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Residual Standard Deviation (residual + standard_deviation)
Selected AbstractsMeshing noise effect in design of experiments using computer experimentsENVIRONMETRICS, Issue 5-6 2002J. P. Caire Abstract This work is intended to show the influence of grid length and meshing technique on the empirical modeling of current distribution in an industrial electroplating reactor. This study confirms the interest of usual DOEs for computer experiments. Any 2D mesh generator induced, in this sensitive case, a significant noise representing only less than 5 per cent of the response. The ,experimental error' obeys a normal distribution and the associated replicate SDs represents 20 per cent of the global residual standard deviation. The geometry seems also to influence the corresponding noise. If the current density uniformity could be considered as a severe test, it is obvious that the noise generated by meshing would be amplified for 3D grids that will be in common use in future years. Copyright © 2002 John Wiley & Sons, Ltd. [source] Estimating the digestibility of Sahelian roughages from faecal crude protein concentration of cattle and small ruminantsJOURNAL OF ANIMAL PHYSIOLOGY AND NUTRITION, Issue 9-10 2006E. Schlecht Summary Studies on diet selection and feed intake of ruminants in extensive grazing systems often require the use of simple approaches to determine the organic matter digestibility (OMD) of the ingested feed. Therefore, we evaluated the validity of the one-factorial exponential regression established by Lukas et al. [Journal of Animal Science 83 (2005) 1332], which estimates OMD from the faecal crude protein (FCP) concentration. The equation was applied to two sets of data obtained with free grazing and pen-fed cattle, sheep and goats ingesting low and high amounts of green and dry vegetation of Sahelian pastures as well as millet leaves and cowpea hay. Data analysis showed that the livestock species did not influence the precision of estimation of OMD from FCP. For the linear regression between measured and estimated OMD (%) across n = 431 individual observations, a regression coefficient of r2 = 0.65 and a residual standard deviation (RSD) of 5.87 were obtained. The precision of estimation was influenced by the data set (p = 0.033), the type of feed (p < 0.001) and the feeding level (p = 0.009), and interactions occurred between type of feed and feeding level (p = 0.021). Adjusting the intercept and the slope of the established exponential function to the present data resulted in a compression of the curve; while r2 remained unchanged, the RSD of the regression between measured and estimated OMD was reduced, when compared with the results obtained from the equation of Lukas et al. (2005). Estimating OMD from treatment means of FCP greatly improved the correlation between measured and estimated OMD for both the established function and the newly fit equation. However, if anti-nutritional dietary factors increase the concentration of faecal nitrogen from feed or endogenous origin, the approach might considerably overestimate diet digestibility. [source] Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix,JOURNAL OF CHEMOMETRICS, Issue 1 2009Edmund R. Malinowski Abstract Median absolute deviation (MAD) is a well-established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F -tests, extensive calibration tables, time-consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd. [source] Selecting significant factors by the noise addition method in principal component analysisJOURNAL OF CHEMOMETRICS, Issue 7 2001Brian K. Dable Abstract The noise addition method (NAM) is presented as a tool for determining the number of significant factors in a data set. The NAM is compared to residual standard deviation (RSD), the factor indicator function (IND), chi-squared (,2) and cross-validation (CV) for establishing the number of significant factors in three data sets. The comparison and validation of the NAM are performed through Monte Carlo simulations with noise distributions of varying standard deviation, HPLC/UV-vis chromatographs of a mixture of aromatic hydrocarbons, and FIA of methyl orange. The NAM succeeds in correctly identifying the proper number of significant factors 98% of the time with the simulated data, 99% in the HPLC data sets and 98% with the FIA data. RSD and ,2 fail to choose the proper number of factors in all three data sets. IND identifies the correct number of factors in the simulated data sets but fails with the HPLC and FIA data sets. Both CV methods fail in the HPLC and FIA data sets. CV also fails for the simulated data sets, while the modified CV correctly chooses the proper number of factors an average of 80% of the time. Copyright © 2001 John Wiley & Sons, Ltd. [source] Application of robust procedures