Importance of interpolation when constructing double-bootstrap confidence intervals

We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

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.     

Maternal Postpartum Depression Increases Vulnerability for Toddler Behavior Problems through Infant Cortisol Reactivity

The current study examined the role of hypothalamic‐pituitary‐adrenal reactivity (a physiological indicator of stress) in early infancy as a mediator of the relationship between maternal postpartum depression and toddler behavior problems. Participants were 137 at‐risk mothers and their children participating in a longitudinal study of intergenerational transmission of risk. Mothers’ depression was measured five times during the infants’ first 18 months. Infant cortisol was collected during a social stressor (the still‐face paradigm) when infants were 6 months old, and mothers reported on toddlers’ internalizing and externalizing symptoms at 18 months. Among this sample of high‐risk mother–infant dyads, early postpartum depression predicted atypical infant cortisol reactivity at 6 months, which mediated the effect of maternal depression on increased toddler behavior problems. Clinical implications are discussed.     

Changing Opportunities for Learning in Everyday Life: Infant Body Position Over the First Year

Developmental theories depend on characterizing the input to potential learning mechanisms—infants’ everyday experiences. The current study employed a novel ecological momentary assessment (EMA) to measure two aspects of the physical context of those experiences: body position and location. Infant body position was selected because it relates to the development of a variety of other skills. Caregivers of 3‐, 6‐, 9‐, and 12‐month‐olds reported infants’ body position—held, supine, reclined, prone, sitting, or upright—in response to text message notifications over a week to capture infants’ experiences across the entire range of their daily activities. Findings revealed a tremendous disparity in the distribution of body position experiences over the first year. Younger infants spend more time held, supine, and reclined, whereas older infants spend more time sitting and upright. Body position experiences differed substantially between same‐age infants who possess a motor skill (e.g., ability to sit or walk) compared with those who did not, suggesting that developing motor skills change infants’ everyday experiences. Finally, the success of the methodology suggests that similar EMAs might be used to study a wide range of infants’ naturalistic experiences.     

Issues in the integration of religious education and worldviews education in an intercultural context

ABSTRACT

The Council of Europe’s 2008 ‘Recommendation’ advocates the study of ‘non-religious convictions’ in schools in addition to religions. In 2018, there is evidence of growing academic interest in the inclusion of non-religious worldviews in the school curriculum, but few European countries include such a study within religious education. The guidance document, Signposts, recognises that the integration of religions and non-religious worldviews is problematic for policy makers, teacher trainers and schools and that there is a need for further research. Norway and England are at significant but different stages in the process of integration. This article presents a comparative study which draws on the findings of research in both countries which has investigated the process at classroom and policy levels, and issues raised by this. Four issues are explored: practical challenges; differing understandings of the concept of worldviews; the inclusion of non-religious worldviews as a political issue and influences on the selection of worldviews. The article concludes with a discussion of issues and findings within a supranational context and makes recommendations which highlight the value of integration and the need for both contextual studies and further comparative research.     

Mobilities and peace

This article considers how an increasingly visible set of mobilities has implications for how peace and conflict are imagined and responded to. We are particularly interested in how these mobilities take form in everyday actions and shape new forms of peace and challenge existing ones. The article considers fixed categories associated with orthodox peace such as the international, borders and the state that are predicated on territorialism, centralized governance, and static citizenship. The article can be read as a critique of liberal peacebuilding and a contribution to current debates on migration, space and the everyday. Through conceptual scoping we develop the notion of mobile peace to characterize the fluid ways in which is being constructed through the mobilitiy of people and ideas.     

Elementary School-age Children's Attitudes Toward Children in Same-Sex Parent Families

As numbers of families with same-sex parents increase in the United States, children are more likely to encounter diverse family structures. Given that young children can demonstrate in-group bias, prejudicial attitudes, and social exclusion, it is important to understand how children perceive their peers in diverse families. To our knowledge, no studies have assessed elementary-school-age children's attitudes about same-sex parent families. Here, 131 elementary school students (M_age = 7.79 years; 61 girls) viewed images of same-sex (female and male) and other-sex couples with a child and then were asked about their perceptions of these families, particularly the children. Results indicated participants' preferences toward children with other-sex versus same-sex parents. Developmental and practical implications about children's attitudes toward sexual minority parent families are discussed.     

Socializing Children About Family Structure: Perspectives of Lesbian and Gay Adoptive Parents

Despite increasing numbers of lesbian- and gay- (LG-) parent families, little research on LG-adoptive-parent families has examined parental beliefs and perceptions related to discussing their sexual minority status with their children. This study assessed 266 LG adoptive parents (160 lesbian mothers, 106 gay fathers) from the Modern Adoptive Families (MAF) study, a nationwide survey (2012–2013) of adoptive parents' pre- and post-placement experiences. A cultural socialization lens provided the framework for examining LG parenting beliefs and practices. Two measurement scales were developed to examine parents' perceptions and self-efficacy related to socializing their child about being in a sexual-minority-parent family. Results indicate that LG parents endorse the importance of unique socialization practices and generally feel confident engaging in these practices. Parent education, transracial adoption, endorsement of racial socialization, and socialization self-efficacy were positively associated with endorsement of socialization practices. Excellent reliability suggests the 2 scales have the potential of being psychometrically sound instruments with which to measure parental endorsement and related self-efficacy of socialization practices for families headed by sexual minority parents. Findings contribute to a deeper understanding of socialization and communication patterns in LG-headed families, especially those formed through adoption. Research, policy, and practice implications are discussed.