Sum Scores in Twin Growth Curve Models: Practicality Versus Bias

To study behavioral or psychiatric phenotypes, multiple indices of the behavior or disorder are often collected that are thought to best reflect the phenotype. Combining these items into a single score (e.g. a sum score) is a simple and practical approach for modeling such data, but this simplicity can come at a cost in longitudinal studies, where the relevance of individual items often changes as a function of age. Such changes violate the assumptions of longitudinal measurement invariance (MI), and this violation has the potential to obfuscate the interpretation of the results of latent growth models fit to sum scores. The objectives of this study are (1) to investigate the extent to which violations of longitudinal MI lead to bias in parameter estimates of the average growth curve trajectory, and (2) whether absence of MI affects estimates of the heritability of these growth curve parameters. To this end, we analytically derive the bias in the estimated means and variances of the latent growth factors fit to sum scores when the assumption of longitudinal MI is violated. This bias is further quantified via Monte Carlo simulation, and is illustrated in an empirical analysis of aggression in children aged 3-12 years. These analyses show that measurement non-invariance across age can indeed bias growth curve mean and variance estimates, and our quantification of this bias permits researchers to weigh the costs of using a simple sum score in longitudinal studies. Simulation results indicate that the genetic variance decomposition of growth factors is, however, not biased due to measurement non-invariance across age, provided the phenotype is measurement invariant across birth-order and zygosity in twins.