Autoregressive latent trajectory (ALT) models combine features of latent growth curve models and autoregressive models into a single modeling framework. The development of ALT models has focused primarily on models with linear growth components, but some social processes follow nonlinear trajectories. Although it is straightforward to extend ALT models to allow for some forms of nonlinear trajectories, the identification status of such models, approaches to comparing them with alternative models, and the interpretation of parameters have not been systematically assessed. In this paper we focus on two forms of nonlinear autoregressive latent trajectory (NLALT) models. The first form allows for a quadratic growth trajectory, a popular form of nonlinear latent growth curve models. The second form derives from latent basis models, or freed loading models, that allow for arbitrary growth processes. We discuss details concerning parameterization, model identification, estimation, and testing for the two forms of NLALT models. We include a simulation study that illustrates potential biases that may arise from fitting alternative models to data derived from an autoregressive process and individual-specific nonlinear trajectories. In addition, we include an extended empirical example modeling growth trajectories of weight from birth through age 2.

中文翻译：

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非线性自回归潜在轨迹模型

自回归潜在轨迹 (ALT) 模型将潜在增长曲线模型和自回归模型的特征结合到单个建模框架中。ALT 模型的开发主要集中在具有线性增长组件的模型上，但一些社会过程遵循非线性轨迹。尽管扩展 ALT 模型以允许某些形式的非线性轨迹很简单，但尚未系统评估此类模型的识别状态、将它们与替代模型进行比较的方法以及参数的解释。在本文中，我们关注两种形式的非线性自回归潜在轨迹 (NLALT) 模型。第一种形式允许二次增长轨迹，这是非线性潜在增长曲线模型的流行形式。第二种形式来自潜在的基础模型，或释放加载模型，允许任意增长过程。我们讨论了有关两种形式的 NLALT 模型的参数化、模型识别、估计和测试的详细信息。我们包括一项模拟研究，该研究说明了将替代模型拟合到自回归过程和个体特定非线性轨迹得出的数据时可能产生的潜在偏差。此外，我们还包括一个扩展的经验示例，对从出生到 2 岁的体重增长轨迹进行建模。我们包括一项模拟研究，该研究说明了将替代模型拟合到自回归过程和个体特定非线性轨迹得出的数据时可能产生的潜在偏差。此外，我们还包括一个扩展的经验示例，用于模拟从出生到 2 岁的体重增长轨迹。我们包括一项模拟研究，该研究说明了将替代模型拟合到自回归过程和个体特定非线性轨迹得出的数据时可能产生的潜在偏差。此外，我们还包括一个扩展的经验示例，用于模拟从出生到 2 岁的体重增长轨迹。