Correlation in a Bayesian framework

The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p‐values and posterior probabilities of the null hypothesis in the one‐sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks.     

A Weighted Least Squares Approach to Levene's Test of Homogeneity of Variance

In 1960 Levene suggested a potentially robust test of homogeneity of variance based on an ordinary least squares analysis of variance of the absolute values of mean-based residuals. Levene's test has since been shown to have inflated levels of significance when based on the F-distribution, and tests a hypothesis other than homogeneity of variance when treatments are unequally replicated, but the incorrect formulation is now standard output in several statistical packages. This paper develops a weighted least squares analysis of variance of the absolute values of both mean-based and median-based residuals. It shows how to adjust the residuals so that tests using the F -statistic focus on homogeneity of variance for both balanced and unbalanced designs. It shows how to modify the F -statistics currently produced by statistical packages so that the distribution of the resultant test statistic is closer to an F-distribution than is currently the case. The weighted least squares approach also produces component mean squares that are unbiased irrespective of which variable is used in Levene's test. To complete this aspect of the investigation the paper derives exact second-order moments of the component sums of squares used in the calculation of the mean-based test statistic. It shows that, for large samples, both ordinary and weighted least squares test statistics are equivalent; however they are over-dispersed compared to an F variable.     

The exponentiated power exponential regression model with different regression structures: application in nursing data

We define the exponentiated power exponential distribution and propose a regression model with different systematic structures based on the new distribution. We show that the new regression model can be applied to dispersion data since it represents a parametric family of models that includes as sub-models some widely-known regression models. It then can be used more effectively in the analysis of real data. We use maximum likelihood estimation and derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. Some global-influence measurements are also investigated and simulation studies are performed to evaluate the accuracy of the estimates. We provide an application of the regression model with four systematic structures to nursing activities score data in the Unit of the Medical Clinic of University of São Paulo (USP) Hospital.     

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Infant Behavior and Competence Following Prenatal Exposure to a Natural Disaster: The QF2011 Queensland Flood Study

This study utilized a natural disaster to investigate the effects of prenatal maternal stress (PNMS) arising from exposure to a severe flood on maternally reported infant social–emotional and behavioral outcomes at 16 months, along with potential moderation by infant sex and gestational timing of flood exposure. Women pregnant during the Queensland floods in January 2011 completed measures of flood‐related objective hardship and posttraumatic stress (PTS). At 16 months postpartum, mothers completed measures describing depressive symptoms and infant social–emotional and behavioral problems (n = 123) and competence (n = 125). Greater maternal PTS symptoms were associated with reduced infant competence. A sex difference in infant behavioral problems emerged at higher levels of maternal objective hardship and PTS; boys had significantly more behavioral problems than girls. Additionally, greater PTS was associated with more behavioral problems in boys; however, this effect was attenuated by adjustment for maternal depressive symptoms. No main effects or interactions with gestational timing were found. Findings highlight specificity in the relationships between PNMS components and infant outcomes and demonstrate that the effects of PNMS exposure on behavior may be evident as early as infancy. Implications for the support of families exposed to a natural disaster during pregnancy are discussed.     

A preliminary look at relationships between married gay men and lesbians and their parents-in-law: Five case studies

With marriage between lesbians and between gays now legal in the United States, it is important to gain an understanding of how in-law relationships function for this population. Five case studies, part of a larger study of in-law relationships, are presented that help further knowledge of the potential obstacles that some couples may face in relation to their in-laws. Common experiences include relationships improving over time; struggling with acceptance; feeling closer to parents-in-law because other adult children or adult children-in-law have fallen out of favor; recognizing the significant role that the child-in-law’s spouse plays in the relationship between the child-in-law and the parent-in-law; understanding the role that the larger community plays; considering both parents-in-law as separate voices in the in-law dyad; and experiencing feelings of ambivalence that arise between family members. Practice implications for clinicians are included as are implications for future research.     

Sources of socialization for interpersonal trust: an exploration of low-income Black adolescents’ experiences

Much of the literature on interpersonal trust is quantitative in nature, using scales developed primarily with White middle-class and upper-class adults. To understand how another racial group of a different socioeconomic background and age views interpersonal trust, we considered the experiences of 22 low-income Black adolescents. The adolescents participated in a relationship education program and were interviewed about their interpersonal trust experiences. Results of a qualitative data analysis revealed that most adolescents defined interpersonal trust based on honesty and fidelity, with a particular emphasis on monogamy in romantic relationships. Adolescents identified direct messages from family members and personal relationship experiences as sources of socialization for interpersonal trust. Although some adolescents reported that the relationship education program enhanced their understanding of and willingness to trust, others maintained that trust can only be learned through personal experiences. Though the adolescents generally trusted family members, they experienced challenges trusting friends and romantic partners. Despite this, adolescents considered interpersonal trust a vital and a necessary part of romantic relationships. We discuss implications of the findings for relationship stability and satisfaction.     

Modeling stereotypes and negative self‐stereotypes as a function of interactions among groups with power asymmetries

Stereotypes is one of the most researched topics in social psychology. Within this context, negative self‐stereotypes pose a particular challenge for theories. In the current work, we propose a model that suggests that negative self‐stereotypes can theoretically be accounted for by the need to communicate in a social system made up by groups with unequal power. Because our theory is dynamic, probabilistic, and interactionist, we use a computational simulation technique to show that the proposed model is able to reproduce the phenomenon of interest, to provide novel accounts of related phenomena, and to suggest novel empirical predictions. We describe our computational model, our variables' dynamic behavior and interactions, and link our analyses to the literature on stereotypes and self‐stereotypes, the stability of stereotypes (in particular, gender and racial stereotypes), the effects of power asymmetries, and the effects of intergroup contact.     

Extending Bayesian back-calculation to estimate age and time specific HIV incidence

Lifetime Data Analysis - CD4-based multi-state back-calculation methods are key for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their...     

The Role of Self-Conscious Emotions in the Sexual Health of Gay and Bisexual Men: Psychometric Properties and Theoretical Validation of the Sexual Shame and Pride Scale

Researchers have theorized about the role of sexual shame as a mechanism through which sexual minority stress manifests into mental health difficulties, such as sexual compulsivity for gay and bisexual men (GBM), and about the resilience-promoting effects of sexual pride. However, no validated measures to date have directly tapped into these constructs rather than using proxies for them, such as internalized homonegativity. We developed the Sexual Shame and Pride Scale (SSPS) and conducted a psychometric evaluation of it using a sample of 260 highly sexually active GBM. The scale had the expected structure in factor analysis and showed evidence of internal consistency and test–retest reliability. Correlational analyses demonstrated the convergent validity of sexual shame and sexual pride with relevant constructs. Regression analyses demonstrated the predictive validity of sexual shame in relation to sexual compulsivity, accounting for unique variability even after adjusting for previously demonstrated etiological factors, and the predictive validity of both shame and pride, which interacted to consistently predict four sexual behavior outcomes. Findings suggest the SSPS is a psychometrically valid and reliable measure that may be useful in future empirical work and highlight preliminary evidence for the role of these constructs in the sexual health of GBM.