Better Confidence Intervals for RMSEA in Growth Models given Nonnormal Data

Currently, the best confidence interval (CI) for RMSEA in covariance structure analysis given nonnormal data is proposed by Brosseau-Liard, Savalei, and Li (BSL). A key assumption for the BSL CI often overlooked is that all the nonzero eigenvalues are equal in a matrix related to the model and data nonnormality. This assumption rarely holds in practice, especially for mean and covariance structure analysis, and violating this assumption can entail serious mistakes when the model's degrees of freedom are small. One important application of moment structure analysis with small degrees of freedom is growth models. In this paper, we propose a new CI method for RMSEA in growth models given nonnormal data, without assuming equal eigenvalues. Although we focus on growth models, our method applies to any other models in moment structure analysis. Simulation results verify the new method is trustworthy and better than all the current methods.