论文标题
看似无关的回归和测量误差：通过马尔可夫链蒙特卡洛和平均场变异贝叶斯近似估计
Seemingly Unrelated Regression with Measurement Error: Estimation via Markov chain Monte Carlo and Mean Field Variational Bayes Approximation
论文作者
论文摘要
在协变量中使用测量误差的线性回归是一个经过深入研究的主题，但是，统计/计量经济学文献几乎是静音的，可以估算具有测量误差的多方程模型。本文考虑了一个看似无关的回归模型，该模型在协变量中具有测量误差，并引入了两种新型估计方法：纯贝叶斯算法（基于马尔可夫链蒙特卡洛技术）及其平均场变异贝叶斯（MFVB）近似值。 MFVB方法具有快速计算并可以处理大数据的额外优点。与测量误差模型有关的问题是参数识别，这可以通过在测量误差方差上使用先验分布来解决。这些方法显示在多个仿真研究中表现良好，在该研究中，我们分析了由于可靠性比的不同值或数据生成过程中使用的真实未观察到的数量的不同值而产生的后验估计的影响。本文进一步在从健康文献中汲取的应用程序中实现了所提出的算法，并表明数据中的测量误差可以改善模型拟合。
Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a seemingly unrelated regression model with measurement error in the covariates and introduces two novel estimation methods: a pure Bayesian algorithm (based on Markov chain Monte Carlo techniques) and its mean field variational Bayes (MFVB) approximation. The MFVB method has the added advantage of being computationally fast and can handle big data. An issue pertinent to measurement error models is parameter identification, and this is resolved by employing a prior distribution on the measurement error variance. The methods are shown to perform well in multiple simulation studies, where we analyze the impact on posterior estimates arising due to different values of reliability ratio or variance of the true unobserved quantity used in the data generating process. The paper further implements the proposed algorithms in an application drawn from the health literature and shows that modeling measurement error in the data can improve model fitting.
