  Since the emergence of genome-wide association studies (GWASs), estimation of
the narrow sense heritability explained by common single-nucleotide
polymorphisms (SNPs) via linear mixed model approaches became widely used. As
in most GWASs, most of the heritability analyses are performed using univariate
approaches i.e. considering each phenotype independently. In this study, we
propose a Bayesian matrix-variate mixed model that takes into account the
genetic correlation between phenotypes in addition to the genetic correlation
between individuals which is usually modelled via a relatedness matrix. We
showed that when the relatedness matrix is estimated using all the genome-wide
SNPs, our model is equivalent to a matrix normal regression with matrix normal
prior on the effect sizes. Using real data we demonstrate that there is a boost
in the heritability explained when phenotypes are jointly modelled (25-35%
increase). In fact based on their standard error, the joint modelling provides
more accurate estimates of the heritability over the univariate modelling.
Moreover, our Bayesian approach provides slightly higher estimates of
heritability compared to the maximum likelihood method. On the other hand,
although our method performs less well in phenotype prediction, we note that an
initial imputation step relatively increases the prediction accuracy.
