Detecting Growth Shape Misspecifications in Latent Growth Models: An Evaluation of Fit Indexes

In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification when a linear model was fit to scores presenting nonlinear growth trajectories, in terms of being sensitive to severity of misspecification, and providing stable results with different types of nonlinearity and sample sizes.