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Splines
Kinds of Splines Terms modified by Splines Selected AbstractsCorrigendum: ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALISED SPLINESAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2010M. P. Wand No abstract is available for this article. [source] X-ray magnetic circular dichroism measurements using an X-ray phase retarder on the BM25 A-SpLine beamline at the ESRFJOURNAL OF SYNCHROTRON RADIATION, Issue 3 2010Roberto Boada Circularly polarized X-rays produced by a diamond X-ray phase retarder of thickness 0.5,mm in the Laue transmission configuration have been used for recording X-ray magnetic circular dichroism (XMCD) on the bending-magnet beamline BM25A (SpLine) at the ESRF. Field reversal and helicity reversal techniques have been used to carry out the measurements. The performance of the experimental set-up has been demonstrated by recording XMCD in the energy range from 7 to 11,keV. [source] Comparative analysis of ArnCl2 (2 , n , 30) clusters taking into account molecular relaxation effectsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2006G. G. Ferreira Abstract Cluster structures are discussed in a nonrigid analysis, using a modified minima search method based on stochastic processes and classical dynamics simulations. The relaxation process is taken into account considering the internal motion of the Cl2 molecule. Cluster structures are compared with previous works in which the Cl2 molecule is assumed to be rigid. The interactions are modeled using pair potentials: the Aziz and Lennard,Jones potentials for the ArAr interaction, a Morse potential for the ClCl interaction, and a fully spherical/anisotropic Morse,Spline,van der Waals (MSV) potential for the ArCl interaction. As expected, all calculated energies are lower than those obtained in a rigid approximation; one reason may be attributed to the nonrigid contributions of the internal motion of the Cl2 molecule. Finally, the growing processes in molecular clusters are discussed, and it is pointed out that the growing mechanism can be affected due to the nonrigid initial conditions of smaller clusters such as ArnCl2 (n , 4 or 5), which are seeds for higher-order clusters. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Extensions of the Penalized Spline of Propensity Prediction Method of ImputationBIOMETRICS, Issue 3 2009Guangyu Zhang SummaryLittle and An (2004,,Statistica Sinica,14, 949,968) proposed a penalized spline of propensity prediction (PSPP) method of imputation of missing values that yields robust model-based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fitted that includes the spline of the estimated logit propensity score as a covariate. The predicted unconditional mean of the missing variable has a double robustness (DR) property under misspecification of the imputation model. We show that a simplified version of PSPP, which does not center other regressors prior to including them in the prediction model, also has the DR property. We also propose two extensions of PSPP, namely, stratified PSPP and bivariate PSPP, that extend the DR property to inferences about conditional means. These extended PSPP methods are compared with the PSPP method and simple alternatives in a simulation study and applied to an online weight loss study conducted by Kaiser Permanente. [source] Smoothing Spline-Based Score Tests for Proportional Hazards ModelsBIOMETRICS, Issue 3 2006Jiang Lin Summary We propose "score-type" tests for the proportional hazards assumption and for covariate effects in the Cox model using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate. The tests are based on the penalized partial likelihood and are derived by viewing the inverse of the smoothing parameter as a variance component and testing an equivalent null hypothesis that the variance component is zero. We show that the tests have a size close to the nominal level and good power against general alternatives, and we apply them to data from a cancer clinical trial. [source] Inference in Spline-Based Models for Multiple Time-to-Event Data, with Applications to a Breast Cancer Prevention TrialBIOMETRICS, Issue 4 2003Kiros Berhane Summary. As part of the National Surgical Adjuvant Breast and Bowel Project, a controlled clinical trial known as the Breast Cancer Prevention Trial (BCPT) was conducted to assess the effectiveness of tamoxifen as a preventive agent for breast cancer. In addition to the incidence of breast cancer, data were collected on several other, possibly adverse, outcomes, such as invasive endometrial cancer, ischemic heart disease, transient ischemic attack, deep vein thrombosis and/or pulmonary embolism. In this article, we present results from an illustrative analysis of the BCPT data, based on a new modeling technique, to assess the effectiveness of the drug tamoxifen as a preventive agent for breast cancer. We extended the flexible model of Gray (1994, Spline-based test in survival analysis, Biometrics50, 640,652) to allow inference on multiple time-to-event outcomes in the style of the marginal modeling setup of Wei, Lin, and Weissfeld (1989, Regression analysis of multivariate incomplete failure time data by modeling marginal distributions, Journal of the American Statistical