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.     

Telling adults about one's plight as a victim of bullying: Student- and context-related factors predicting disclosure

We examined student- and context-related factors related to whether bullied students tell adults about their plight at school or at home. The sample included 1,266 students in primary (Grades 4–6) and lower secondary (Grades 8–9) schools, who had answered an online questionnaire at two measurement points about 5 months apart and were identified as victims of bullying on the basis of the latter. Only 55.4% of the bullied students had told their situation to someone, and much fewer had told an adult. Telling an adult at home was more common (34.0%) than telling a teacher (20.6%) or some other adult at school (12.7%). In a longitudinal structural equation model (SEM), factors related to increased likelihood of telling an adult were female gender, lower grade level, the chronicity of victimization, perceived negative teacher attitude towards bullying (teacher not tolerating bullying), and perceived peer support for victims (classmates’ tendency to defend students who are victimized).     

Longitudinal associations between relational and sexual well-being in couples transitioning to parenthood

There is limited understanding of the dynamic between relational and sexual well-being as couples adjust to new parenthood, despite this being a vulnerable period for couples' relationships. This study was aimed at examining the bidirectional links between relationship quality and sexual well-being (i.e., sexual satisfaction, sexual distress) across the transition to parenthood. We assessed new parent couples (N = 257) across four time points (two prenatal) from mid-pregnancy through 6 months postpartum. Parallel dyadic latent growth curve modeling was employed to examine the associations between trajectories of perceived relationship quality, sexual satisfaction, and sexual distress. New parents' declines in relationship quality were associated with declines in own and partners' sexual satisfaction and with increases in own sexual distress. Mothers' prenatal relationship quality and sexual distress predicted subsequent changes in own sexual distress and fathers' relationship quality, respectively. Results indicate that changes to new parents' relational and sexual well-being mutually influence each other over time. Current results indicate that the impact of the transition on couples' relationships is partly determined by own and partners' prenatal factors, to which clinicians and researchers can attend to early on. Cross-domain links between relational and sexual well-being should be considered in research and clinical practice.     

Eating Disorder Examination Questionnaire (EDE-Q): norms for young adult women

In order to establish norms for the Eating Disorder Examination Questionnaire (EDE-Q) among young adult women, the questionnaire was administered to a large general population sample of women aged 18-42 yr in the Australian Capital Territory (ACT) region of Australia. Normative data were derived for EDE-Q subscales and for the occurrence of specific eating disorder behaviours, for each of five age bands (18-22, 23-27, 28-32, 33-37, 38-42 yr). Mean scores (SDs) for the Restraint, Eating Concern, Weight Concern and Shape Concern subscales for the total sample (n = 5,255) were, respectively, 1.30 (1.40), 0.76 (1.06), 1.79 (1.51) and 2.23 (1.65). The mean global score was 1.52 (1.25). The regular occurrence of objective and subjective overeating episodes was reported by 10.6% and 12.7% of participants, respectively. The regular use of self-induced vomiting, laxative misuse, and use of diuretics, was reported by 1.4%, 1.0%, and 0.3%, of participants, respectively, while 2.2% of participants reported regularly using diet pills. "Extreme dietary restraint" and "excessive exercise" were reported by 3.4% and 4.9% of participants, respectively. Both attitudinal and behavioural features of eating disorder psychopathology tended to decrease with increasing age. These data will inform researchers intending to use the EDE-Q in epidemiological studies.     

Stimulus affectivity of the Danish Word Association Test as measured by response heterogeneity and Rasch scaled number of prolonged reaction times

With the purpose of increasing the knowledge of the psychometric properties of the 70-item Danish Word Association Test, data from three samples of non-patients and psychiatric patients (N = 326) were used to provide two measures of affectivity of the stimulus words, response heterogeneity and reaction time prolongation. It was possible to fit an item response theory one-parameter measurement (Rasch) model to the number of reaction time prolongations (> or =3 seconds) for 54 of the stimulus words. Correlation between Rasch-model item parameters and response heterogeneity was high (r = 0.86), while no correlation was found between either of these measures and frequency of the stimulus words in the Danish language. Both measures of stimulus affectivity supported a theoretically based classification of stimulus words as emotional or neutral. Response heterogeneity measures and Rasch measurement item and person parameters for reaction time prolongations are provided.     

