Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

Formulating Mixed Models for Experiments, Including Longitudinal Experiments

Mixed models have become important in analyzing the results of experiments, particularly those that require more complicated models (e.g., those that involve longitudinal data). This article describes a method for deriving the terms in a mixed model. Our approach extends an earlier method by Brien and Bailey to explicitly identify terms for which autocorrelation and smooth trend arising from longitudinal observations need to be incorporated in the model. At the same time we retain the principle that the model used should include, at least, all the terms that are justified by the randomization. This is done by dividing the factors into sets, called tiers, based on the randomization and determining the crossing and nesting relationships between factors. The method is applied to formulate mixed models for a wide range of examples. We also describe the mixed model analysis of data from a three-phase experiment to investigate the effect of time of refinement on Eucalyptus pulp from four different sources. Cubic smoothing splines are used to describe differences in the trend over time and unstructured covariance matrices between times are found to be necessary.

Sampling, WLS, and Mixed Models

Mixed models may be defined with or without reference to sampling, and can be used to predict realized random effects, as when estimating the latent values of study subjects measured with response error. When the model is specified without reference to sampling, a simple mixed model includes two random variables, one stemming from an exchangeable distribution of latent values of study subjects and the other, from the study subjects` response error distributions. Positive probabilities are assigned to both potentially realizable responses and artificial responses that are not potentially realizable, resulting in artificial latent values. In contrast, finite population mixed models represent the two-stage process of sampling subjects and measuring their responses, where positive probabilities are only assigned to potentially realizable responses. A comparison of the estimators over the same potentially realizable responses indicates that the optimal linear mixed model estimator (the usual best linear unbiased predictor, BLUP) is often (but not always) more accurate than the comparable finite population mixed model estimator (the FPMM BLUP). We examine a simple example and provide the basis for a broader discussion of the role of conditioning, sampling, and model assumptions in developing inference.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Efetividade de programa de suplementação alimentar no ganho ponderal de crianças

OBJETIVO: Avaliar a efetividade de programa governamental de suplementação alimentar no ganho ponderal de crianças. MÉTODOS: Estudo de coorte com dados secundários de 25.433 crianças de baixa renda com idade entre seis e 24 meses que ingressaram em programa de distribuição de leite fortificado Projeto Vivaleite, realizado no Estado de São Paulo de 2003 a 2008. O ganho ponderal foi medido por meio dos valores de escores z de peso para idade, calculados pelo padrão da Organização Mundial da Saúde (2007), obtidos, na rotina do programa, ao ingressar e a cada quatro meses durante a permanência. As crianças foram divididas em três grupos de escore z ao entrar: sem comprometimento de peso (z > -1); risco de baixo peso (-2 < z < -1) e baixo peso (z < -2). Utilizou-se regressão linear multinível (modelo misto), permitindo a comparação, em cada idade, das médias ajustadas do escore z dos ingressantes e participantes há pelo menos quatro meses, ajustadas para correlação entre medidas repetidas. RESULTADOS: Verificou-se efeito positivo do programa no ganho de peso das crianças, variando em função do estado nutricional ao ingressar; para as que entraram sem comprometimento de peso, o ganho médio ajustado foi 0,183 escore z;entre as que entraram com risco de baixo peso, foi 0,566; e entre as ingressantes com baixo peso, foi 1,005 escore z. CONCLUSÕES: O programa é efetivo para o ganho ponderal de crianças menores de dois anos, com efeito mais pronunciado entre as crianças que entram no programa em condições menos favoráveis de peso.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Effect of eccentric contraction velocity on muscle damage in repeated bouts of elbow flexor exercise

Eccentric exercise induces muscle damage, but controversy exists concerning the effect of contraction velocity on the magnitude of muscle damage, and little is known about the effect of contraction velocity on the repeated-bout effect. This study examined slow (60 degrees.s(-1)) and fast (180 degrees.s(-1)) velocity eccentric exercises for changes in indirect markers of muscle damage following 3 exercise bouts that were performed every 2 weeks. Fifteen young men were divided into 2 groups based on the velocity of eccentric exercise: 7 in the Ecc60 (60 degrees.s(-1)) group, and 8 in the Ecc180 (180 degrees.s(-1)) group. The exercise consisted of 30 maximal eccentric contractions of the elbow flexors at each velocity, in which the elbow joint was forcibly extended from 60 degrees to 180 degrees (full extension) on an isokinetic dynamometer. Changes in maximal voluntary isometric contraction strength, range of motion, muscle soreness, and plasma creatine kinase activity before and for 4 days after the exercise were compared in the 2 groups using a mixed-model analysis (group x bout x time). No significant differences between groups were evident for changes in any variables following exercise bouts; however, the changes were significantly smaller (p < 0.05) after the second and third bouts than after the first bout. These results indicate that the contraction velocity does not influence muscle damage or the repeated-bout effect.

