A Two Stage Quasi-Likelihood Estimation Method for High Dimensional Generalized Structural Equation Models
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.