Linear Recursive Equations, Covariance Selection, and Path Analysis
通过定义可约零模式并利用乘法模型，将计量经济学家Wold的线性递归方程和遗传学家Wright的路径分析与Dempster的协方差选择统计理论联系起来，证明可约零模式是递归方程参数与可分解协方差选择模型参数一一对应的条件，并由此给出可分解协方差矩阵的最大似然估计闭式表达式、推导路径分析中隐含相关性的Wright规则，以及描述拟合递归方程的搜索过程。
Abstract By defining a reducible zero pattern and by using the concept of multiplicative models, we relate linear recursive equations that have been introduced by econometrician Herman Wold (1954) and path analysis as it was proposed by geneticist Sewall Wright (1923) to the statistical theory of covariance selection formulated by Arthur Dempster (1972). We show that a reducible zero pattern is the condition under which parameters as well as least squares estimates in recursive equations are one-to-one transformations of parameters and of maximum likelihood estimates, respectively, in a decomposable covariance selection model. As a consequence, (a) we can give a closed-form expression for the maximum likelihood estimate of a decomposable covariance matrix, (b) we can derive Wright's rule for computing implied correlations in path analysis, and (c) we can describe a search procedure for fitting recursive equations.