A Multilevel Meta‑Analysis

Insecure attachment to primary caregivers is associated with the development of depression symptoms in children and youth. This association has been shown by individual studies testing the relation between attachment and depression and by meta-analyses focusing on broad internalizing problems instead of depression or adult samples only. We therefore meta-analytically examined the associations between attachment security and depression in children and adolescents, using a multilevel approach. In total, 643 effect sizes were extracted from 123 independent samples. A significant moderate overall effect size was found (r = .31), indicating that insecure attachment to primary caregivers is associated with depression. Multivariate analysis of the significant moderators that impacted on the strength of the association between attachment security and depression showed that country of the study, study design, gender, the type of attachment, and the type of instrument to assess attachment uniquely contributed to the explanation of variance. This study suggests that insecure attachment may be a predictor of the development of depression in children and adolescents. When treating depression in children, attachment should therefore be addressed

The Psychosocial Work Environment, Employee Mental Health and Organizational Interventions: Improving Research and Practice by Taking a Multilevel Approach

Although there have been several calls for incorporating multiple levels of analysis in employee health and wellbeing research, studies examining the interplay between individual, workgroup, organizational and broader societal factors in relation to employee mental health outcomes remain an exception rather than the norm. At the same time, organizational intervention research and practice also tends to be limited by a single-level focus, omitting potentially important influences at multiple levels of analysis. The aims of this conceptual paper are to help progress our understanding of work-related determinants of employee mental health by: (i) providing a rationale for routine multilevel assessment of the psychosocial work environment; (ii) discussing how a multilevel perspective can improve related organizational interventions and (iii) highlighting key theoretical and methodological considerations relevant to these aims. We present five recommendations for future research, relating to using appropriate multilevel research designs, justifying group level constructs, developing group-level measures, expanding investigations to the organizational level, and developing multilevel approaches to intervention design, implementation and evaluation

Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomized error. Furthermore, we provide in this setting the first non-trivial lower error bounds for general randomized algorithms, which, in particular, may be adaptive or non-linear. These lower bounds show that our multilevel algorithms are optimal. Our analysis refines and extends the analysis provided in [F. J. Hickernell, T. M\"uller-Gronbach, B. Niu, K. Ritter, J. Complexity 26 (2010), 229-254], and our error bounds improve substantially on the error bounds presented there. As an illustrative example, we discuss the unanchored Sobolev space and employ randomized quasi-Monte Carlo multilevel algorithms based on scrambled polynomial lattice rules.Comment: 31 pages, 0 figure

From rough path estimates to multilevel Monte Carlo

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations driven by Gaussian noise in the aforementioned sense. Our focus lies on numerical implementations, and more specifically on the saving possible via multilevel methods. Our analysis relies on a subtle combination of pathwise estimates, Gaussian concentration, and multilevel ideas. Numerical examples are given which both illustrate and confirm our findings.Comment: 34 page

Recent developments in multilevel optimization

Recent developments in multilevel optimization are briefly reviewed. The general nature of the multilevel design task, the use of approximations to develop and solve the analysis design task, the structure of the formal multidiscipline optimization problem, a simple cantilevered beam which demonstrates the concepts of multilevel design and the basic mathematical details of the optimization task and the system level are among the topics discussed