Can We Distinguish between Different Longitudinal Models for Estimating Nonlinear Trajectories?

Substantive theory rarely provides specific enough information to guide our selection of the optimal model for longitudinal data. Instead, researchers are more likely to rely on models common to their field, even if they are not appropriate. The purpose of our study is to assess whether researchers can use overall goodness-of-fit measures from structural equation models to correctly find the data generating model (DGM) from among a broad set of different longitudinal models. We use four different DGM adapted from published empirical studies. We compare goodness-of-fit statistics (e.g., p-value, CFI, RMSEA, etc.) of the DGM with those of six alternative models. Overall, the Bayesian Information Criterion (BIC) performed best in selecting the DGM, though no fit statistic was flawless. In the absence of substantive theory, we recommend that researchers begin with the most general longitudinal model and test whether it can be simplified by eliminating parameters.