Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

Rediscovering the Positive Psychology of Sport Participation: Happiness in a Ski Resort Context

Interrelated functions of the three orientations to happiness were examined by a cross-sectional survey, in the context of a ski resort experience. Accordingly, a conceptual framework of pleasure, flow, and involvement influencing satisfaction was established. Utilizing structural equation modeling, the conceptual framework was tested by analyzing data collected from 279 participants who enjoyed skiing and/or snowboarding. Results from bootstrap test indicated that direct and total effects from flow had the highest predictive power on satisfaction. In contrast, pleasure showed higher explanatory power on subjective experiences of flow and meaning, and influenced satisfaction only by indirect effects through those elements. Together, these findings support the research model synthesizing the behavioral constructs of sport participation with subjective well-being perspectives. Moreover, the expanded model in a sporting context further evidences the functional roles of the orientations to happiness by results consistent with extant literature of positive psychology. Roles of embodiments of orientations to happiness in an action-based exercise and its implications are further discussed.     

A comparison of parental attention and preferred items during tummy time: A consecutive controlled case series evaluation

Tummy time is an activity for infants to practice their early motor skills. Although most pediatricians recommend tummy time, parents may avoid the procedures due to indices of infant discomfort during this period. This consecutive controlled case series evaluation compared the effects of preferred items selected from a preference assessment with those of parental attention on head evaluation and negative vocalizations during tummy time. In addition, we directly evaluated parental choice by inviting parents to select which tummy time treatment they wanted to implement. We found that both preferred items and parental attention effectively increased head elevation and decreased negative vocalizations during tummy time; however, parents tended to prefer the treatment that included the preferred item.     

Pursuing goals with others: group identification and motivation resulting from things done versus things left undone

This article addresses what factors best motivate individuals to work toward shared goals. We propose that when individuals do not identify highly with a group, their contributions will mimic others': An emphasis on things done will increase their contributions toward achieving a goal, because such emphasis suggests the goal is worth pursuing. Conversely, we propose that when individuals identify highly with a group, their contributions will compensate for others': An emphasis on things left undone will increase their own contributions, because missing contributions suggest insufficient progress toward a goal they already consider worthwhile. Five studies lend support to these predictions by measuring contributions to goals centered on idea generation and helping victims of various global disasters (earthquake in Haiti, wildfires in Southern California, rioting in Kenya).     

The dynamics of self-regulation

Research on the dynamics of self-regulation addresses situations in which people select goal-directed actions with respect to other existing or still missing actions towards accomplishing that goal. In such situations people can follow two possible patterns: they can highlight a goal by attending to it more if they have attended to it, or they can balance their goals by attending to a goal more if they have not attended to it. The choice of which pattern to follow depends on the representation of goal actions: when actions signal commitment, people highlight, and when actions signal progress, people balance. We identify several variables that determine whether people follow a dynamic of commitment-induced highlighting or progress-induced balancing. We then discuss the implications of this model for seeking, giving, and responding to feedback.     

A comparison of cortico-cortical communication during air-pistol shooting in elite disabled and non-disabled shooters

This study examined the difference in electroencephalographic (EEG) coherence, an index of cortico-cortical communication, during air pistol shooting between disabled and non-disabled elite shooters. Participants included 22 non-disabled and 12 disabled members of the Korean national air-pistol shooting team at the world class level. Electrocortical activation was recorded during 20 self-paced 10-meter air pistol shots. Higher cortico-cortical communication between brain regions was observed in disabled shooters. The higher functional communication appears to be a strategy to compensate for the attenuated function of the brain resulting from spinal cord injury. This compensatory mechanism could explain why there is no significant difference in shooting performance between elite disabled and non-disabled shooters.     

Dynamics of self-regulation: How (un)accomplished goal actions affect motivation

Two factors increase the motivation to adhere to a goal: goal commitment and lack of goal progress. When people ask about commitment, focusing on what they have accomplished (to date) signals to them high commitment and increases motivation. Conversely, when commitment is certain and people ask about goal progress, focusing on what they have yet to accomplish (to go) signals to them lack of progress and increases motivation. Accordingly, 4 studies show that emphasizing to-date information increases goal adherence when commitment is uncertain--that is, when participants study for a relatively unimportant exam, consume luxuries, fulfill a desire, and make first-time contributions to a charity. Conversely, emphasizing to-go information increases goal adherence when commitment is certain--that is, when participants study for an important exam, consume necessities, fulfill a need, and make repeated contributions to a charity.     

Bayesian Mixture Model of Extended Redundancy Analysis

Psychometrika - Extended redundancy analysis (ERA), a generalized version of redundancy analysis (RA), has been proposed as a useful method for examining interrelationships among multiple sets of...