An examination of indexes for determining the number of clusters in binary data sets

The problem of choosing the correct number of clusters is as old as cluster analysis itself. A number of authors have suggested various indexes to facilitate this crucial decision. One of the most extensive comparative studies of indexes was conducted by Milligan and Cooper (1985). The present piece of work pursues the same goal under different conditions. In contrast to Milligan and Cooper's work, the emphasis here is on high-dimensional empirical binary data. Binary artificial data sets are constructed to reflect features typically encountered in real-world data situations in the field of marketing research. The simulation includes 162 binary data sets that are clustered by two different algorithms and lead to recommendations on the number of clusters for each index under consideration. Index results are evaluated and their performance is compared and analyzed.Author names are listed in alphabetical order.This piece of research was supported by the Austrian Science Foundation (FWF) under grant SFB#010 (Adaptive Information Systems and Modeling in Economics and Management Science).The authors would like to thank the anonymous reviewers and especially the associate editor for their helpful comments and suggestions.     

Spontaneous number discrimination of multi-format auditory stimuli in cotton-top tamarins (Saguinus oedipus)

Studies using operant training have demonstrated that laboratory animals can discriminate the number of objects or events based on either auditory or visual stimuli, as well as the integration of both auditory and visual modalities. To date, studies of spontaneous number discrimination in untrained animals have been restricted to the visual modality, leaving open the question of whether such capacities generalize to other modalities such as audition. To explore the capacity to spontaneously discriminate number based on auditory stimuli, and to assess the abstractness of the representation underlying this capacity, a habituation-discrimination procedure involving speech and pure tones was used with a colony of cotton-top tamarins. In the habituation phase, we presented subjects with either two- or three-speech syllable sequences that varied with respect to overall duration, inter-syllable duration, and pitch. In the test phase, we presented subjects with a counterbalanced order of either two- or three-tone sequences that also varied with respect to overall duration, inter-syllable duration, and pitch. The proportion of looking responses to test stimuli differing in number was significantly greater than to test stimuli consisting of the same number. Combined with earlier work, these results show that at least one non-human primate species can spontaneously discriminate number in both the visual and auditory domain, indicating that this capacity is not tied to a particular modality, and within a modality, can accommodate differences in format.     

The duality of non-conceptual content in Husserl’s phenomenology of perception

Recently, a number of epistemologists have argued that there are no non-conceptual elements in representational content. On their view, the only sort of non-conceptual elements are components of sub-personal organic hardware that, because they enjoy no veridical role, must be construed epistemologically irrelevant. By reviewing a 35-year-old debate initiated by Dagfinn Følledal, I believe Husserlian phenomenology can be updated to offer an important contribution to this discussion. On my interpretation, what Husserl calls “hyletic data” may be read as that subjective quality of experience inarticulable as a propositional attitude – and, thus, hyletic data are non-conceptual. In anticipation of the recent conceptualist position, Føllesdal and his adherents argued that what Husserl had called “noema” or representational content is, however, entirely conceptual. A closer inspection of the relevant texts, however, reveals that Husserl admits non-conceptual elements into his characterization of the noema. If that is correct, then Husserl must have been a dualist about non-conceptual content. In turn, I believe what explains this dualism is a non-foundationalist reconstruction of Husserl’s phenomenological reduction.An earlier version of this paper was delivered at Fordham University on the occasion of the 33rd Annual Meeting of the Husserl Circle. I am grateful to Prof. Steven Crowell who, in his capacity as respondent, offered incisive and helpful commentary. I also thank Prof. John J. Drummond for organizing the meeting, and all those present during my talk; as well as two anonymous reviewers for Phenomenology and the Cognitive Sciences, who offered helpful questions and comments.     

Fuzzy partition models for fitting a set of partitions

Methodology is described for fitting a fuzzy consensus partition to a set of partitions of the same set of objects. Three models defining median partitions are described: two of them are obtained from a least-squares fit of a set of membership functions, and the third (proposed by Pittau and Vichi) is acquired from a least-squares fit of a set of joint membership functions. The models are illustrated by application to both a set of hard partitions and a set of fuzzy partitions and comparisons are made between them and an alternative approach to obtaining a consensus fuzzy partition proposed by Sato and Sato; a discussion is given of some interesting differences in the results.We are grateful to Dr. M.G. Pittau for carrying out the analyses of the macroeconomic data using the method of Sato and Sato (1994).