RKHS_FA_DIAG.md
In BGLR: Bayesian Generalized Linear Regression

Factor analysis

Example adapted from MTM package. In Factor Analysis (FA), a covariance matrix is decomposed into common and specific factors according to O = BB' + PSI where B is a matrix of loadings (regressions of the original random effects into common factors) and PSI is a diagonal matrix whose non-null entries give the variances of factors that are trait-specific. The loadings are assigned flat priors (normal priors with null mean and large variance) and the variances of the specific factors are assigned scaled-invers chi-squared with df and scale given by parameters df0 and S0 (which if not given are assigned default values). The following example specifies a 1-common factor model. The matrix M in the example is a logical matrix of the same dimensions as B with TRUE for loadings that the user want to estimate, and FALSE for those that should be zeroed out.


library(BGLR)
data(wheat)
K<-wheat.A
y<-wheat.Y

M <- matrix(nrow = 4, ncol = 1, TRUE)
ETA<-list(list(K=K,model="RKHS",Cov=list(type="FA",M=M)))

fm<-Multitrait(y=y,ETA=ETA,resCov=list(type="DIAG"), nIter=1000,burnIn=500)

#Residual covariance matrix
fm$resCov

#Genetic covariance matrix
fm$ETA[[1]]$Cov

#Random effects
fm$ETA[[1]]$u

Return to examples