A Diagnostic Test for the Mixing Distribution in a Generalised Linear Mixed Model

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

Diesel spray mixing limited vaporization with non-ideal and multi-component fuel thermophysical property effects

Internal combustion engines are, and will continue to be, a primary mode of power generation for ground transportation. Challenges exist in meeting fuel consumption regulations and emission standards while upholding performance, as fuel prices rise, and resource depletion and environmental impacts are of increasing concern. Diesel engines are advantageous due to their inherent efficiency advantage over spark ignition engines; however, their NOx and soot emissions can be difficult to control and reduce due to an inherent tradeoff. Diesel combustion is spray and mixing controlled providing an intrinsic link between spray and emissions, motivating detailed, fundamental studies on spray, vaporization, mixing, and combustion characteristics under engine relevant conditions. An optical combustion vessel facility has been developed at Michigan Technological University for these studies, with detailed tests and analysis being conducted. In this combustion vessel facility a preburn procedure for thermodynamic state generation is used, and validated using chemical kinetics modeling both for the MTU vessel, and institutions comprising the Engine Combustion Network international collaborative research initiative. It is shown that minor species produced are representative of modern diesel engines running exhaust gas recirculation and do not impact the autoignition of n-heptane. Diesel spray testing of a high-pressure (2000 bar) multi-hole injector is undertaken including non-vaporizing, vaporizing, and combusting tests, with sprays characterized using Mie back scatter imaging diagnostics. Liquid phase spray parameter trends agree with literature. Fluctuations in liquid length about a quasi-steady value are quantified, along with plume to plume variations. Hypotheses are developed for their causes including fuel pressure fluctuations, nozzle cavitation, internal injector flow and geometry, chamber temperature gradients, and turbulence. These are explored using a mixing limited vaporization model with an equation of state approach for thermopyhysical properties. This model is also applied to single and multi-component surrogates. Results include the development of the combustion research facility and validated thermodynamic state generation procedure. The developed equation of state approach provides application for improving surrogate fuels, both single and multi-component, in terms of diesel spray liquid length, with knowledge of only critical fuel properties. Experimental studies are coupled with modeling incorporating improved thermodynamic non-ideal gas and fuel

Caregiver Responses to the Language Mixing of a Young Trilingual

The situation once described by Hoffmann (1985), in which children grow up exposed to three languages from an early age, is a reality for an increasing number of families. In Europe – as elsewhere – greater mobility is leading to greater numbers of mixed-language couples (Piller 2002), and, by extension, multilingual families. For such families, questions concerning the acquisition and maintenance of three or more languages in a natural environment are of direct relevance. Researchers in bilingualism have already pointed out the importance of social context for the acquisition of two languages in childhood, focusing in particular on the quantity and quality of exposure to the languages (De Houwer 1990; Döpke 1992; Okita 2002; Lanza 2004) or the prestige of the languages (Lambert 1977). In this paper, I will make use of the insights gained by such researchers and test them in a trilingual setting. The paper will focus mainly on one aspect, namely the conversational style of parents and caretakers. The data come from research being carried out in Switzerland and consist of 33 interviews with multilingual families, as well as case studies of two trilingual children. The findings attest to the importance of conversational style, but at the same time indicate that a number of further factors are also of great significance.

Diffusive equilibration of N2, O2 and CO2 mixing ratios in a 1.5-million-years-old ice core

In the framework of the International Partnerships in Ice Core Sciences, one of the most important targets is to retrieve an Antarctic ice core that extends over the last 1.5 million years (i.e. an ice core that enters the climate era when glacial–interglacial cycles followed the obliquity cycles of the earth). In such an ice core the annual layers of the oldest ice would be thinned by a factor of about 100 and the climatic information of a 10 000 yr interval would be contained in less than 1 m of ice. The gas record in such an Antarctic ice core can potentially reveal the role of greenhouse gas forcing on these 40 000 yr cycles. However, besides the extreme thinning of the annual layers, also the long residence time of the trapped air in the ice and the relatively high ice temperatures near the bedrock favour diffusive exchanges. To investigate the changes in the O2 / N2 ratio, as well as the trapped CO2 concentrations, we modelled the diffusive exchange of the trapped gases O2, N2 and CO2 along the vertical axis. However, the boundary conditions of a potential drilling site are not yet well constrained and the uncertainties in the permeation coefficients of the air constituents in the ice are large. In our simulations, we have set the drill site ice thickness at 2700 m and the bedrock ice temperature at 5–10 K below the ice pressure melting point. Using these conditions and including all further uncertainties associated with the drill site and the permeation coefficients, the results suggest that in the oldest ice the precessional variations in the O2 / N2 ratio will be damped by 50–100%, whereas CO2 concentration changes associated with glacial–interglacial variations will likely be conserved (simulated damping 5%). If the precessional O2 / N2 signal will have disappeared completely in this future ice core, orbital tuning of the ice-core age scale will be limited.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Precise Measurement of the Neutrino Mixing Parameter θ₂₃ from Muon Neutrino Disappearance in an Off-Axis Beam