Association84, 1065,1073). This proposed model makes inference possible for multiple time-to-event data while allowing for greater flexibility in modeling the effects of prognostic factors with nonlinear exposure-response relationships. Results from simulation studies on the small-sample properties of the asymptotic tests will also be presented. [source] Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic ProgramQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2005Julia C. C. Tsai Abstract This paper presents an automatic and more robust implementation of multivariate adaptive regression splines (MARS) within the orthogonal array (OA)/MARS continuous-state stochastic dynamic programming (SDP) method. MARS is used to estimate the future value functions in each SDP level. The default stopping rule of MARS employs the maximum number of basis functions Mmax, specified by the user. To reduce the computational effort and improve the MARS fit for the wastewater treatment SDP model, two automatic stopping rules, which automatically determine an appropriate value for Mmax, and a robust version of MARS that prefers lower-order terms over higher-order terms are developed. Computational results demonstrate the success of these approaches. Copyright © 2005 John Wiley & Sons, Ltd. [source] Using Penalized Splines to Model Age- and Season-of-Birth-Dependent Effects of Childhood Mortality Risk Factors in Rural Burkina FasoBIOMETRICAL JOURNAL, Issue 1 2009Heiko Becher Abstract Several previous studies have identified risk factors for childhood mortality in high risk areas, such as Sub-Saharan Africa. Among these are lifestyle factors related for example to nutrition or sanitation. Other factors are related to social class, ethnicity and poverty in general. Few studies have investigated a dependence of these factors by age and season of birth which is the focus in this study. We perform a survival analysis of 9121 children born between 1998 and 2001 in a rural area of western Burkina Faso. The whole population is under demographic surveillance since 1993. All cause mortality is used as the endpoint and follow-up information until the age of five years is available. Recently developed spline regression methods are used for the analysis. Ethnic group, religion, age of mother, twin status, sex, and distance to next health center are used as covariates all of which having a clear effect on survival in standard Cox regression analysis. With penalized spline regression, a more detailed risk pattern is observed. Ethnicity is more related to death at early age, as well as age of mother. The effect of the risk factors considered also appear to be related with season of birth (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Application of Penalized Splines in Analyzing Neuronal DataBIOMETRICAL JOURNAL, Issue 1 2009John T. Maringwa Abstract Neuron experiments produce high-dimensional data structures. Therefore, application of smoothing techniques in the analysis of neuronal data from electrophysiological experiments has received considerable attention of late. We investigate the use of penalized splines in the analysis of neuronal data. This is first illustrated when interested in the temporal trend of a single neuron. An approach to investigate the maximal firing rate, based on the penalizedspline model is proposed. Determination of the time of maximal firing rate is based on non-linear optimization of the objective function with the corresponding confidence intervals constructed based on the first-order derivative function. To distinguish between the curves from different experimental conditions in a moment-by-moment sense, bias adjusted simulation-based simultaneous confidence bands leading to global inference in the time domain are constructed. The bands are an extension of the approach proposed by Ruppert et al. (2003). These methods are in a second step extended towards the analysis of a population of neurons via a marginal or population-averaged model (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Bayesian Adaptive Regression Splines for Hierarchical DataBIOMETRICS, Issue 3 2007Jamie L. Bigelow Summary This article considers methodology for hierarchical functional data analysis, motivated by studies of reproductive hormone profiles in the menstrual cycle. Current methods standardize the cycle lengths and ignore the timing of ovulation within the cycle, both of which are biologically informative. Methods are needed that avoid standardization, while flexibly incorporating information on covariates and the timing of reference events, such as ovulation and onset of menses. In addition, it is necessary to account for within-woman dependency when data are collected for multiple cycles. We propose an approach based on a hierarchical generalization of Bayesian multivariate adaptive regression splines. Our formulation allows for an unknown set of basis functions characterizing the population-averaged and woman-specific trajectories in relation to covariates. A reversible jump Markov chain Monte Carlo algorithm is developed for posterior computation. Applying the methods to data from the North Carolina Early Pregnancy Study, we investigate differences in urinary progesterone profiles between conception and nonconception