Fit criteria for heterogenous growth curve models and related nonlinear models

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Latent growth curve modeling (LGM) is a technique used to identify the developmental trajectories of individuals over a period of time. An extension of a conventional LGM is the heterogenous growth curve model (HGM), which permits a modeling of the growth trajectory that flexibly depends on the individual initial status. In particular, the HGMs are able to represent the directedness of individual growth trajectories over time. Whereas the goodness of fit of a conventional LGM is usually evaluated by a chi-square test, descriptive fit indices, or concordance coefficients, there exist no adequate model fit criteria for heterogenous LGMs. Because of this, we aim at developing a goodness of fit test for HGM. The main objectives are (1) new development and testing of an overall model fit for a HGM based on a quasi-maximum likelihood approach, (2) modification of these tests to devise descriptive fit measures for HGMs and other types of nonlinear models, (3) evaluation of the tests and model fit criteria using Monte Carlo studies as well as empirical data, and (4) the implementation of the new measures in appropriate software.