New data from the T2K neutrino oscillation experiment produce the most precise measurement of the neutrino mixing parameter θ 23 . Using an off-axis neutrino beam with a peak energy of 0.6 GeV and a data set corresponding to 6.57×10 20 protons on target, T2K has fit the energy-dependent ν μ oscillation probability to determine oscillation parameters. The 68% confidence limit on sin 2 (θ 23 ) is 0.514 +0.055 −0.056 (0.511±0.055 ), assuming normal (inverted) mass hierarchy. The best-fit mass-squared splitting for normal hierarchy is Δm 2 32 =(2.51±0.10)×10 −3   eV 2 /c 4 (inverted hierarchy: Δm 2 13 =(2.48±0.10)×10 −3   eV 2 /c 4 ). Adding a model of multinucleon interactions that affect neutrino energy reconstruction is found to produce only small biases in neutrino oscillation parameter extraction at current levels of statistical uncertainty.

Population mixing and the risk of childhood leukaemia in Switzerland: a census-based cohort study.

Childhood leukaemia (CL) may have an infectious cause and population mixing may therefore increase the risk of CL. We aimed to determine whether CL was associated with population mixing in Switzerland. We followed children aged <16 years in the Swiss National Cohort 1990-2008 and linked CL cases from the Swiss Childhood Cancer Registry to the cohort. We calculated adjusted hazard ratios (HRs) for all CL, CL at age <5 years and acute lymphoblastic leukaemia (ALL) for three measures of population mixing (population growth, in-migration and diversity of origin), stratified by degree of urbanisation. Measures of population mixing were calculated for all municipalities for the 5-year period preceding the 1990 and 2000 censuses. Analyses were based on 2,128,012 children of whom 536 developed CL. HRs comparing highest with lowest quintile of population growth were 1.11 [95 % confidence interval (CI) 0.65-1.89] in rural and 0.59 (95 % CI 0.43-0.81) in urban municipalities (interaction: p = 0.271). Results were similar for ALL and for CL at age <5 years. For level of in-migration there was evidence of a negative association with ALL. HRs comparing highest with lowest quintile were 0.60 (95 % CI 0.41-0.87) in urban and 0.61 (95 % CI 0.30-1.21) in rural settings. There was little evidence of an association with diversity of origin. This nationwide cohort study of the association between CL and population growth, in-migration and diversity of origin provides little support for the population mixing hypothesis.

Cell mixing induced by myc is required for competitive tissue invasion and destruction

Cell-cell intercalation is used in several developmental processes to shape the normal body plan. There is no clear evidence that intercalation is involved in pathologies. Here we use the proto-oncogene myc to study a process analogous to early phase of tumour expansion: myc-induced cell competition. Cell competition is a conserved mechanism driving the elimination of slow-proliferating cells (so-called 'losers') by faster-proliferating neighbours (so-called 'winners') through apoptosis and is important in preventing developmental malformations and maintain tissue fitness. Here we show, using long-term live imaging of myc-driven competition in the Drosophila pupal notum and in the wing imaginal disc, that the probability of elimination of loser cells correlates with the surface of contact shared with winners. As such, modifying loser-winner interface morphology can modulate the strength of competition. We further show that elimination of loser clones requires winner-loser cell mixing through cell-cell intercalation. Cell mixing is driven by differential growth and the high tension at winner-winner interfaces relative to winner-loser and loser-loser interfaces, which leads to a preferential stabilization of winner-loser contacts and reduction of clone compactness over time. Differences in tension are generated by a relative difference in F-actin levels between loser and winner junctions, induced by differential levels of the membrane lipid phosphatidylinositol (3,4,5)-trisphosphate. Our results establish the first link between cell-cell intercalation induced by a proto-oncogene and how it promotes invasiveness and destruction of healthy tissues.