nt is that it’s unbiased. </p>

<p>For that, we get rid of $\beta$, fixed-effect coefficients, by taking a matrix $S$ such that $SX = 0$. </p>

<p>The idea behind it is this: if $y$ has gaussian distribution with mean $X\beta + Gu$ and var.-covar. matrix $V=\sigma_g^2GG^T + \sigma^2I$, the transformed phenotype vector $Sy$ will still have gaussian distribution (because the transformation is linear) but with mean $0$ and variance $SVS^T$, containing no trace of $\beta$. Then ML estimate of $Sy$ is maximize