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Full-Text Articles in Physical Sciences and Mathematics
The Analysis Of Longitudinal Data Using Mixed Model L-Splines, S. Welham, Brian Cullis, M. Kenward, R Thompson
The Analysis Of Longitudinal Data Using Mixed Model L-Splines, S. Welham, Brian Cullis, M. Kenward, R Thompson
Professor Brian Cullis
L-splines are a large family of smoothing splines defined in terms of a linear differential operator. This article develops L-splines within the context of linear mixed models and uses the resulting mixed model L-spline to analyze longitudinal data from a grassland experiment. In the spirit of time-series analysis, a periodic mixed model L-spline is developed, which partitions data into a smooth periodic component plus smooth long-term trend.
A Comparison Of Mixed Model Splines For Curve Fitting, S Welham, Brian Cullis, M Kenward, R Thompson
A Comparison Of Mixed Model Splines For Curve Fitting, S Welham, Brian Cullis, M Kenward, R Thompson
Professor Brian Cullis
Three types of polynomial mixed model splines have been proposed: smoothing splines, Psplines and penalized splines using a truncated power function basis. The close connections between these models are demonstrated, showing that the default cubic form of the splines differs only in the penalty used. A general definition of the mixed model spline is given that includes general constraints and can be used to produce natural or periodic splines. The impact of different penalties is demonstrated by evaluation across a set of functions with specific features, and shows that the best penalty in terms of mean squared error of prediction …
Analysis Of Yield And Oil From A Series Of Canola Breeding Trials. Part I. Fitting Factor Analytic Mixed Models With Pedigree Information, C Beeck, W Cowling, A Smith, Brian Cullis
Analysis Of Yield And Oil From A Series Of Canola Breeding Trials. Part I. Fitting Factor Analytic Mixed Models With Pedigree Information, C Beeck, W Cowling, A Smith, Brian Cullis
Professor Brian Cullis
In this paper multiplicative mixed models have been used for the analysis of multi-environment trial (MET) data for canola oil and grain yield. Information on pedigrees has been included to allow for the modelling of additive and nonadditive genetic effects. The MET data set included a total of 19 trials (synonymous with sites or environments), which were sown across southern Australia in 2007 and 2008. Each trial was designed as a p-rep design using DiGGeR with the default prespecified spatial model. Lines in their first year of testing were unreplicated, whereas there were two or three replications of advanced …
Estimation In A Multiplicative Mixed Model Involving A Genetic Relationship Matrix, Alison M. Kelly, Brian R. Cullis, Arthur R. Gilmour, John A. Eccleston, Robin Thompson
Estimation In A Multiplicative Mixed Model Involving A Genetic Relationship Matrix, Alison M. Kelly, Brian R. Cullis, Arthur R. Gilmour, John A. Eccleston, Robin Thompson
Professor Brian Cullis
Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we …
The Analysis Of Crop Cultivar Breeding And Evaluation Trials: An Overview Of Current Mixed Model Approaches, A Smith, Brian Cullis, R Thompson
The Analysis Of Crop Cultivar Breeding And Evaluation Trials: An Overview Of Current Mixed Model Approaches, A Smith, Brian Cullis, R Thompson
Professor Brian Cullis
The analysis of series of crop variety trials has a long history with the earliest approaches being based on ANOVA methods. Kempton (1984) discussed the inadequacies of this approach, summarized the alternatives available at that time and noted that all of these approaches could be classified as multiplicative models. Recently, mixed model approaches have become popular for the analysis of series of variety trials. There are numerous reasons for their use, including the ease with which incomplete data (not all varieties in all trials) can be handled and the ability to appropriately model within-trial error variation. Currently, the most common …