cycles. [source] Low-Rank Smoothing Splines on Complicated DomainsBIOMETRICS, Issue 1 2007Haonan Wang Summary Smoothing over a domain with irregular boundaries or interior gaps and holes is addressed. Consider the problem of estimating mercury in sediment concentrations in the estuarine waters in New Hampshire. A modified version of low-rank thin plate splines (LTPS) is introduced where the geodesic distance is applied to evaluate dissimilarity of any two data observations: loosely speaking, distances between locations are not measured as the crow flies, but as the fish swims. The method is compared with competing smoothing techniques, LTPS, and finite element L-splines. [source] Semiparametric Regression Splines in Matched Case-Control StudiesBIOMETRICS, Issue 4 2003Inyoung Kim Summary. We develop semiparametric methods for matched case-control studies using regression splines. Three methods are developed: 1) an approximate cross-validation scheme to estimate the smoothing parameter inherent in regression splines, as well as 2) Monte Carlo expectation maximization (MCEM) and 3) Bayesian methods to fit the regression spline model. We compare the approximate cross-validation approach, MCEM, and Bayesian approaches using simulation, showing that they appear approximately equally efficient; the approximate cross-validation method is computationally the most convenient. An example from equine epidemiology that motivated the work is used to demonstrate our approaches. [source] Evaluation of reduced rank semiparametric models to assess excess of risk in cluster analysisENVIRONMETRICS, Issue 4 2009Marco Geraci Abstract The existence of multiple environmental hazards is obviously a threat to human health and, from a statistical point of view, the modeling and the detection of disease clusters potentially related to those hazards offer challenging tasks. In this paper, we consider low rank thin plate spline (TPS) models within a semiparametric approach to focused clustering for small area health data. Both the distance from a putative source and a general, unspecified clustering process are modeled in the same fashion and they are entered log-additively in mixed Poisson-Normal models. Some issues related to the identification of the random effects arising from this approach are investigated. Under different simulated scenarios, we evaluate the proposed models using conditional Akaike's weights and tests for variance components, providing a comprehensive model selection methodology easy to implement. We examine observations of lung cancer deaths taken in Ohio between 1987 and 1988. These data were analyzed on several occasions to investigate the risk associated with a putative source in Hamilton county. In our analysis, we found a strong south-eastward spatial trend which is confounded with a significant radial distance effect decreasing between 0 and 150 km from the point source. Copyright © 2008 John Wiley & Sons, Ltd. [source] Smoothing splines for trend estimation and prediction in time seriesENVIRONMETRICS, Issue 3 2009Richard Morton Abstract We consider the use of generalized additive models with correlated errors for analysing trends in time series. The trend is represented as a smoothing spline so that it can be extrapolated. A method is proposed for choosing the smoothing parameter. It is based on the ability to predict a short term into the future. The choice not only addresses the purpose in hand, but also performs very well, and avoids the tendency to under-smooth or to interpolate the data that can occur with other data-driven methods used to choose the smoothing parameter. The method is applied to data from a chemical process and to stream salinity measurements. Copyright © 2008 John Wiley & Sons, Ltd. [source] Meshless thermo-elastoplastic analysis by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Yoshihiro OchiaiArticle first published online: 18 SEP 200 Abstract In general, internal cells are required to solve thermo-elastoplasticity problems by a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. A conventional multiple-reciprocity boundary element method (MRBEM) cannot be used to solve elastoplasticity problems, because the distribution of initial strain or stress cannot be determined analytically. In this study, it is shown that without the use of internal cells, two-dimensional thermo-elastoplasticity problems can be solved by a triple-reciprocity BEM using a thin plate spline. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solve several problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Muscle moment arms of the gibbon hind limb: implications for hylobatid locomotionJOURNAL OF ANATOMY, Issue 4 2010Anthony J. Channon Abstract Muscles facilitate skeletal movement via the production of a torque or moment about a joint. The magnitude of the moment produced depends on both the force of muscular contraction and the size of the moment arm used to rotate the joint. Hence, larger muscle moment arms generate larger joint torques and forces at the point of application. The moment arms of a number of gibbon hind limb muscles were measured on four cadaveric specimens (one Hylobates lar, one H. moloch and two H. syndactylus). The tendon travel technique was used, utilizing an electro-goniometer and a linear