一种收敛且解唯一的SEM算法.pdfVIP

Pure Mathematics 理论数学, 2016, 6(1), 1-9 Published Online January 2016 in Hans. /journal/pm /10.12677/pm.2016.61001 An Algorithm of Structural Equation Model with Convergence and Unique Solution * Qian Liu, Shengshuang Chen , Hengqing Tong Department of Mathematics, College of Science, Wuhan University of Technology, Wuhan Hubei nd th th Received: Nov. 2 , 2015; accepted: Jan. 14 , 2016; published: Jan. 20 , 2016 Copyright © 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract The algorithm of structural equation model, partial least squares (PLS), has been widely applied to solve indefinite equations. But the iterative algorithm may have the problem of non-convergent and non-unique. In this paper, we propose an optimized algorithm based on the unit modular length constraint of latent variables and the prescription constraint of path coefficients. Simulta- neously, we prove the convergence of the algorithm and take a set of data to validate the unique- ness of the solution. Keywords Unit Modular Length Constraint, Prescription Constraint, Convergence, Uniqueness 一种收敛且解唯一的SEM算法 * 刘 倩，陈盛双 ，童恒庆 武汉理工大学理学院数学系，湖北 武汉 收稿日期：2015年11月2 日；录用日期：2016年1月14 日；发布日期：2016年1月20 日 *通讯作者。 文章引用: 刘倩, 陈盛双, 童恒庆. 一种收敛且解唯一的SEM 算法[J]. 理论数学, 2016, 6(1): 1-9. /10.12677/pm.2016.61001 刘倩 等 摘 要 结构方程模型的PLS算法已广泛应用于求解不定方程组，但这种迭代算法可能存在着不收敛或者解不唯 一的问题。本文基于对潜变量进行单位模长约束和对路径系数进行配方约束改进原有算法，由此提出一 种收敛且解唯一的优化算法，并证明该算法的收敛性以及利用一组算例对解的唯一性进行说明。 关键词 单位模长约束，配方约束，收敛性，唯一性 1.