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Residual Distribution (residual + distribution)
Selected AbstractsGamma regression improves Haseman-Elston and variance components linkage analysis for sib-pairsGENETIC EPIDEMIOLOGY, Issue 2 2004Mathew J. Barber Abstract Existing standard methods of linkage analysis for quantitative phenotypes rest on the assumptions of either ordinary least squares (Haseman and Elston [1972] Behav. Genet. 2:3,19; Sham and Purcell [2001] Am. J. Hum. Genet. 68:1527,1532) or phenotypic normality (Almasy and Blangero [1998] Am. J. Hum. Genet. 68:1198,1199; Kruglyak and Lander [1995] Am. J. Hum. Genet. 57:439,454). The limitations of both these methods lie in the specification of the error distribution in the respective regression analyses. In ordinary least squares regression, the residual distribution is misspecified as being independent of the mean level. Using variance components and assuming phenotypic normality, the dependency on the mean level is correctly specified, but the remaining residual coefficient of variation is constrained a priori. Here it is shown that these limitations can be addressed (for a sample of unselected sib-pairs) using a generalized linear model based on the gamma distribution, which can be readily implemented in any standard statistical software package. The generalized linear model approach can emulate variance components when phenotypic multivariate normality is assumed (Almasy and Blangero [1998] Am. J. Hum Genet. 68: 1198,1211) and is therefore more powerful than ordinary least squares, but has the added advantage of being robust to deviations from multivariate normality and provides (often overlooked) model-fit diagnostics for linkage analysis. Genet Epidemiol 26:97,107, 2004. © 2004 Wiley-Liss, Inc. [source] Estimation of a residual distribution with small numbers of repeated measurementsTHE CANADIAN JOURNAL OF STATISTICS, Issue 3 2002Edward Susko Abstract The authors consider the estimation of a residual distribution for different measurement problems with a common measurement error process. The problem is motivated by issues arising in the analysis of gene expression data but should have application in other similar settings. It is implicitly assumed throughout that there are large numbers of measurements but small numbers of repeated measurements. As a consequence, the distribution of the estimated residuals is a biased estimate of the residual distribution. The authors present two methods for the estimation of the residual distribution with some restriction on the form of the distribution. They give an upper bound for the rate of convergence for an estimator based on the characteristic function and compare its performance with that of another estimator with simulations. Estimation de la loi des erreurs à partir d'un petit nombre de mesures répétées Les auteurs s' intéressent à l' estimation d' une loi des erreurs supposée commune à un ensemble de situations expérimentales. Leur préoccupation émane de problèmes concernant l' analyse de l' expression des génes, mais la méthodologie qu' ils proposent a une portée plus large. Leur technique suppose l' accés à un grand nombre de données mais à un petit nombre de mesures répétées. La loi des résidus constitue alors un estimateur biaisé de celle des erreurs. Les auteurs présentent deux méthodes d' estimation de cette dernière, sous certaines hypothèses quant à sa forme. Us majorent le taux de convergence d' un premier estimateur dérivé de la fonction caractéristique et comparent sa performance à celle d' un second au moyen de simulations. [source] A box scheme for transcritical flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2002T. C. Johnson Abstract The accurate computer simulation of river and pipe flow is of great importance in the design of urban drainage networks. The use of implicit numerical schemes allows the time step to be chosen on the basis of accuracy rather than stability, offering a potential computational saving over explicit methods. The highly successful Box Scheme is an implicit method which can be used to model a wide range of subcritical and supercritical flows. However, care must be taken over the modelling of transcritical flows since, unless the correct internal boundary conditions are imposed, the scheme becomes unstable. The necessity of accurately tracking all the critical interfaces and treating them accordingly can be algorithmically complex and in practice the underlying mathematical model is often modified to ensure that the flow remains essentially subcritical. Such a modification however inevitably leads to additional errors and incorrect qualitative behaviour can be observed. In this paper we show how the technique of ,residual distribution' can be successfully implemented in order to accurately model unsteady transcritical flow without the need to know a priori which regions of the computational domain correspond to subcritical and supercritical flow. When used in conjunction with a form of artificial smoothing, the resulting method generates very high resolution results even for transcritical problems involving shocks, as can be seen in the numerical results. Copyright © 2002 John Wiley & Sons, Ltd. [source] Assessing river biotic condition at a continental scale: a European approach using functional metrics and fish assemblagesJOURNAL OF APPLIED ECOLOGY, Issue 1 2006D. PONT Summary 1The need for sensitive biological measures of aquatic ecosystem integrity applicable at large spatial scales has been highlighted by the implementation of the European Water Framework Directive. Using fish communities as indicators of habitat quality in rivers, we developed a multi-metric index to test our capacity to (i) correctly model a variety of metrics based on assemblage structure and functions, and (ii) discriminate between the effects of natural vs. human-induced environmental variability at a continental scale. 2Information was collected for 5252 sites distributed among 1843 European rivers. Data included variables on fish assemblage structure, local environmental variables, sampling strategy and a river basin classification based on native fish fauna similarities accounting for regional effects on local assemblage structure. Fifty-eight metrics reflecting different aspects of fish assemblage structure and function were selected from the available literature and tested for their potential to indicate habitat degradation. 3To quantify possible deviation from a ,reference condition' for any given site, we first established and validated statistical models describing metric responses to natural environmental variability in the absence of any significant human disturbance. We considered that the residual distributions of these models described the response range of each metric, whatever the natural environmental variability. After testing the sensitivity of these residuals to a gradient of human disturbance, we finally selected 10 metrics that were combined to obtain a European fish assemblage index. We demonstrated that (i) when considering only minimally disturbed sites the index remains invariant, regardless of environmental variability, and (ii) the index shows a significant negative linear response to a gradient of human disturbance. 4Synthesis and applications. In this reference condition modelling approach, by including a more complete description of environmental variability at both local and regional scales it was possible to develop a novel fish biotic index transferable between catchments at the European scale. The use of functional metrics based on biological attributes of species instead of metrics based on species themselves reduced the index sensitivity to the variability of fish fauna across different biogeographical areas. [source] | ||||||||||