for estimation of breeding values in multiple-trait random regression test-day modelJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 1 2007J. Jamrozik Summary Robust procedures for estimation of breeding values were applied to multiple-trait random regression test-day (TD) model to reduce the influence of outliers on inferences. Robust estimation methods consisted of correcting selected observations (defined as outliers) in the process of solving mixed-model equations in such a way that ,new' observations gave residuals (actual observation minus predicted) within k residual standard deviations for a given day in milk in 305-day lactation. Data were 980 503 TD records on 63 346 Canadian Jersey cows. Milk, fat, protein and somatic cell score in the first three lactations were analysed jointly in the model that included fixed herd-TD effect and regressions within region,age,season of calving, and regressions with random coefficients for animal genetic and permanent environmental effects. All regressions were orthogonal polynomials of order 4. Robust procedures for k = 1.5, 2.0, 2.5, 2.75 and 3.0 were contrasted with the regular best linear unbiased prediction (BLUP) method in terms of numbers and distributions of outliers, and estimated breeding values (EBV) of animals. Distributions of outliers were similar across traits and lactations. Early days in milk (from 5 to 15) were associated with larger frequency of outliers compared with the remaining part of lactation. Several, computationally simple, robust methods (for k > 2.0) reduced the influence of outlier observations in the model and improved the overall model performance. Differences in rankings of animals from robust evaluations were small compared with the regular BLUP method. No clear associations between changes in EBV (rankings) of top animals from different methods and the occurrence of outliers were detected. [source] The use of endogenous nitrogen for microbial crude protein synthesis in the rumen of growing bullsJOURNAL OF ANIMAL PHYSIOLOGY AND NUTRITION, Issue 5 2000H. Kluth Summary The objective of this study was to quantify endogenous nitrogen (N) recycled for microbial protein synthesis in the rumen. Four growing bulls (Schwarzbuntes Milchrind; bodyweight: 240,310 kg) with duodenal T-shaped cannulas were fed diets containing four levels of crude protein content (200, 156, 102 and 63 g/kg dry matter, respectively). The diets were based on wheat, barley, tapioca meal, soybean extracted meal, dried beet pulp, meadow hay and straw. The diets had an energy level of 11.1, 10.9, 10.2 and 9.6 MJ metabolizable energy/kg dry matter. Faeces and urine were collected in four 7-day balance periods. Duodenal flow rate was estimated by TiO2, pelleted with grain, as a marker. The relationship between urine N excretion, the amount of microbial N reaching the duodenum, ruminal N balance and N retention were examined and the amount of endogenous N available for microbial protein synthesis without negative effects on the N retention was determined. It can be concluded that up to 16% of the microbial N supply could be covered by recycled endogenous N, but N retention should not be decreased by more than 1.5 residual standard deviations of maximal N retention. [source] Epothilones: Quantitative Structure Activity Relations Studied by Support Vector Machines and Artificial Neural NetworksMOLECULAR INFORMATICS, Issue 7 2003Annalen Bleckmann Abstract In this paper the relation between the structure of epothilones (a new class of anti-tumour agents) and their potential to influence the tubulin-microtubule equilibrium is investigated. Insights into the character of the tubulin-epothilone interactions are derived as the accuracy and reliability of support vector machines and artificial neural networks to model such relations quantitatively is compared. Both methods are well qualified to model relationships between the structure of epothilone derivatives and their anti-tumour activities. Artificial neural networks achieve lower residual standard deviations (22%) compared to support vector machines (25%) and better classification results (89% compared to 75%). However, the reproducibility of the results is greater for support vector machines, which suggests a stronger convergence. The mapping of the influence of individual structural descriptors on the three-dimensional epothilone structure suggests one side of the rather flat molecule to be more important for its activity. The "LIBSVM" software which is used for simulating the support vector machines is freely available from www.csie.ntu.edu.tw/~cjlin/libsvm. The Program "Smart" which is used for simulating artificial neural networks is free for academic use and can be obtained together with the database of epothilones and their activities from www.jens-meiler.de. [source] | ||||||||||