The Construction of a Growth Model with Residual Structure Equation Modeling: An Example Analysis

The present study employs simulation to demonstrate that, in conducting growth model analyses, it is essential not only to specify a growth model at the between-individual but also to estimate the within-individual residual structure using residual structure equation modeling. This approach serves to mitigate any potential biases in parameter estimates that may arise from assuming residual independence, particularly in the variances of random intercept and random slope, as well as the covariance between random intercept and slope. The study also demonstrates that in the absence of time-related covariance among residuals at the within-individual, the incorporation of a residual structure equation model into a growth model does not result in biased parameter estimates. It is therefore recommended that applied researchers give priority to growth model specifications that include residual structure equation modeling in order to obtain unbiased parameter estimates.