We propose a new estimation method for the Stable Trait, Auto Regressive Trait, and State (STARTS) model, which is well known for its frequent occurrence of improper solutions. The proposed approach is implemented through a two-stage estimation procedure that combines matrix decomposition factor analysis (MDFA) based on eigenvalue decomposition with conventional SEM estimation principles. By reformulating the STARTS model within a factor-analytic framework, this study presents a novel way of applying MDFA in the context of structural equation modeling (SEM). Through a simulation study and an empirical application to ToKyo Teen Cohort data, the proposed method was shown to entail a substantially lower risk of improper solutions than commonly used maximum likelihood, conditional ML, and (unweighted) least squares estimators, while tending to yield solutions similar to those obtained by ML. Compared with Bayesian estimation, the proposed method does not require the specification of appropriate (weakly informative) prior distributions and may effectively mitigate bias issues that arise when the number of time points is small. Applying the proposed method, as well as conducting sensitivity analyses informed by it, will enable researchers to more effectively delineate the range of plausible conclusions from data in estimating the STARTS model and other SEMs.

翻译：我们针对稳定特质、自回归特质与状态（STARTS）模型提出了一种新的估计方法，该模型因频繁出现非恰当解而广为人知。所提出的方法通过两阶段估计程序实现，该程序结合了基于特征值分解的矩阵分解因子分析（MDFA）与传统的结构方程模型（SEM）估计原理。通过将STARTS模型在因子分析框架内重新表述，本研究提出了一种在结构方程建模（SEM）背景下应用MDFA的新颖方式。通过模拟研究以及对东京青少年队列数据的实证应用，结果表明，与常用的最大似然法、条件ML法以及（未加权）最小二乘估计法相比，所提方法产生非恰当解的风险显著降低，同时倾向于得到与ML法相似的解。与贝叶斯估计相比，所提方法无需设定恰当的（弱信息）先验分布，并且可以有效缓解时间点数较少时出现的偏差问题。应用所提方法以及基于此进行的敏感性分析，将使研究人员在估计STARTS模型及其他SEM模型时，能够更有效地从数据中界定合理结论的范围。