15 research outputs found
WGNAM: whole-genome nested association mapping
A powerful QTL analysis method for nested association mapping populations is presented. Based on a one-stage multi-locus model, it provides accurate predictions of founder specific QTL effects
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Covariance Clustering: Modelling Covariance in Designed Experiments When the Number of Variables is Greater than Experimental Units
The size and complexity of datasets resulting from comparative research experiments in the agricultural domain is constantly increasing. Often the number of variables measured in an experiment exceeds the number of experimental units composing the experiment. When there is a necessity to model the covariance relationships that exist between variables in these experiments, estimation difficulties can arise due to the resulting covariance structure being of reduced rank. A statistical method, based in a linear mixed model framework, is presented for the analysis of designed experiments where datasets are characterised by a greater number of variables than experimental units, and for which the modelling of complex covariance structures between variables is desired. Aided by a clustering algorithm, the method enables the estimation of covariance through the introduction of covariance clusters as random effects into the modelling framework, providing an extension of the traditional variance components model for building covariance structures. The method was applied to a multi-phase mass spectrometry-based proteomics experiment, with the aim of exploring changes in the proteome of barley grain over time during the malting process. The modelling approach provides a new linear mixed model-based method for the estimation of covariance structures between variables measured from designed experiments, when there are a small number of experimental units, or observations, informing covariance parameter estimates
Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling
Modelling response surfaces using tensor cubic smoothing splines is presented for three designed experiments. The aim is to show how the analyses can be carried out using the asreml software in the R environment, and details of the analyses including the code to do so are presented in a tutorial style. The experiments were all run over time and involve an explanatory quantitative treatment variable; one experiment is a field trial which has a spatial component and involves an additional treatment. Thus, in addition to the response surface for the time by explanatory variable, modelling of temporal and, for the third experiment, of temporal and spatial effects at the residual level is required. A linear mixed model is used for analysis, and a mixed model representation of the tensor cubic smoothing spline is described and seamlessly incorporated in the full linear mixed model. The analyses show the flexibility and capacity of asreml for complex modelling
WGNAM: whole-genome nested association mapping
A powerful QTL analysis method for nested association mapping populations is presented. Based on a one-stage multi-locus model, it provides accurate predictions of founder specific QTL effects
Residual Variance–Covariance Modelling in Analysis of Multivariate Data from Variety Selection Trials
Field trials for variety selection often exhibit spatial correlation between plots. When multivariate data are analysed from these field trials, there is the added complication in having to simultaneously account for correlation between the traits at both the residual and genetic levels. This may be temporal correlation in the case of multi-harvest data from perennial crop field trials, or between-trait correlation in multi-trait data sets. Use of parsimonious yet plausible models for the variance–covariance structure of the residuals for such data is a key element to achieving an efficient and inferentially sound analysis. In this paper, a model is developed for the residual variance–covariance structure firstly by considering a multivariate autoregressive model in one spatial direction and then extending this to two spatial directions. Conditions for ensuring that the processes are directionally invariant are presented. Using a canonical decomposition, these directionally invariant processes can be transformed into a set of independent separable processes. This simplifies the estimation process. The new model allows for flexible modelling of the spatial and multivariate interaction and allows for different spatial correlation parameters for each harvest or trait. The methods are illustrated using data from lucerne breeding trials at several environments
RWGAIM: An efficient high-dimensional random whole genome average (QTL) interval mapping approach
Mapping of quantitative trait loci (QTLs) underlying variation in quantitative traits continues to be a powerful tool in genetic study of plants and other organisms. Whole genome average interval mapping (WGAIM), a mixed model QTL mapping approach using all intervals or markers simultaneously, has been demonstrated to outperform composite interval mapping, a common approach for QTL analysis. However, the advent of high-throughput high-dimensional marker platforms provides a challenge. To overcome this, a dimension reduction technique is proposed for WGAIM for efficient analysis of a large number of markers. This approach results in reduced computing time as it is dependent on the number of genetic lines (or individuals) rather than the number of intervals (or markers). The approach allows for the full set of potential QTL effects to be recovered. A proposed random effects version of WGAIM aims to reduce bias in the estimated size of QTL effects. Lastly, the two-stage outlier procedure used in WGAIM is replaced by a single stage approach to reduce possible bias in the selection of putative QTL in both WGAIM and the random effects version. Simulation is used to demonstrate the efficiency of the dimension reduction approach as well as demonstrate that while the approaches are very similar, the random WGAIM performs better than the original and modified fixed WGAIM by reducing bias and in terms of mean square error of prediction of estimated QTL effects. Finally, an analysis of a doubled haploid population is used to illustrate the three approaches.Arunas P. Verbyla, Julian D. Taylor and Klara L. Verbyl
Exact and approximate REML for heteroscedastic regression
Exact REML for heteroscedastic linear models is compared with a number of approximate REML methods which have been proposed in the literature, especially with the methods proposed by Lee and Nelder (LN98) and Smyth and Verbyla (SV99) for simultaneous mean-dispersion modelling in generalized linear models. It is shown that neither of the LN98 or SV99 methods reduces to REML in the normal linear case. Asymptotic variances and efficiencies are obtained for these and other estimators of the same general form. A new algorithm is suggested, similar to one suggested by Huele et al., which returns the correct REML estimators and an improved approximation to the standard errors. It is possible to obtain REML estimators by alternating between two generalized linear models but the final fitted generalized linear model objects will not return the correct standard errors for the variance coefficients. The true REML likelihood calculations therefore fit only partially into the double generalized linear model framework
Anisotropic Matern correlation and spatial prediction using REML
The Matérn correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a model-based approach to geostatistics, in which parameter estimation is achieved via REML and prediction is within the E-BLUP framework. In this article we develop a general class of linear mixed models using an anisotropic Matérn class with an extended metric. The approach is illustrated by application to soil salinity data in a rice-growing field in Australia, and to fine-scale soil pH data. It is found that anisotropy is an important aspect of both datasets, emphasizing the value of a straightforward and accessible approach to modeling anisotropy. © 2007 American Statistical Association and the International Biometric Society