In recent years, longitudinal data have become increasingly relevant in many applications, heightening interest in selecting the best longitudinal model to analyze them. Too often, traditional practice rather than substantive theory guides the specific model selected. This opens the possibility that alternative models might better correspond to the data. In this paper, we present a general longitudinal model that we call the Latent Variable-Autoregressive Latent Trajectory (LV-ALT) model that includes most other longitudinal models with continuous outcomes as special cases. It is capable of specializing to most models dictated by theory or prior research while having the capacity to compare them to alternative ones. If there is little guidance on the best model, the LV-ALT provides a way to determine the appropriate empirical match to the data. We present the model, discuss its identification and estimation, and illustrate how the LV-ALT reveals new things about a widely used empirical example.

中文翻译：

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潜在变量-自回归潜在轨迹模型：纵向数据分析的通用框架

近年来，纵向数据在许多应用中变得越来越重要，人们对选择最佳纵向模型进行分析的兴趣日益浓厚。很多时候，传统实践而不是实质性理论指导选择的特定模型。这开启了替代模型可能更好地对应数据的可能性。在本文中，我们提出了一个通用的纵向模型，我们称之为潜在变量-自回归潜在轨迹 (LV-ALT) 模型，其中包括大多数其他具有连续结果的纵向模型作为特殊情况。它能够专门研究由理论或先前研究决定的大多数模型，同时能够将它们与替代模型进行比较。如果对最佳模型几乎没有指导，LV-ALT 提供了一种方法来确定与数据的适当经验匹配。