A Cautionary Note on Identification and Scaling Issues in Second-order Latent Growth Models

The second-order latent growth models (2(nd)-order LGMs) have been recommended to analyze longitudinal data when latent constructs are measured by multiple indicators. However, identification and scaling issues in 2(nd)-order LGMs have not been well understood. Using both formulas and a numerical example, we show that under strong longitudinal factor invariance estimates of growth parameters in 2(nd)-order LGMs depend on how the latent factor is scaled. With the marker-variable identification method, estimates of growth parameters depend on the choice of marker variable and the constants applied to its loading and intercept. With the effect-coding identification method, three sets of constraints applied to loadings and intercepts lead to meaningful interpretation of growth trajectories. When the latent factor at the reference time point is standardized, estimates of growth parameters are unique. We suggest users explicitly state the identification and scaling method in interpreting estimated growth parameters when a 2(nd)-order LGM is applied.