The distribution of McKay's approximation for the coefficient of variation

McKay's approximation for the coefficient of variation is type II noncentral beta distributed and asymptotically normal with mean n - 1 and variance smaller than 2(n - 1)

A resampling test for principal component analysis of genotype-by-environment interaction

In crop science, genotype-by-environment interaction is oftenexplored using the "genotype main effects and genotype-by-environmentinteraction effects" (GGE) model. Using this model, a singularvalue decomposition is performed on the matrix of residuals from a fit ofa linear model with main effects of environments. Provided that errorsare independent, normally distributed and homoscedastic, the significanceof the multiplicative terms of the GGE model can be tested usingresampling methods. The GGE method is closely related to principalcomponent analysis (PCA). The present paper describes i) the GGEmodel, ii) the simple parametric bootstrap method for testing multiplicativegenotype-by-environment interaction terms, and iii) how thisresampling method can also be used for testing principal components inPC

Optimal calibration in immunoassay and inference on the coefficient of variation

This thesis examines and develops statistical methods for design and analysis with applications in immunoassay and other analytical techniques. In immunoassay, concentrations of components in clinical samples are measured using antibodies. The responses obtained are related to the concentrations in the samples. The relationship between response and concentration is established by fitting a calibration curve to responses of samples with known concentrations, called calibrators or standards. The concentrations in the clinical samples are estimated, through the calibration curve, by inverse prediction. The optimal choice of calibrator concentrations is dependent on the true relationship between response and concentration. A locally optimal design is conditioned on a given true relationship. This thesis presents a novel method that accounts for the variation in the true relationships by considering unconditional variances and expected values. For immunoassay, it is suggested that the average coefficient of variation in inverse predictions be minimised. In immunoassay, the coefficient of variation is the most common measure of variability. Several clinical samples or calibrators may share the same coefficient of variation, although they have different expected values. It is shown here that this phenomenon can be a consequence of a random variation in the dispensed volumes, and that inverse regression is appropriate when the random variation is in concentration rather than in response. An estimator of a common coefficient of variation that is shared by several clinical samples is proposed, and inferential methods are developed for common coefficients of variation in normally distributed data. These methods are based on McKay's chi-square approximation for the coefficient of variation. This study proves that McKay's approximation is noncentral beta distributed, and that it is asymptotically normal with mean n - 1 and variance slightly smaller than 2(n - 1)

Notes on correctness of p-values when analyzing experiments using SAS and R

It is commonly believed that if a two-way analysis of variance (ANOVA) is carried out in R, then reported p-values are correct. This article shows that this is not always the case. Results can vary from non-significant to highly significant, depending on the choice of options. The user must know exactly which options result in correct p-values, and which options do not. Furthermore, it is commonly supposed that analyses in SAS and R of simple balanced experiments using mixed-effects models result in correct p-values. However, the simulation study of the current article indicates that frequency of Type I error deviates from the nominal value. The objective of this article is to compare SAS and R with respect to correctness of results when analyzing small experiments. It is concluded that modern functions and procedures for analysis of mixed-effects models are sometimes not as reliable as traditional ANOVA based on simple computations of sums of squares

Bayesian Analysis of Nonnegative Data Using Dependency-Extended Two-Part Models

This article is motivated by the challenge of analysing an agricultural field experiment with observations that are positive on a continuous scale or zero. Such data can be analysed using two-part models, where the distribution is a mixture of a positive distribution and a Bernoulli distribution. However, traditional two-part models do not include any dependencies between the two parts of the model. Since the probability of zero is anticipated to be high when the expected value of the positive part is low, and the other way around, this article introduces dependency-extended two-part models. In addition, these extensions allow for modelling the median instead of the mean, which has advantages when distributions are skewed. The motivating example is an incomplete block trial comparing ten treatments against weed. Gamma and lognormal distributions were used for the positive response, although any density on the support of real numbers can be accommodated. In a cross-validation study, the proposed new models were compared with each other and with a baseline model without dependencies. Model performance and sensitivity to choice of priors were investigated through simulation. A dependency-extended two-part model for the median of the lognormal distribution performed best with regard to mean square error in prediction. Supplementary materials accompanying this paper appear online

The use of a reference variety for comparisons in incomplete series of crop variety trials

In series of crop variety trials, `test varieties' are compared with one other and with a `reference' variety that is included in all trials. The series is typically analyzed with a linear mixed model and the method of generalized least squares. Usually, the estimates of the expected differences between the test varieties and the reference variety are presented. When the series is incomplete, i.e. when all test varieties were not included in all trials, the method of generalized least squares may give estimates of expected differences to the reference variety that do not appear to accord with observed differences. The present paper draws attention to this phenomenon and explores the recurrent idea of comparing test varieties indirectly through the use of the reference. A new `reference treatment method' was specified and compared with the method of generalized least squares when applied to a five-year series of 85 spring wheat trials. The reference treatment method provided estimates of differences to the reference variety that agreed with observed differences, but was considerably less efficient than the method of generalized least squares

Production and nutrient composition of forage legume fractions produced by juicing and leaf stripping

