Further simulations were carried out to illustrate the attenuation effect and the bias in variance components. For simple genetic models, the twin correlations are sufficient statistics for the variance decomposition. Therefore it is enough to show how correlations based on sum scores behave as a function of number of items and beta parameters. Data were simulated using bivariate normally distributed latent values, with correlations 0.9, 0.7, 0.5, 0.3 and 0.1. These latent values were used to simulate corresponding sum scores using a one-parameter logistic IRT measurement model under a variety of conditions. First of all, we used different degrees of discrimination of the items (i.e., the variance of the latent trait: 0.676, 1 and 100). Second, we varied the way in which the items are distributed across the scale, either evenly scattered so that sum score distributions are symmetrical, or only scattered on the upper half part of the scale, that is, using only items that less than 50% of the population endorses, which results in positively skewed sum score distributions (cf. Derks et al. 2004; van den Oord et al. 2003). Third, we varied the number of items (5, 10, 20, 50, 100) to investigate attenuation.
