小样本数据潜变量建模:贝叶斯估计的应用

Latent Variable Modeling with Small Sample Data: The Application of Bayesian Estimation

旨在通过一项基于计划行为理论的锻炼行为实证研究案例,说明贝叶斯结构方程模型如何应对小样本数据。贝叶斯方法之所以适用于小样本数据主要因为:贝叶斯方法不依赖大样本理论且允许估计测量模型中所有可能的残差协方差,经典统计方法中这些均无法实现;借助贝叶斯定理,采用信息先验的贝叶斯估计允许将先前研究的结果与当前研究进行整合,从而使假设获得检验的机会,这也是经典统计方法无法实现的。与最大似然估计相比,贝叶斯估计有助于降低对样本量的要求、避免不适当解、更好地反映研究者的理论构想和先验信念、促进科学知识的积累。然而,贝叶斯估计并非万能,必须确保合理、透明地使用先验信息。

The aim is to provide an empirical example of physical exercise based on the theory of planned behavior to show how Bayesian structural equation model analysis small sample data.Bayesian approach can be used with small sample sizes since they do not rely on large sample theory and allows estimating all possible residual covariance in measurement model,neither of which are possible with frequentist methods;and Bayesian estimation with informative priors allows results from all previous research to be combined with estimates of study effects using Bayes'theorem,yielding support for hypotheses that is not obtained with frequentist methods.Compared with maximum likelihood estimation,Bayesian estimation might help to eliminate the worry about small sample sizes and the inadmissible parameters,better reflects the researcher's theories and prior beliefs,and create cumulative knowledge.Nonetheless,Bayesian estimation is not a panacea,it is absolutely necessary to be transparent with regard to which priors were used and why.