The fit function minimized in the diagonally weighted version of WLS estimation that is standard in the GenomicSEM software package is the following: FWLS(θ)=(s−σ(θ))′Ds−1(s−σ(θ)), where S and Σ(θ) have been half-vectorized to produce s and σ(θ) respectively, and DS is VS with its off-diagonal elements set to 0. We choose the diagonally weighted version of WLS because it is more tractable to implement for large (highly multivariate) matrices and is more stable than fully weighted WLS in finite samples.46,47
