Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love
Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love
复制标题
DOI：
10.1198/tast.2010.10052
复制
发表时间：
2010-11-01
影响因子：
1.8
通讯作者：
Reich, Brian J.
中科院分区：
文献类型：
--
作者：
Hodges, James S.;Reich, Brian J.
许多统计学家都有过这样的经历：拟合一个具有不相关误差的线性模型，然后添加一个空间相关误差项（随机效应），结果发现固定效应系数的估计值发生了很大变化。我们表明，在线性模型中添加一个空间相关的误差项相当于添加一个饱和的典型回归量集合，其系数向零收缩，其中空间地图决定了典型回归量和系数收缩的相对程度。添加空间相关的误差项也可以看作是扩大了与数据的特定对比相关的误差方差，其中空间地图决定了对比和误差方差膨胀的程度。我们展示了如何通过将空间随机效应限制到固定效应的正交补（残差空间）来避免这种空间混淆，我们称之为有限空间回归。我们考虑了五种对空间混淆的解释，并得出了关于人们应该做什么的暗示。在这样做的过程中，我们揭穿了一个普遍的信念，即添加一个空间相关的随机效应来调整空间结构缺失协变量的固定效应估计。这篇文章在网上有补充资料。
Many statisticians have had the experience of fitting a linear model with uncorrelated errors, then adding a spatially-correlated error term (random effect) and finding that the estimates of the fixed-effect coefficients have changed substantially. We show that adding a spatially-correlated error term to a linear model is equivalent to adding a saturated collection of canonical regressors, the coefficients of which are shrunk toward zero, where the spatial map determines both the canonical regressors and the relative extent of the coefficients' shrinkage. Adding a spatially-correlated error term can also be seen as inflating the error variances associated with specific contrasts of the data, where the spatial map determines the contrasts and the extent of error-variance inflation. We show how to avoid this spatial confounding by restricting the spatial random effect to the orthogonal complement (residual space) of the fixed effects, which we call restricted spatial regression. We consider five proposed interpretations of spatial confounding and draw implications about what, if anything, one should do about it. in doing so, we debunk the common belief that adding a spatially-correlated random effect adjusts fixed-effect estimates for spatially-structured missing covariates. This article has supplementary material online.