  As the amount and complexity of genetic information increases it is necessary
that we explore some efficient ways of handling these data. This study takes
the "divide and conquer" approach for analyzing high dimensional genomic data.
Our aims include reducing the dimensionality of the problem that has to be
dealt one at a time, improving the performance and interpretability of the
models. We propose using the inherent structures in the genome; to divide the
bigger problem into manageable parts. In plant and animal breeding studies a
distinction is made between the commercial value (additive + epistatic genetic
effects) and the breeding value (additive genetic effects) of an individual
since it is expected that some of the epistatic genetic effects will be lost
due to recombination. In this paper, we argue that the breeder can take
advantage of some of the epistatic marker effects in regions of low
recombination. The models introduced here aim to estimate local epistatic line
heritability by using the genetic map information and combine the local
additive and epistatic effects. To this end, we have used semi-parametric mixed
models with multiple local genomic relationship matrices with hierarchical
testing designs and lasso post-processing for sparsity in the final model and
speed. Our models produce good predictive performance along with genetic
association information.
