This dissertation examines the sensitivity of six fit indices in detecting various types of misspecifications in the application of a linear-linear piecewise multilevel latent growth curve model that uses continuous multivariate normal data. The study results show that all fit indices are more sensitive to misspecifications on the within level than those on the between level structure of the model. On the within level, all fit indices are more sensitive to the misspecification in the covariance structure than that in the residual structure; on the between level, all fit indices are more sensitive to the misspecification in the marginal mean structure than that in the covariance structure. Actually, none of the fit indices are practically significantly sensitive to the misspecification in the between-level covariance structure. Partially-saturated estimation method helps NFI, TLI, and Mc to be sensitive to the appropriate sample size when evaluating the misspecification in the between-level covariance structure; however, it helps none of the fit indices when detecting models misspecified in the between-level covariance structure.

All fit indices are principally influenced by the severity of misfit if it happens on the within level; however, they are primarily affected by group size if the misspecification occurs at the between level. When severity level increases, all fit indices have more power to detect misspecification in the within-level covariance structure. When group size increases, NFI, TLI, CFI, Mc, and RMSEA are more likely to commit Type II errors in detecting misspecifications in the marginal mean structure and in both the marginal mean and the covariance structures. Compared with other fit indices, NFI is most vulnerable to sample size and least sensitive to severity level of misfit. SRMR, however, behaves differentially from all other fit indices in that it is most sensitive to the intraclass correlation coefficient when detecting studied misspecifications on the between level structure. Furthermore, the recommended cutoff values lead to high Type II errors for all fit indices in detecting various types of misspecifications, and it is infeasible to find a substitute new set of criteria based on the current data conditions.