WLS estimation more heavily prioritizes reducing misfit in those cells in the S matrix that are estimated with greater precision. This has the desirable property of potentially decreasing sampling variance of the Genomic SEM parameter estimates, which may boost power for SNP discovery and increase polygenic prediction. However, because the precision of cells in the S matrix is contingent upon the sample sizes for the contributing univariate GWASs, WLS may produce a solution that is dominated by the patterns of association involving the most well powered GWASs, and contain substantial local misfit in cells of S that are informed by lower powered GWASs. In other words, WLS relative to ML may more heavily prioritize minimizing sampling variance of the parameter estimates in the so-called variance bias tradeoff.48 We expect that this will only occur when the model is overidentified (i.e., df > 0), such that exact fit cannot be obtained, and that divergence in WLS and ML estimates will be most pronounced when there is lower sample overlap and the contributing univariate GWASs differ substantially in power. ML estimation may be preferred when the goal is to most evenly weight the contribution of the univariate sample statistics.
