Fit criteria for heterogenous growth curve models and related nonlinear models

潜在生长曲线建模(LGM)是一种用于识别个体在一段时间内的发展轨迹的技术。非均质增长曲线模型(HGM)是传统增长曲线模型的一个扩展，它允许对增长轨迹进行建模，该轨迹灵活地依赖于个体的初始状态。特别是，HGM能够代表随着时间的推移个人增长轨迹的方向性。传统LGM的拟合优度通常是通过卡方检验、描述性拟合指数或协调系数来评估的，但对于异质LGM来说，并没有合适的模型拟合标准。正因为如此，我们的目标是开发一种HGM的拟合优度测试。主要目标是：(1)以准最大似然法为基础，新开发和测试适合于高精度气候变化的总体模型；(2)对这些测试进行修改，以设计出适用于高精度气候变化模型和其他类型的非线性模型的描述性拟合措施；(3)利用蒙特卡罗研究和经验数据对测试和模型拟合标准进行评估；以及(4)在适当的软件中实施新措施。

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.