AI 中文总结
针对高维广义结构方程模型估计的计算挑战，提出两阶段拟似然期望最大化框架，分离结构与测量模型，可缩短运行时间、提升数值稳定性并降低误差，为复杂潜变量模型分析提供灵活可扩展的方案。
AI 中文摘要
估计高维广义结构方程模型面临严峻的计算挑战，传统的同时估计器常存在数值不稳定性和过高的计算成本，且对于泊松、负二项分布、伽马分布等分布族尚无易处理的算法。为克服这些局限，本文提出一种两阶段拟似然期望最大化（Two Stage Quasi-Likelihood Expectation-Maximization）框架，该方法将结构模型与测量模型分离：首先近似潜变量在观测指标下的条件分布；其次采用边际拟似然估计方程评估结构参数，通过精确计算或蒙特卡洛积分推导所需的条件矩，完全避免了对全联合似然的评估。大量模拟实验表明，该方法大幅缩短了计算运行时间，提供了数值稳定的框架，可最小化均方误差和结构偏差，为分析复杂潜变量模型提供了可扩展且灵活的解决方案。
英文摘要
Estimating high dimensional Generalized Structural Equation Models presents severe computational challenges. Traditional simultaneous estimators frequently suffer from numerical instability and prohibitive computational costs. Moreover, there are no tractable algorithms for families such as Poisson, negative binomial, and gamma. To overcome these limitations, this article introduces a Two Stage Quasi-Likelihood Expectation-Maximization framework. The proposed method isolates the structural model from the measurement model. First, it approximates the conditional distribution of the latent variables given the observed indicators. Second, it employs marginal quasi-likelihood estimating equations to evaluate the structural parameters, deriving the necessary conditional moments either exactly or through Monte Carlo integration. This approach completely avoids the need to evaluate the full joint likelihood. Extensive simulations demonstrate that our method drastically reduces computational runtime, providing a numerically stable framework that minimizes the mean squared error and structural bias to yield a scalable and flexible solution for analyzing complex latent variable models.
Comments26 pages, 1 table, 1 figure
