Fit Indices for Mean Structures With Growth Curve Models

Abstract Motivated by the need to effectively evaluate the quality of the mean structure in growth curve modeling (GCM), this article proposes to separately evaluate the goodness of fit of the mean structure from that of the covariance structure. Several fit indices are defined, and rationales are discussed. Particular considerations are given for polynomial and piecewise polynomial models because fit indices for them are valid regardless of the underlying population distribution of the data. Examples indicate that the newly defined fit indices remove the confounding issues with indices jointly evaluating mean and covariance structure models and provide much more reliable evaluation of the mean structure in GCM. Examples also show that pseudo R-squares and concordance correlations are unable to reflect the goodness of mean structures in GCM. Proper use of the fit indices for the purpose of model diagnostics is discussed. A window-based program, WebSEM, is also introduced for easily computing these fit indices by applied researchers. Translational Abstract Growth curve modeling (GCM) is an important tool for studying intraindividual change and interindividual variation in growth trajectories. In particular, the method enables researchers to model the change in growth trajectories using background variables. The success of GCM depends on two components: mean structure and variance-covariance structure. However, existing methods do not distinguish the goodness of fit of the two components. In particular, a well-fitted covariance structure can easily mask a poorly specified mean structure when the two components are jointly evaluated, although the primary interest in GCM is the growth trajectories or mean change. By separately evaluating the two components, this article develops fit indices to more effectively evaluate the quality of the mean structure. The developed fit indices are parallel to widely used fit indices for evaluating covariance structure models. They are also robust to distribution violations when evaluating the mean structures of polynomial and piecewise polynomial growth curve models. Examples, analyses and Monte Carlo results endorse the new fit indices, which can be easily computed by a window-based online program WebSEM (https://websem.psychstat.org/).