getK {BGGE}  R Documentation 
Create kernel matrix for GE genomic prediction models
getK(Y, X, kernel = c("GK", "GB"), setKernel = NULL, bandwidth = 1, model = c("SM", "MM", "MDs", "MDe"), quantil = 0.5, intercept.random = FALSE)
Y 

X 
Marker matrix with individuals in rows and markers in columns. Missing markers are not allowed. 
kernel 
Kernel to be created internally. Methods currently implemented are the Gaussian 
setKernel 

bandwidth 

model 
Specifies the genotype \times environment model to be fitted. It currently supported the
models 
quantil 
Specifies the quantile to create the Gaussian kernel. 
intercept.random 
if 
The aim is to create kernels to fit GE interaction models applied to genomic prediction.
Two standard genomic kernels are currently supported:
GB
creates a linear kernel resulted from the crossproduct of centered and standardized
marker genotypes divide by the number of markers p:
GB = \frac{XX^T}{p}
Another alternative is the Gaussian Kernel GK
, resulted from:
GK (x_i, x_{i'}) = exp(\frac{h d_{ii'}^2}{q(d)})
where d_{ii'}^2 is the genetic distance between individuals based on markers scaled
by some percentile {q(d)} and bandwidth is the bandwidth parameter. However,
other kernels can be provided through setKernel
. In this case, arguments X
,
kernel
and h
are ignored.
Currently, the supported models for GE kernels are:
SM
: is the singleenvironment main genotypic effect model  It fits the data for a
single environment, and only one kernel is produced.
MM
: is the multienvironment main genotypic effect model  It consideres the main
random genetic effects across environments. Thus, just one kernel is produced, of order
n \times n, related to the main effect across environments.
MDs
: is the multienvironment single variance genotype x environment deviation
model  It is an extension of MM
by adding the random interaction effect of
environments with genotype information. Thus, two kernels are created, one related to the
main effect across environment, and the second is associated with single genotype by environment effect.
MDe
: is the multienvironment, environmentspecific variance genotype x environment
deviation model  It separates the genetic effects into the main genetic
effects and the specific genetic effects (for each environment). Thus, one kernel
for across environments effect and j kernels are created, one for each
environment.
These GE genomic models were compared and named by Sousa et al. (2017) and can be increased by using
the kernel related to random intercept of genotype through intercept.random
.
This function returns a twolevel list, which specifies the kernel and the type of matrix.
The latter is a classification according to its structure, i. e.,
if the matrix is dense or a block diagonal. For the main effect (G
),
the matrix is classified as dense (D). On the other hand, matrices for environmentspecific and
genotype by environment effect (GE
) are considered diagonal block (BD). This classification is used
as part of the prediction through the BGGE function.
Jarquin, D., J. Crossa, X. Lacaze, P. Du Cheyron, J. Daucourt, J. Lorgeou, F. Piraux, L. Guerreiro, P. Pérez, M. Calus, J. Burgueño, and G. de los Campos. 2014. A reaction norm model for genomic selection using highdimensional genomic and environmental data. Theor. Appl. Genet. 127(3): 595607.
LopezCruz, M., J. Crossa, D. Bonnett, S. Dreisigacker, J. Poland, J.L. Jannink, R.P. Singh, E. Autrique, and G. de los Campos. 2015. Increased prediction accuracy in wheat breeding trials using a marker × environment interaction genomic selection model. G3: Genes, Genomes, Genetics. 5(4): 56982.
Perez Elizalde, S. J. Cuevas, P. PerezRodriguez, and J. Crossa. 2015. Selection of the Bandwidth Parameter in a Bayesian Kernel Regression Model for GenomicEnabled Prediction. Journal of Agricultural, Biological, and Environmental Statistics (JABES), 20(4):512532.
Sousa, M. B., Cuevas, J., Oliveira, E. G. C., PerezRodriguez, P., Jarquin, D., FritscheNeto, R., Burgueno, J. & Crossa, J. (2017). Genomicenabled prediction in maize using kernel models with genotype x environment interaction. G3: Genes, Genomes, Genetics, 7(6), 19952014.
# create kernel matrix for model MDs using wheat dataset library(BGLR) data(wheat) X < scale(wheat.X, scale = TRUE, center = TRUE) rownames(X) < 1:599 pheno_geno < data.frame(env = gl(n = 4, k = 599), GID = gl(n=599, k=1, length = 599*4), value = as.vector(wheat.Y)) K < getK(Y = pheno_geno, X = X, kernel = "GB", model = "MDs")