Genomic selection (GS) is an important method used in plant and animal breeding. The experimental data provided in this study contain counting data. These datasets were used to support research on efficient methodologies for multivariate count data outcomes including a multivariate Poisson deep neural network (MPDN) model, a conventional multivariate generalized Poisson regression model, and a univariate Poisson deep learning models. The results of the analyses are presented in a corresponding publication.