结构方程模型的预测建模方法

提出一种结构方程模型的动态预测建模方法,从而可以在无须未来样本数据的情况下,预测系统要素之间未来的因果关系。采用矩阵谱分解,将协方差矩阵唯一分解为特征值矩阵和特征向量矩阵乘积的形式.分别应用经典的线性回归方法和高维群点主轴旋转预测方法对特征值矩阵和特征向量矩阵建立预测模型,提出一种协方差矩阵的后推预测算法.采用极大似然法,迭代估计未来结构方程模型的各种参数.仿真实验例示了该方法的主要计算步骤.计算结果显示,利用本模型得到的拟合值精度较高,预测模型真实可信,表明这种方法可以用于分析和预测结构方程模型.

Forecast modeling for structural equation model

Based on the historical data,a forecast modeling method for structural equation model was discussed,where the future relationship between the system factors was described without future sample.By applying spectra of matrix,the covariance matrix was decomposed of eigenvectors and eigenvalues. Typical linear regression method was adopted to predict eigenvalues,and predictive method of orthonomal matrix based on rotations of principal axes was adopted to predict eigenvector matrix,so it structured a forecast method of covariance matrix.The maximum likelihood method was applied to estimate the parameters of future structural equation model.The experimental simulation illustrated main computational procedures of the predictive model.The results show a high precise of the predictive values.The agreement of the final computation results with the experimental data indicates this method could be used to analyze and forecast structural equation model.