Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony. (C) 2012 Elsevier B.V. All rights reserved.

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

Socioeconomic, Temporal and Regional Variation in Body Mass Index among 188,537 Swiss Male Conscripts Born between 1986 and 1992

BACKGROUND Rising levels of overweight and obesity are important public-health concerns worldwide. The purpose of this study is to elucidate their prevalence and trends in Switzerland by analyzing variations in Body Mass Index (BMI) of Swiss conscripts. METHODS The conscription records were provided by the Swiss Army. This study focussed on conscripts 18.5-20.5 years of age from the seven one-year birth cohorts spanning the period 1986-1992. BMI across professional status, area-based socioeconomic position (abSEP), urbanicity and regions was analyzed. Two piecewise quantile regression models with linear splines for three birth-cohort groups were used to examine the association of median BMI with explanatory variables and to determine the extent to which BMI has varied over time. RESULTS The study population consisted of 188,537 individuals. Median BMI was 22.51 kg/m2 (22.45-22.57 95% confidence interval (CI)). BMI was lower among conscripts of high professional status (-0.46 kg/m2; 95% CI: -0.50, -0.42, compared with low), living in areas of high abSEP (-0.11 kg/m2; 95% CI: -0.16, -0.07 compared to medium) and from urban communities (-0.07 kg/m2; 95% CI: -0.11, -0.03, compared with peri-urban). Comparing with Midland, median BMI was highest in the North-West (0.25 kg/m2; 95% CI: 0.19-0.30) and Central regions (0.11 kg/m2; 95% CI: 0.05-0.16) and lowest in the East (-0.19 kg/m2; 95% CI: -0.24, -0.14) and Lake Geneva regions (-0.15 kg/m2; 95% CI: -0.20, -0.09). Trajectories of regional BMI growth varied across birth cohorts, with median BMI remaining high in the Central and North-West regions, whereas stabilization and in some cases a decline were observed elsewhere. CONCLUSIONS BMI of Swiss conscripts is associated with individual and abSEP and urbanicity. Results show regional variation in the levels and temporal trajectories of BMI growth and signal their possible slowdown among recent birth cohorts.

NLCHECK: Stata module to check linearity assumption after model estimation

nlcheck is a simple diagnostic tool that can be used after fitting a model to quickly check the linearity assumption for a given predictor. nlcheck categorizes the predictor into bins, refits the model including dummy variables for the bins, and then performs a joint Wald test for the added parameters. Alternative, nlcheck uses linear splines for the adaptive model. Support for discrete variables is also provided. Optionally, nlcheck also displays a graph of the adjusted linear predictions from the original model and the adaptive model

Utilisation de splines monotones afin de condenser des tables de mortalité dans un contexte bayésien

Dans ce mémoire, nous cherchons à modéliser des tables à deux entrées monotones en lignes et/ou en colonnes, pour une éventuelle application sur les tables de mortalité. Nous adoptons une approche bayésienne non paramétrique et représentons la forme fonctionnelle des données par splines bidimensionnelles. L’objectif consiste à condenser une table de mortalité, c’est-à-dire de réduire l’espace d’entreposage de la table en minimisant la perte d’information. De même, nous désirons étudier le temps nécessaire pour reconstituer la table. L’approximation doit conserver les mêmes propriétés que la table de référence, en particulier la monotonie des données. Nous travaillons avec une base de fonctions splines monotones afin d’imposer plus facilement la monotonie au modèle. En effet, la structure flexible des splines et leurs dérivées faciles à manipuler favorisent l’imposition de contraintes sur le modèle désiré. Après un rappel sur la modélisation unidimensionnelle de fonctions monotones, nous généralisons l’approche au cas bidimensionnel. Nous décrivons l’intégration des contraintes de monotonie dans le modèle a priori sous l’approche hiérarchique bayésienne. Ensuite, nous indiquons comment obtenir un estimateur a posteriori à l’aide des méthodes de Monte Carlo par chaînes de Markov. Finalement, nous étudions le comportement de notre estimateur en modélisant une table de la loi normale ainsi qu’une table t de distribution de Student. L’estimation de nos données d’intérêt, soit la table de mortalité, s’ensuit afin d’évaluer l’amélioration de leur accessibilité.

