斜交双因子模型的收敛性和参数估计的准确性

The Convergence and Parameter Estimation Accuracy of the Oblique Two-Factor Model

摘要: 本文研究了斜交双因子模型的性质，重点探讨了提升参数估计准确性的方法。通过比较极大似然法与贝叶斯法在估计斜交双因子模型时的表现，分析了贝叶斯法对先验分布误差的鲁棒性，并考察了不同先验分布对贝叶斯法估计有效性的影响。研究发现，1) 引入先验信息的贝叶斯法能够显著提升模型的收敛性和参数估计的准确性；2) 即使先验分布存在一定程度的误差或不完全精确，贝叶斯法仍能够较好地估计斜交双因子模型。基于此，本文建议在斜交双因子模型的估计过程中，采用带有先验信息的贝叶斯法，并利用变量间的皮尔逊相关系数作为先验分布的均值，从而提升模型的准确性和稳健性。

Abstract: This study investigates the properties of the oblique two-factor model, focusing on methods to improve parameter estimation accuracy. By comparing the performance of Maximum Likelihood (ML) estimation and Bayesian estimation in estimating the oblique two-factor model, the robustness of Bayesian estimation to prior distribution errors is analyzed, and the impact of different prior distributions on the effectiveness of Bayesian estimation is examined. The study finds that: 1) Bayesian estimation with informative priors significantly improves the model’s convergence rate and parameter estimation accuracy; 2) Even when the prior distribution contains some degree of error or is not perfectly accurate, Bayesian estimation still provides reliable estimates for the oblique two-factor model. Based on these findings, the study recommends using Bayesian estimation with informative priors in the estimation of the oblique two-factor model, with the Pearson correlation between variables serving as the mean of the prior distribution, in order to enhance the model’s accuracy and robustness.