AI 中文总结
本研究针对传统结构方程模型树存在的不当解多、计算成本高的问题，开发了矩阵分解潜在增长模型树，模拟显示其能减少不当解发生且计算效率高。
AI 中文摘要
潜在增长模型（LGMs）已被广泛用于描述个体变化轨迹、群体内的平均变化模式以及变化的个体差异。结构方程模型树（SEM Tree）通过使用外部协变量进行递归划分来划分样本，并通过预先指定的SEM模板模型的参数来表征组间差异。因此，以LGM作为模板模型的SEM Tree可作为纵向数据的有用分类方法。然而，当前的SEM Tree实现可能面临重要的实际障碍，包括高计算成本以及因模型误设或数据特征（如测量次数有限）导致的频繁不当解。在本研究中，我们开发了矩阵分解潜在增长模型树（MDLGM Tree），其应用了矩阵分解因子分析（MDFA）方法，这是一种基于特征值分解的模型估计方法。先前关于MDFA及其向SEM扩展的研究表明，该方法可降低不当解的风险，同时产生与最大似然估计所得估计值高度相似的结果。通过一系列模拟，我们证明，与传统SEM Tree相比，MDLGM Tree大幅减少了不当解的发生，且在计算时间方面也具有很高的效率。
英文摘要
Latent growth models (LGMs) have been widely used to describe individual trajectories of change, average change patterns, and individual differences in change within a group. Structural equation model tree (SEM Tree) partitions samples through recursive partitioning using external covariates and characterizes between-group differences via parameters of prespecified SEM template models. An SEM Tree with an LGM as its template model may therefore serve as a useful classification method for longitudinal data. However, current SEM Tree implementations may face important practical obstacles, including high computational cost and frequent improper solutions caused by model misspecification or data characteristics (e.g., a limited number of measurement occasions). In the present study, we developed a matrix decomposition LGM tree (MDLGM Tree), which applies the matrix decomposition factor analysis (MDFA) approach, an eigenvalue-decomposition-based method for model estimation. Previous studies on MDFA and its extensions to SEM have shown that this approach can reduce the risk of improper solutions while yielding estimates highly similar to those obtained by maximum likelihood estimation. Through a series of simulations, we demonstrated that, compared with conventional SEM Tree, the MDLGM Tree greatly reduces the occurrence of improper solutions and is also highly efficient in terms of computation time.
Comments95 pages, 50 figures