voltage displacement transducer. The data were analysed using a technique based on a differentiated cubic spline and normalized to remove the effect of body size. The data demonstrated a functional differentiation between voluminous muscles with short fascicles having small muscle moment arms and muscles with longer fascicles and comparatively smaller physiological cross-sectional area having longer muscle moment arms. The functional implications of these particular configurations were simulated using a simple geometric fascicle strain model that predicts that the rectus femoris and gastrocnemius muscles are more likely to act primarily at their distal joints (knee and ankle, respectively) because they have short fascicles. The data also show that the main hip and knee extensors maintain a very small moment arm throughout the range of joint angles seen in the locomotion of gibbons, which (coupled to voluminous, short-fascicled muscles) might help facilitate rapid joint rotation during powerful movements. [source] Are parametric models suitable for estimating avian growth rates?JOURNAL OF AVIAN BIOLOGY, Issue 4 2007William P. Brown For many bird species, growth is negative or equivocal during development. Traditional, parametric growth curves assume growth follows a sigmoidal form with prescribed inflection points and is positive until asymptotic size. Accordingly, these curves will not accurately capture the variable, sometimes considerable, fluctuations in avian growth over the course of the trajectory. We evaluated the fit of three traditional growth curves (logistic, Gompertz, and von Bertalanffy) and a nonparametric spline estimator to simulated growth data of six different specified forms over a range of sample sizes. For all sample sizes, the spline best fit the simulated model that exhibited negative growth during a portion of the trajectory. The Gompertz curve was the most flexible for fitting simulated models that were strictly sigmoidal in form, yet the fit of the spline was comparable to that of the Gompertz curve as sample size increased. Importantly, confidence intervals for all of the fitted, traditional growth curves were wholly inaccurate, negating the apparent robustness of the Gompertz curve, while confidence intervals of the spline were acceptable. We further evaluated the fit of traditional growth curves and the spline to a large data set of wood thrush Hylocichla mustelina mass and wing chord observations. The spline fit the wood thrush data better than the traditional growth curves, produced estimates that did not differ from known observations, and described negative growth rates at relevant life history stages that were not detected by the growth curves. The common rationale for using parametric growth curves, which compress growth information into a few parameters, is to predict an expected size or growth rate at some age or to compare estimated growth with other published estimates. The suitability of these traditional growth curves may be compromised by several factors, however, including variability in the true growth trajectory. Nonparametric methods, such as the spline, provide a precise description of empirical growth yet do not produce such parameter estimates. Selection of a growth descriptor is best determined by the question being asked but may be constrained by inherent patterns in the growth data. [source] The Nut in Screw TheoryJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 8 2003Michael Griffis This study in projective geometry reveals that the principle of duality applies to the screw. Here, the screw is demonstrated to be an element of a projective three-dimensional space (P3), right alongside the line. Dual elements for the screw and line are also revealed (the nut and spline). Reciprocity is demonstrated for a pair of screws, and incidence is demonstrated for screw and its dual element. Reciprocity and incidence are invariant for projective transformations of P3, but only incidence is invariant for the more general linear transformations of screws. This latter transformation is analogous to a projective transformation of a projective five-dimensional space (P5), which is shown to induce a contact transformation of the original P3, where some points lying on a Kummer surface are directly mapped. © 2003 Wiley Periodicals, Inc. [source] Bayesian regression with multivariate linear splinesJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2001C. C. Holmes We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both predictions and local linear parameters. The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data. [source] A hierarchical Bayesian model for predicting the functional consequences of amino-acid polymorphismsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 1 2005Claudio J. Verzilli Summary., Genetic polymorphisms in deoxyribonucleic acid coding regions may have a phenotypic effect on the carrier, e.g. by influencing susceptibility to disease. Detection of deleterious mutations via association studies is hampered by the large number of candidate sites; therefore methods are needed to narrow down the search to the most promising sites. For this, a possible approach is to use structural and sequence-based information of the encoded protein to predict