Leibniz Institute for Science and Mathematics Education, Kiel, Germany.
Centre for International Student Assessment, Germany.
Multivariate Behav Res. 2023 May-Jun;58(3):560-579. doi: 10.1080/00273171.2022.2039585. Epub 2022 Mar 16.
The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model provides a general approach for estimating reciprocal effects between constructs over time. However, previous research has shown that this model is difficult to estimate using the maximum likelihood (ML) method (e.g., nonconvergence). In this article, we introduce a Bayesian approach for estimating the bivariate STARTS model and implement it in the software Stan. We discuss issues of model parameterization and show how appropriate prior distributions for model parameters can be selected. Specifically, we propose the four-parameter beta distribution as a flexible prior distribution for the autoregressive and cross-lagged effects. Using a simulation study, we show that the proposed Bayesian approach provides more accurate estimates than ML estimation in challenging data constellations. An example is presented to illustrate how the Bayesian approach can be used to stabilize the parameter estimates of the bivariate STARTS model.
双变量稳定特质-自回归特质-状态（STARTS）模型为估计随时间推移的结构之间的相互影响提供了一种通用方法。然而，先前的研究表明，使用最大似然（ML）方法很难估计这种模型（例如，不收敛）。在本文中，我们介绍了一种用于估计双变量 STARTS 模型的贝叶斯方法，并在 Stan 软件中实现了它。我们讨论了模型参数化的问题，并展示了如何选择模型参数的适当先验分布。具体来说，我们提出了四参数 beta 分布作为自回归和交叉滞后效应的灵活先验分布。通过模拟研究，我们表明，在具有挑战性的数据结构中，所提出的贝叶斯方法比 ML 估计提供了更准确的估计。通过一个示例来说明如何使用贝叶斯方法来稳定双变量 STARTS 模型的参数估计。
