Equivalent models in the context of latent curve analysis

An equivalent model found in an application of Structural Equation Modeling (SEM) can provide an alternative substantive interpretation of the given model yet be indistinguishable in terms of overall model fit. It is possible for Latent Curve Models (LCMs) to possess a series of such equivalent models, as these models are a type of SEM. However, this issue of equivalent models has not been addressed within this modeling context. In this thesis, the issue of equivalent models as manifested in a common set of LCMs is analytically and empirically investigated. Overall results indicate that previous rules for equivalent models extend to the LCM framework. Analytical results reveal exact transformations of parameters between equivalent models, extending the analytical rules defined by Raykov and Penev. A method for obtaining transformations for standard errors is introduced and such transformations are calculated for a common set of LCMs. Empirical results illustrate the consequences of specifying an equivalent model using real data. Circumstances which result in different substantive interpretations among equivalent models are discussed. Specifically, circumstances under which differences in parameter estimates, standard errors, and ultimate significance levels between equivalent models are large are considered. Recommendations for how best to manage equivalent models in LCMs are discussed