Abstract

Spatial confounding, that is, collinearity between fixed effects and random effects in a spatial generalized linear mixed model, can adversely affect estimates of the fixed effects. Restricted spatial regression methods have been proposed as a remedy for spatial confounding. Such methods replace inference for the fixed effects of the original model with inference for those effects under a model in which the random effects are restricted to a subspace orthogonal to the column space of the fixed effects model matrix; thus, they “deconfound” the two types of effects. We prove, however, that frequentist inference for the fixed effects of a deconfounded linear model is generally inferior to that for the fixed effects of the original spatial linear model; in fact, it is even inferior to inference for the corresponding nonspatial model. We show further that deconfounding also leads to inferior predictive inferences, though its impact on prediction appears to be relatively small in practice. Based on these results, we argue that deconfounding a spatial linear model is bad statistical practice and should be avoided.

摘要

空间混杂，即空间广义线性混合模型中固定效应和随机效应之间的共线性，会对固定效应的估计产生不利影响。已提出限制空间回归方法作为空间混杂的补救措施。此类方法将原始模型的固定效应的推断替换为对模型下的那些效应的推断，其中随机效应被限制在与固定效应模型矩阵的列空间正交的子空间中；因此，他们“消除了”这两种影响。然而，我们证明，对去混杂线性模型的固定效应的频率论推断通常不如对原始空间线性模型的固定效应的推断；事实上，它甚至不如相应的非空间模型的推理。我们进一步表明，去混杂也会导致较差的预测推断，尽管它对预测的影响在实践中似乎相对较小。基于这些结果，我们认为对空间线性模型进行去混杂是不好的统计实践，应该避免。