The large-scale import of soybean products into the EU decreases the self-sufficiency of livestock production. The fractionation of grassland forage crops presents an opportunity to locally produce protein-rich feed for monogastrics. Two promising fractionation methods, twin-screw press juicing and leaf stripping, were evaluated in parallel in field experiments established in Norway and Sweden to compare the nutrient composition and yield of the resulting biorefined and residual fractions. The clearest delineation between the methods was in the ash-free neutral detergent fibre (aNDFom) concentration, with juicing producing a biorefined fraction with a lower aNDFom than leaf stripping. Variability in the allocation of crude protein (CP) and biomass to the biorefined fractions occurred in both methods between cuts and locations and is likely due to differing stand characteristics and inconsistency in machine functionality. Additional work is needed to understand how characteristics such as stand density, botanical composition, and plant phenological stage impact each fractionation method's ability to allocate protein, fibre, and biomass into the resulting fractions. Future studies should focus particularly on determining standardised settings for leaf stripping machinery based on a range of stand characteristics to ensure consistency in the yield and nutrient composition of the resulting fractions

Testing components of two-way interaction in multi-environment trials

Experiments with two factors are commonly analyzed using two-way analysis of variance, where testing significance of interaction is straightforward. However, using bilinear models, interaction can be analyzed further. The additive main effects and multiplicative interaction (AMMO model uses singular value decomposition for partitioning interaction into multiplicative terms, such that the first terms typically account for a large portion of the sum of squares, whereas the last terms are of minor importance. This model is used extensively for analysis of genotype-by-environment interaction in multi-environment trials. A recurring question is how to determine the number of terms to retain in the model. If data is replicated, which is usually the case, the F-R test can be used for this purpose. The simple parametric bootstrap method is another option, although this test was developed for unreplicated data. Since both of these tests of significance may be applied in cases with replication, researchers need advice on which of the methods to use. We discuss several statistical models and show that the two methods address different questions

Biological variation of biochemical urine and serum analytes in healthy dogs

BackgroundBiological variation (BV) of urinary (U) biochemical analytes has not been described in absolute terms, let alone as a ratio of the U-creatinine or fractional excretion in healthy dogs. These analytes are potential diagnostic tools for different types of kidney damage and electrolyte disorders in dogs. ObjectivesWe aimed to investigate the BV of specific gravity, osmolality, creatinine, urea, protein, glucose, chloride, sodium, potassium, calcium, and phosphate in urine from healthy pet dogs. MethodsBlood and urine samples from 13 dogs were collected once weekly for 8 weeks. Samples were analyzed in duplicate and in randomized order. For each sample, U-analyte and serum concentrations were measured, and U-analyte/U-creatinine and fractional excretion (FE) were calculated. Components of variance, estimated by restricted maximum likelihood, were used to determine within-subject variation (CVI), between-subject variation (CVG), and analytical variation (CVA). Index of individuality (II) and reference change values were calculated. ResultsCV(I) for all urine analytes varied between 12.6% and 35.9%, except for U-sodium, U-sodium/U-Cr, and FE-sodium, which had higher CV(I)s (59.5%-60.7%). For U-protein, U-sodium, U-potassium, U-sodium/U-creatinine, FE-urea, FE-glucose, FE-sodium, FE-potassium, and FE-phosphate II were low, indicating that population-based RIs were appropriate. The remaining analytes had an intermediate II, suggesting that population-based RIs should be used with caution. ConclusionThis study presents information on the biological variation of urinary and serum biochemical analytes from healthy dogs. These data are important for an appropriate interpretation of laboratory results

Cross-validation of stagewise mixed-model analysis of Swedish variety trials with winter wheat and spring barley

In cultivar testing, linear mixed models have been used routinely to analyze multienvironment trials. A single‐stage analysis is considered as the gold standard, whereas two‐stage analysis produces similar results when a fully efficient weighting method is used, namely when the full variance–covariance matrix of the estimated means from Stage 1 is forwarded to Stage 2. However, in practice, this may be hard to do and a diagonal approximation is often used. We conducted a cross‐validation with data from Swedish cultivar trials on winter wheat (Triticum aestivum L.) and spring barley (Hordeum vulgare L.) to assess the performance of single‐stage and two‐stage analyses. The fully efficient method and two diagonal approximation methods were used for weighting in the two‐stage analyses. In Sweden, cultivar recommendation is delineated by zones (regions), not individual locations. We demonstrate the use of best linear unbiased prediction (BLUP) for cultivar effects per zone, which exploits correlations between zones and thus allows information to be borrowed across zones. Complex variance–covariance structures were applied to allow for heterogeneity of cultivar × zone variance. The single‐stage analysis and the three weighted two‐stage analyses all performed similarly. Loss of information caused by a diagonal approximation of the variance–covariance matrix of adjusted means from Stage 1 was negligible. As expected, BLUP outperformed best linear unbiased estimation. Complex variance–covariance structures were dispensable. To our knowledge, this study is the first to use cross‐validation for comparing single‐stage analyses with stagewise analyses