Development of a Continuous Emulsion Copolymerization Process in a Tubular Reactor

This contribution describes the development of a continuous emulsion copolymerization processs for vinyl acetate and n-butyl acrylate in a tubular reactor. Special features of this reactor include the use of oscillatory (pulsed) flow and internals (sieve plates) to prevent polymer fouling and promote good radial mixing, along with a controlled amount of axial mixing. The copolymer system studied (vinyl acetate and butyl acrylate) is strongly prone to composition drift due to very different reactivity ratios. An axially dispersed plug flow model, based on classical free radical copolymerization kinetics, was developed for this process and used successfully to optimize the lateral feeding profile to reduce compositional drift. An energy balance was included in the model equations to predict the effect of temperature variations on the process. The model predictions were validated with experimental data for monomer conversion, copolymer composition, average particle size, and temperature measured along the reactor length.

Biomechanical failure properties and microstructural content of ruptured and unruptured abdominal aortic aneurysms

Purpose: To test the hypothesis that ruptured abdominal aortic aneurysms (AAA) are globally weaker than unruptured ones. Methods: Four ruptured and seven unruptured AAA specimens were harvested whole from fresh cadavers during autopsies performed over an 18-month period. Multiple regionally distributed longitudinally oriented rectangular strips were cut from each AAA specimen for a total of 77 specimen strips. Strips were subjected to uniaxial extension until failure. Sections from approximately the strongest and weakest specimen strips were studied histologically and histochemically. From the load-extension data, failure tension, failure stress and failure strain were calculated. Rupture site characteristics such as location, arc length of rupture and orientation of rupture were also documented. Results: The failure tension, a measure of the tissue mechanical caliber was remarkably similar between ruptured and unruptured AAA (group mean +/- standard deviation of within-subject means: 11.2 +/- 2.3 versus 11.6 +/- 3.6 N/cin; p=0.866 by mixed model ANOVA). In post-hoc analysis, there was little difference between the groups in other measures of tissue mechanical caliber as well such as failure stress (95 +/- 28 versus 98 +/- 23 N/cm(2); p=0.870), failure strain (0.39 +/- 0.09 versus 0.36 +/- 0.09; p=0.705), wall thickness (1.7 +/- 0.4 versus 1.5 +/- 0.4 mm; p=0.470), and % coverage of collagen within tissue cross section (49.6 +/- 12.9% versus 60.8 +/- 9.6%; p=0.133). In the four ruptured AAA, primary rupture sites were on the lateral quadrants (two on left; one on left-posterior; one on right). Remarkably, all rupture lines had a longitudinal orientation and ranged from 1 to 6 cm in length. Conclusion: The findings are not consistent with the hypothesis that ruptured aortic aneurysms are globally weaker than unruptured ones. (C) 2011 Elsevier Ltd. All rights reserved.

Altered plasma response to zinc and iron tolerance test after Roux-en-Y gastric bypass

Background: The duodenum and proximal jejunum are excluded after Roux-en-Y gastric bypass but these intestinal sites are where iron and zinc are most absorbed. Therefore, they are among the nutrients whose digestive and absorptive process can be impaired after surgery. The aim of the present study was to investigate the iron and zinc plasma response to a tolerance test before and after bariatric surgery. The study was performed at Sao Paulo University School of Medicine of Ribeirao Preto, Brazil. Methods: In a longitudinal paired study, 9 morbidly obese women (body mass index >= 40 kg/m(2)) underwent an iron and zinc tolerance test before and 3 months after surgery. The iron and zinc levels were determined at 0, 1, 2, 3, and 4 hours after a physiologic unique oral dose. The mineral concentrations in die plasma and 24-hour urine sample were assayed using an atomic absorption spectrophotometer. The anthropometric measurements and 3-day food record were also evaluated. A linear mixed model was used to compare the plasma concentration versus interval after the oral dose, before and after surgery. Results: The pre- and postoperative test results revealed a significantly lower plasma zinc response (P <.01) and a delayed response to iron intake after surgery. The total plasma iron concentration area, during the 4 hours, was not different after surgery (P >.05). The 24-hour urinary iron and zinc excretion did not differ between the pre- and postoperative phases. Conclusion: The present data showed a compromised response to the zinc tolerance test after gastric bypass surgery, suggesting an impaired absorption of zinc. More attention must be devoted to zinc nutritional status after surgery. (Surg Obes Relat Dis 2011;7:309-314.) (C) 2011 American Society for Metabolic and Bariatric Surgery. All rights reserved.

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study

Predictors of random effects are usually based on the popular mixed effects (ME) model developed under the assumption that the sample is obtained from a conceptual infinite population; such predictors are employed even when the actual population is finite. Two alternatives that incorporate the finite nature of the population are obtained from the superpopulation model proposed by Scott and Smith (1969. Estimation in multi-stage surveys. J. Amer. Statist. Assoc. 64, 830-840) or from the finite population mixed model recently proposed by Stanek and Singer (2004. Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 1119-1130). Predictors derived under the latter model with the additional assumptions that all variance components are known and that within-cluster variances are equal have smaller mean squared error (MSE) than the competitors based on either the ME or Scott and Smith`s models. As population variances are rarely known, we propose method of moment estimators to obtain empirical predictors and conduct a simulation study to evaluate their performance. The results suggest that the finite population mixed model empirical predictor is more stable than its competitors since, in terms of MSE, it is either the best or the second best and when second best, its performance lies within acceptable limits. When both cluster and unit intra-class correlation coefficients are very high (e.g., 0.95 or more), the performance of the empirical predictors derived under the three models is similar. (c) 2007 Elsevier B.V. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.