Both WLS and ML fit functions will produce consistent estimates of the model parameters when the model is true.47 However, the “naïve” SEs and fit statistic produced in Stage 2 estimation will be incorrect, because neither estimator uses the full VS matrix in estimation. Thus, robust corrections must be applied to produce consistent estimates of SEs and test statistics. The correct sampling covariance matrix of the Stage Two, Genomic SEM parameter estimates (i.e., Vθ) can be obtained using a sandwich correction:13,47 Vθ=(Δ^′Γ−1Δ^)−1Δ^′Γ−1VsΓ−1Δ^(Δ^′Γ−1Δ^)−1 where Δ~=∣∂LD^(θ)∂θ′∣θ=θ~ is the matrix of model derivatives evaluated at the parameter estimates , Γ is the naïve Stage 2 weight matrix that takes its form depending on the estimation method used (WLS or ML), and VS is the sampling covariance matrix of S obtained using multivariable LDSC.
