On occasion, summary statistics will be provided from OLS GWASs of categorical outcomes (e.g., case/control status). Such an analysis is sometimes referred to as a linear probability model, as it (incorrectly) assumes that the association between the predictor and the probability of being in the comparison (e.g. case) group relative to the reference (e.g. control) group is linear. Parameters from the linear probability model are dependent not only on the strength of the association between the SNP and the continuous underlying liability, but also on the MAF and the proportion of comparison group members (cases) in the sample. Thus, parameters from the linear probability model cannot be used directly in Genomic SEM. However, particularly in the case of complex traits, for which the effect sizes for individual SNPs are small, results from the linear probability model can be used to very closely approximate logistic regression coefficients and SEs that are amenable for use in Genomic SEM.49 This approximation can be obtained as Z=bSNP,P∗∗SEbSNP,P∗∗, blogitSNP,P∗=Zν(1−ν)NσSNP2, and SEbSNP,P=blogitSNP,P∗Z, where bSNP,P∗∗ is equal to the regression coefficient from the linear probability model, blogitSNP,P∗