Local influence for Student-t partially linear models

In this paper we extend partial linear models with normal errors to Student-t errors Penalized likelihood equations are applied to derive the maximum likelihood estimates which appear to be robust against outlying observations in the sense of the Mahalanobis distance In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data the local influence curvatures are derived and some diagnostic graphics are proposed A motivating example preliminary analyzed under normal errors is reanalyzed under Student-t errors The local influence approach is used to compare the sensitivity of the model estimates (C) 2010 Elsevier B V All rights reserved

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O uso de Thin-Plate Splines na transformação de coordenadas com modelagem de distorções entre realizações de referenciais geodésicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Transformação de coordenadas com modelagem de distorções entre SAD69 e SIRGAS2000 com o uso de Thin-Plate Splines

Several countries have been passed by change processes in their fundamental geodesic structure with the focus on the adoption of geocentric reference systems. In Brazil, the adoption of the SIRGAS2000 evolves the coexistence of two realizations from the COrrego Alegre system, two realizations from the SAD69 system and one realization from the SIRGAS2000 system. To make use of products in the old reference systems, methods of coordinate transformation between the existent reference frames are necessary. So, in this paper one solution for the transformation between coordinates from different reference frames, based on Thin-Plate Splines (TPS), that allows the estimation of parameters from one linear transformation and also one non-linear model is presented. The TPS model was developed to work with tridimensional coordinates and in this paper the results and analysis are performed with simulated data and also with data from the official Brazilian Geodetic System (SGB). In the check points from SAD69 stations (realization of 1996 - SAD69/96), the values of RMSE obtained were of 78,2 mm in latitude and 67,5 mm in longitude, before the transformation to the SIRGAS2000. In the comparison between the TPS model and ProGriD (Brazilian software provided by IBGE), the statistical indicators were reduced in 97%, by using the TPS model. Based in the obtained results from real dataset, the TPS model appears to be promising, since it allows improving the quality of transformation process with simultaneous distortion modeling.

Determinants of linear growth from infancy to school-aged years: a population-based follow-up study in urban Amazonian children

Background: Although linear growth during childhood may be affected by early-life exposures, few studies have examined whether the effects of these exposures linger on during school age, particularly in low-and middle-income countries. Methods: We conducted a population-based longitudinal study of 256 children living in the Brazilian Amazon, aged 0.1 y to 5.5 y in 2003. Data regarding socioeconomic and maternal characteristics, infant feeding practices, morbidities, and birth weight and length were collected at baseline of the study (2003). Child body length/height was measured at baseline and at follow-up visits (in 2007 and 2009). Restricted cubic splines were used to construct average height-for-age Z score (HAZ) growth curves, yielding estimated HAZ differences among exposure categories at ages 0.5 y, 1 y, 2 y, 5 y, 7 y, and 10 y. Results: At baseline, median age was 2.6 y (interquartile range, 1.4 y-3.8 y), and mean HAZ was -0.53 (standard deviation, 1.15); 10.2% of children were stunted. In multivariable analysis, children in households above the household wealth index median were 0.30 Z taller at age 5 y (P = 0.017), and children whose families owned land were 0.34 Z taller by age 10 y (P = 0.023), when compared with poorer children. Mothers in the highest tertile for height had children whose HAZ were significantly higher compared with those of children from mothers in the lowest height tertile at all ages. Birth weight and length were positively related to linear growth throughout childhood; by age 10 y, children weighing >3500 g at birth were 0.31 Z taller than those weighing 2501 g to 3500 g (P = 0.022) at birth, and children measuring >= 51 cm at birth were 0.51 Z taller than those measuring <= 48 cm (P = 0.005). Conclusions: Results suggest socioeconomic background is a potentially modifiable predictor of linear growth during the school-aged years. Maternal height and child's anthropometric characteristics at birth are positively associated with HAZ up until child age 10 y.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Radar track segmentation with cubic splines for collision risk models in high density terminal areas

This paper presents a method to segment airplane radar tracks in high density terminal areas where the air traffic follows trajectories with several changes in heading, speed and altitude. The radar tracks are modelled with different types of segments, straight lines, cubic spline function and shape preserving cubic function. The longitudinal, lateral and vertical deviations are calculated for terminal manoeuvring area scenarios. The most promising model of the radar tracks resulted from a mixed interpolation using straight lines for linear segments and spline cubic functions for curved segments. A sensitivity analysis is used to optimise the size of the window for the segmentation process.

Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling

We present an isogeometric thin shell formulation for multi-patches based on rational splines over hierarchical T-meshes (RHT-splines). Nitsche’s method is employed to efficiently couple the patches. The RHT-splines have the advantages of allowing a computationally feasible local refine- ment, are free from linear independence, possess high order continuity and satisfy the partition of unity and non-negativity, properties. In addition, C 1 continuity of the RHT-splines obviates to use of rotational degrees of freedom. The good performance of the present method is demonstrated by a number of numerical examples.