Optimal study design with identical power: an application of power equivalence to latent growth curve models

Structural equation models have become a broadly applied data-analytic framework. Among them, latent growth curve models have become a standard method in longitudinal research. However, researchers often rely solely on rules of thumb about statistical power in their study designs. The theory of power equivalence provides an analytical answer to the question of how design factors, for example, the number of observed indicators and the number of time points assessed in repeated measures, trade off against each other while holding the power for likelihood-ratio tests on the latent structure constant. In this article, we present applications of power-equivalent transformations on a model with data from a previously published study on cognitive aging, and highlight consequences of participant attrition on power.