ABSTRACT Change over time is frequently nonlinear, which can present unique statistical challenges. Generally, different approaches for nonlinear growth engage in a tradeoff between interpretable parameters, expedient estimation, or how specific the model must be about the nature of the nonlinearity. Latent basis models are one method that can circumvent tradeoffs that other methods necessitate: it is quick to estimate, simple to interpret, and does not require specification of a particular trajectory. However, latent basis models require a restrictive proportionality assumption that is not required with other methods, which can limit its applicability with empirical data. This paper discusses this proportionality assumption and shows how it can be relaxed by reparameterizing the latent basis model as a multilevel structural equation model. We provide an example to show how relaxing proportionality can improve parameter estimates and person-specific growth curves. We also walkthrough Mplus code to facilitate fitting the model to empirical data.

中文翻译：

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放宽非线性增长的潜在基础模型中的比例假设

摘要随时间的变化通常是非线性的，这可能会带来独特的统计挑战。通常，非线性增长的不同方法会在可解释参数、权宜估计或模型对非线性性质的具体程度之间进行权衡。潜在基础模型是一种可以规避其他方法所必需的权衡的方法：估计速度快，解释简单，并且不需要指定特定轨迹。但是，潜在基础模型需要其他方法不需要的限制性比例假设，这可能会限制其对经验数据的适用性。本文讨论了这种比例假设，并展示了如何通过将潜在基础模型重新参数化为多级结构方程模型来放松它。我们提供了一个示例来展示放宽比例如何改善参数估计和特定于个人的增长曲线。我们还演练了 Mplus 代码，以方便将模型拟合到经验数据。