whether a mutation at a particular site is likely to disrupt the functionality of the protein itself. We propose a hierarchical Bayesian multivariate adaptive regression spline (BMARS) model for supervised learning in this context and assess its predictive performance by using data from mutagenesis experiments on lac repressor and lysozyme proteins. In these experiments, about 12 amino-acid substitutions were performed at each native amino-acid position and the effect on protein functionality was assessed. The training data thus consist of repeated observations at each position, which the hierarchical framework is needed to account for. The model is trained on the lac repressor data and tested on the lysozyme mutations and vice versa. In particular, we show that the hierarchical BMARS model, by allowing for the clustered nature of the data, yields lower out-of-sample misclassification rates compared with both a BMARS and a frequen-tist MARS model, a support vector machine classifier and an optimally pruned classification tree. [source] Design of a miniaturized planar antenna for FCC-UWB communication systemsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 7 2008L. Lizzi Abstract In this letter, the design of a planar antenna compliant with FCC requirements for ultra-wideband (UWB) transmission systems is described. With reference to a planar geometry on a dielectric substrate, the shape of the antenna is described by means of a spline-based representation and it is determined by means of an optimization process aimed at finding the optimal descriptive parameters that allow to fit the user-defined electrical and dimensional requirements. The reliability and effectiveness of the antenna prototype are assessed through simulations as well as experimental measurements. © Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1975,1978, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23519 [source] The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadingsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2010Chia-Cheng Tsai Abstract Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth-order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r , 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz-type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] An adaptive wavelet viscosity method for hyperbolic conservation lawsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2008Daniel Castaño Díez Abstract We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre-orthogonal spline-)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least-squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] Variable kernel density estimationAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2003Martin L. Hazelton Summary This paper considers the problem of selecting optimal bandwidths for variable (sample-point adaptive) kernel density estimation. A data-driven variable bandwidth selector is proposed, based on the idea of approximating the log-bandwidth function by a cubic spline. This cubic spline is optimized with respect to a cross-validation criterion. The proposed method can be interpreted as a selector for either integrated squared error (ISE) or mean integrated squared error (MISE) optimal bandwidths. This leads to reflection upon some of the differences between ISE and MISE as error criteria for variable kernel estimation. Results from simulation studies indicate that the proposed method outperforms a fixed kernel estimator (in terms of ISE) when the target density has a combination of sharp modes and regions of smooth undulation. Moreover, some detailed data analyses suggest that the gains in ISE may understate the improvements in visual appeal obtained using the proposed variable kernel estimator. These numerical studies also show that the proposed estimator outperforms existing variable kernel density estimators implemented using piecewise constant bandwidth functions. [source] Bayesian Inference in Semiparametric Mixed Models for Longitudinal DataBIOMETRICS, Issue 1 2010Yisheng Li Summary We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods. [source] Extensions of the Penalized Spline of Propensity Prediction Method of ImputationBIOMETRICS, Issue 3 2009Guangyu Zhang SummaryLittle and An (2004,,Statistica Sinica,14, 949,968) proposed a penalized spline of propensity prediction (PSPP) method of imputation of missing values that yields robust model-based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fitted that includes the spline of the estimated logit propensity score as a covariate. The predicted unconditional mean of the missing variable has a double robustness (DR) property under misspecification of the imputation model. We show that a simplified version of PSPP, which does not center other regressors prior to including them in the prediction model, also has the DR property. We also propose two extensions of PSPP, namely, stratified PSPP and bivariate PSPP, that extend the DR property to inferences about conditional means. These extended PSPP methods are compared with the PSPP method and simple alternatives in a simulation study and applied to an online weight loss study conducted by Kaiser Permanente. [source] Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk FormBIOMETRICS, Issue 3 