The effect of multiple indicators on the power to detect inter-individual differences in change

Hertzog et al. evaluated the statistical power of linear latent growth curve models (LGCMs) to detect individual differences in change, i.e., variances of latent slopes, as a function of sample size, number of longitudinal measurement occasions, and growth curve reliability. We extend this work by investigating the effect of the number of indicators per measurement occasion on power. We analytically demonstrate that the positive effect of multiple indicators on statistical power is inversely related to the relative magnitude of occasion-specific latent residual variance and is independent of the specific model that constitutes the observed variables, in particular of other parameters in the LGCM. When designing a study, researchers have to consider trade-offs of costs and benefits of different design features. We demonstrate how knowledge about power equivalent transformations between indicator measurement designs allows researchers to identify the most cost-efficient research design for detecting parameters of interest. Finally, we integrate different formal results to exhibit the trade-off between the number of measurement occasions and number of indicators per occasion for constant power in LGCMs.