COMPUTATION OF MAXIMUM LIKELIHOOD ESTIMATES IN CYCLIC STRUCTURAL EQUATION MODELS

• 成果类型: Article
• 署名作者: Drton, Mathias; Fox, Christopher; Wang, Y. Samuel
• 署名单位: University of Washington; University of Washington Seattle; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1602
• 发表日期: 2019
• 页码: 663-690
• 关键词: package; matrix

摘要

Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from nonlinear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is often required to avoid convergence issues. As an alternative approach, we propose a block-coordinate descent method that cycles through the considered variables, updating only the parameters related to a given variable in each step. We show that the resulting block update problems can be solved in closed form even when the structural equation model comprises feedback cycles. Furthermore, we give a characterization of the models for which the block-coordinate descent algorithm is well defined, meaning that for generic data and starting values all block optimization problems admit a unique solution. For the characterization, we represent each model by its mixed graph (also known as path diagram), which leads to criteria that can be checked in time that is polynomial in the number of considered variables.