2006Jianhua Z. Huang Summary The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data. [source] Development and validation of a smoothing-splines-based correction method for improving the analysis of CEST-MR imagesCONTRAST MEDIA & MOLECULAR IMAGING, Issue 4 2008J. Stancanello Abstract Chemical exchange saturation transfer (CEST) imaging is an emerging MRI technique relying on the use of endogenous or exogenous molecules containing exchangeable proton pools. The heterogeneity of the water resonance frequency offset plays a key role in the occurrence of artifacts in CEST-MR images. To limit this drawback, a new smoothing-splines-based method for fitting and correcting Z -spectra in order to compensate for low signal-to-noise ratio (SNR) without any a priori model was developed. Global and local voxel-by-voxel Z -spectra were interpolated by smoothing splines with smoothing terms aimed at suppressing noise. Thus, a map of the water frequency offset (,zero' map) was used to correctly calculate the saturation transfer (ST) for each voxel. Simulations were performed to compare the method to polynomials and zero-only-corrected splines on the basis of SNR improvement. In vitro acquisitions of capillaries containing solutions of LIPOCEST agents at different concentrations were performed to experimentally validate the results from simulations. Additionally, ex vivo investigations of bovine muscle mass injected with LIPOCEST agents were performed as a function of increasing pulse power. The results from simulations and experiments highlighted the importance of a proper ,zero' correction (15% decrease of fictitious CEST signal in phantoms and ex vivo preparations) and proved the method to be more accurate compared with the previously published ones, often providing a SNR higher than 5 in different simulated and experimentally noisy conditions. In conclusion, the proposed method offers an accurate tool in CEST investigation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Predicting species distributions from museum and herbarium records using multiresponse models fitted with multivariate adaptive regression splinesDIVERSITY AND DISTRIBUTIONS, Issue 3 2007Jane Elith ABSTRACT Current circumstances , that the majority of species distribution records exist as presence-only data (e.g. from museums and herbaria), and that there is an established need for predictions of species distributions , mean that scientists and conservation managers seek to develop robust methods for using these data. Such methods must, in particular, accommodate the difficulties caused by lack of reliable information about sites where species are absent. Here we test two approaches for overcoming these difficulties, analysing a range of data sets using the technique of multivariate adaptive regression splines (MARS). MARS is closely related to regression techniques such as generalized additive models (GAMs) that are commonly and successfully used in modelling species distributions, but has particular advantages in its analytical speed and the ease of transfer of analysis results to other computational environments such as a Geographic Information System. MARS also has the advantage that it can model multiple responses, meaning that it can combine information from a set of species to determine the dominant environmental drivers of variation in species composition. We use data from 226 species from six regions of the world, and demonstrate the use of MARS for distribution modelling using presence-only data. We test whether (1) the type of data used to represent absence or background and (2) the signal from multiple species affect predictive performance, by evaluating predictions at completely independent sites where genuine presence,absence data were recorded. Models developed with absences inferred from the total set of presence-only sites for a biological group, and using simultaneous analysis of multiple species to inform the choice of predictor variables, performed better than models in which species were analysed singly, or in which pseudo-absences were drawn randomly from the study area. The methods are fast, relatively simple to understand, and useful for situations where data are limited. A tutorial is included. [source] Nonparametric harmonic regression for estuarine water quality dataENVIRONMETRICS, Issue 6 2010Melanie A. Autin Abstract Periodicity is omnipresent in environmental time series data. For modeling estuarine water quality variables, harmonic regression analysis has long been the standard for dealing with periodicity. Generalized additive models (GAMs) allow more flexibility in the response function. They permit parametric, semiparametric, and nonparametric regression functions of the predictor variables. We compare harmonic regression, GAMs with cubic regression splines, and GAMs with cyclic regression splines in simulations and using water quality data collected from the National Estuarine Reasearch Reserve System (NERRS). While the classical harmonic regression model works well for clean, near-sinusoidal data, the GAMs are competitive and are very promising for more complex data. The generalized additive models are also more adaptive and require less-intervention. Copyright © 2009 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||