LINEAR, GENERALIZED, HIERARCHICAL, BAYESIAN AND RANDOM REGRESSION MIXED MODELS IN GENETICS/GENOMICS IN PLANT BREEDING
This paper presents the state of the art of the statistical modelling as applied to plant breeding. Classes of inference, statistical models, estimation methods and model selection are emphasized in a practical way. Restricted Maximum Likelihood (REML), Hierarchical Maximum Likelihood (HIML) and Bayesian (BAYES) are highlighted. Distributions of data and effects, and dimension and structure of the models are considered for model selection and parameters estimation. Theory and practical examples referring to selection between models with different fixed effects factors are given using the Full Maximum Likelihood (FML). An analytical FML way of defining random or fixed effects is presented to avoid the subjective or conceptual usual definitions. Examples of the applications of the Hierarchical Maximum Likelihood/Hierarchical Generalized Best Linear Unbiased Prediction (HIML/HG-BLUP) procedure are also presented. Sample sizes for achieving high experimental quality and accuracy are indicated and simple interpretation of the estimates of key genetic parameters are given. Phenomics and genomics are approached. Maximum accuracy under the truest model is the key for achieving efficacy in plant breeding programs.