Sum scores calculated across all m phenotypes are only sufficient statistics (exhaustively summarizing all information available in the individual phenotypes) if a) all correlations between the phenotypes are explained by 1 latent factor, b) all phenotypes have identical factor loadings, and c) all phenotypes have identical residual variances [6] (a so-called Rasch model [32]). In the case of 1 factor models (Figure 1a and 1e), we thus chose to simulate phenotypic data according to Rasch models, as this represents the most favorable condition for the univariate sum score method. Factor loadings ranged between .75 (corresponding to .752 = .56% explained variance by the factor, and 1−.752 = .4375% residual variance; A2, E1 in Figure 1g), .55 (.30% explained; E2) and .35 (.12% explained; A3, E3). With these settings, intercorrelations between all m phenotypes are .56, .30, or .12, respectively. The GV effect was then either modeled on the factor (Figure 1a; Figure 1g A1–A3), affecting via the factor all phenotypes defining the factor (in which case the GV effect is weighted by the factor loadings; the lower the factor loading,
