Fit Indices for Mean Structures With Growth Curve Models

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.