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In this paper we propose a Bayesian multi-output regressor stacking (BMORS) model that is a generalization of the multi-trait regressor stacking method. The proposed BMORS model consists of two stages: in the first stage, a univariate genomic best linear unbiased prediction (GBLUP including genotype × environment interaction GE) model is implemented for each of the L traits under study; then the predictions of all traits are included as covariates in the second stage, by implementing a Ridge regression model. The main objectives of this research were to study alternative models to the existing multi-trait multi-environment (BMTME) model with respect to (1) genomic-enabled prediction accuracy, and (2) potential advantages in terms of computing resources and implementation. We compared the predictions of the BMORS model to those of the univariate GBLUP model using 7 maize and wheat datasets. We found that the proposed BMORS produced similar predictions to the univariate GBLUP model and to the BMTME model in terms of prediction accuracy; however, the best predictions were obtained under the BMTME model. In terms of computing resources, we found that the BMORS is at least 9 times faster than the BMTME method. Based on our empirical findings, the proposed BMORS model is an alternative for predicting multi-trait and multi-environment data, which are very common in genomic-enabled prediction in plant and animal breeding programs., (Copyright © 2019 Montesinos-Lopez et al.)

In genomic-enabled prediction, the task of improving the accuracy of the prediction of lines in environments is difficult because the available information is generally sparse and usually has low correlations between traits. In current genomic selection, although researchers have a large amount of information and appropriate statistical models to process it, there is still limited computing efficiency to do so. Although some statistical models are usually mathematically elegant, many of them are also computationally inefficient, and they are impractical for many traits, lines, environments, and years because they need to sample from huge normal multivariate distributions. For these reasons, this study explores two recommender systems: itembased collaborative filtering (IBCF) and the matrix factorization algorithm (MF) in the context of multiple traits and multiple environments. The IBCF and MF methods were compared with two conventional methods on simulated and real data. Results of the simulated and real data sets show that the IBCF technique was slightly better in terms of prediction accuracy than the two conventional methods and the MF method when the correlation was moderately high. The IBCF technique is very attractive because it produces good predictions when there is high correlation between items (environment-trait combinations) and its implementation is computationally feasible, which can be useful for plant breeders who deal with very large data sets. [ABSTRACT FROM AUTHOR]