For each condition of latent correlation, number of items, and variance of the latent variable, we simulated 100,000 twin pairs and correlated their sum scores. Figure 1A shows the result for the condition where the variance was 1 and the items were nicely scattered across the distribution of the latent values, between −2½ and 2½ times the standard deviation (1). The attenuation effect is clearly dependent on the number of items: with 100 items, the correlation on the basis of the sum scores is very close to the true correlations. An analysis treating the sum scores as bivariately normal and applying a variance decomposition will approximate the true proportions. Moreover, the degree of the attenuation is proportional to the true correlation: with 5 items, a true correlation of 0.9 will be attenuated to a correlation of 0.55 (61%) and a true correlation of 0.1 will be attenuated to a correlation of 0.06 (60%). Therefore, when the analysis on 5 items is based on the sum score, and the true MZ correlation equals twice the DZ correlation, this ratio is maintained
