Standardized Estimates of Second-Order Latent Growth Models: A Comparison of Alternative Latent-Standardization Methods

Second-order latent growth models (LGMs) have garnered considerable attention and are increasingly utilized in longitudinal data analyses of latent constructs comprised of multiple items. The growth parameter estimates in these models are intrinsically linked to the model identification methods. Latent-standardization (identification) methods, in which the latent variable is standardized at a reference time point (e.g., eta-1), yield theoretically unique and interpretable growth parameters. Traditional latent-standardization methods indirectly standardize eta-1 via the first-order component of the second-order LGM by constraining item intercepts and/or loadings. Such methods require a two-step modeling procedure and do not truly standardize eta-1. This article proposes a 1-stage method that indirectly standardizes eta-1 through the second-order component of the model by constraining the mean and variance of the level factor. This new single-step modeling method ensures eta-1 is truly standardized, with a mean of 0 and a variance of 1. Theoretical, simulated, and empirical comparisons are conducted across different latent-standardization methods, demonstrating the target accuracy and implementation simplicity of the proposed 1-stage method.