarity between stimulus pairs. The stimulus materials consisted of the permutations of a 4-item pattern with the properties of a dihedral group which insured the existence of sets of elementary transformations. Three analytic techniques were used to determine the generator set of transformations abstracted by subjects. The first analysis consisted of a monotonic regression between dissimilarity ratings and the number of elementary generators of a given permutation. The residual variance of this monotone regression, suitably normalized, was used as a quantitative goodness-of-fit measure. For the stochastic analysis, cumulative distributions of dissimilarity ratings were obtained for permutations requiring one, two, or three generators. The idea was that permutations requiring fewer generators should be associated with distributions of lower dissimilarity values (higher similarity scores) as compared to permutations predicted to be transformationally more complex. The final analysis, a multidimensional scaling of dissimilarity ratings, converted subjects' ratings into spatial structures to determine whether individual subjects' ratings exhibited the predicted spatial arrangement. The monotone regression and stochastic analyses abstracted similar generator sets for individual subjects, some of which provided perfect fits to the data. Although the scaling analysis yielded similar estimates of generators, for some subjects, transformations with the same number of generators yielded unequal “cognitive” distances resulting in some-what deformed spatial structures for these subjects. It was concluded that the results generally supported a generative model as an approximation to subjects' representations of interstimulus relationships.     

Criminal Victimization,Depressive Symptoms,and Behavioral Avoidance Coping in Late Adulthood: The Conditioning Role of Strong Familial Ties

This study examined the association criminal victimization has with two mental health outcomes (i.e., depressive symptoms and behavioral avoidance coping) among older adults. This study also tested whether strong familial ties condition the harmful results of victimization. This study used cross-sectional survey data from interviews conducted in Arizona and Florida with individuals 60 years and older (N?=?2000). Linear regression was used to test the hypotheses. Victims reported higher depressive symptoms and greater behavioral avoidance coping. The link between victimization and depression was weaker among participants with strong attachments to their spouse and to their children. Strong spousal ties also diminished the link between criminal victimization and behavioral avoidance coping. These findings are consistent with research conducted at earlier stages of the life course. Practitioners should work with older crime victims to identify interventions that provide the types of support found in strong familial relationships.     

Company matters: Goal-related social capital in the transition to working life

Using longitudinal data on 343 young adults, the present study investigated the social ties involved in young adults’ work-related goals, how these ties change during transition to working life, and whether social ties contribute to success in dealing with the transition. The results showed that goal-relevant social ties reflected changes in the young adults’ developmental context. Furthermore, social ties that included a person with high socioeconomic status and weaker social ties contributed to employment success, whereas social ties containing one’s supervisor were associated with quality of employment. The results also showed that goal-related social hindrance increased young adults’ intentions to quit and decreased job satisfaction.     

Predicting Chinese international students’ acculturation strategies from socio‐demographic variables and social ties

Different acculturation strategies (i.e. integration, assimilation, separation and marginalization) tend to contribute to different adaptation outcomes for international students. The current study examines Chinese international students’ acculturation strategies under the influence of sociodemographic variables and social ties they developed in the host country. A group of Chinese international students in Belgium (N = 183) participated in an online survey. The results indicate that integration was the most commonly adopted strategy among Chinese international students in Belgium, followed by separation, marginalization and assimilation. The results from three separate multiple regressions show that English proficiency, local language proficiency, prior adaptation experience and female were significant predictors of Chinese students’ social ties (i.e. host‐national ties, international ties and co‐national ties). The discriminant analysis identified host‐national ties, international ties, co‐national ties, local language proficiency and prior adaptation experience as important variables that can distinguish Chinese students’ acculturation strategies.     

Gender differs: Modelling knowledge sharing from a perspective of social network ties

The present paper proposes a model of knowledge sharing, in which coworker congruence, outcome interdependence, perceived organizational support, and procedural justice influence knowledge sharing indirectly through the mediation of instrumental ties and expressive ties, and examined gender differences in causal connections within the model. In a sample of employees in Taiwan, it was shown that the influence of instrumental ties on knowledge sharing is stronger for females than for males; the influence of expressive ties on knowledge sharing is stronger for males than for females; the influence of coworker congruence on expressive ties is stronger for females than for males; the influence of outcome interdependence on instrumental ties is stronger for females than for males; and the influence of perceived organizational support on instrumental ties is stronger for males than for females.     

Generalizing disposability: Residential mobility and the willingness to dissolve social ties

Four studies examined whether residential mobility (RM) leads people to view objects as disposable and, in turn, view social ties as disposable. Study 1 showed that tendencies to dispose of objects and social ties are related. Study 2 demonstrated that a history of RM increases the willingness to dispose of objects and, through that, dispose of social ties. Study 3 showed that increasing the sense of RM increases the willingness to dispose of objects and, through this, dispose of social ties. Study 4 showed that the relational aspect of RM is crucial in affecting relational disposability. Our findings extend research on RM and support Lewin's (1936) conceptualization of mobility being associated with ease of disposing social ties.