Random walks, intrinsic autoregression, state-space models, smoothing splines, and so on have been widely used in various areas of statistics. However, practitioners wanting to fit these models using existing packages for random-effects models are often faced with the difficulty that their covariance matrices are not uniquely determined. Unfortunately, different specifications of the model lead to different covariance structures, giving different analyses. Even if we make a decision on specification it is not immediately obvious how to make inferences from these models. There have been various suggestions on how to overcome such difficulties. However, they differ, implying that there is as yet no agreed remedy. In this article we provide a unified view on these alternatives and show how the analysis can be made invariant with respect to the choice of covariance by inclusion of a suitable set of covariates. Several examples are used to illustrate the approach.

中文翻译：

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用奇异精度矩阵解决随机效应模型的二义性

随机游走、内在自回归、状态空间模型、平滑样条等已广泛应用于统计的各个领域。然而，想要使用现有的随机效应模型包来拟合这些模型的从业者经常面临这样的困难，即他们的协方差矩阵不是唯一确定的。不幸的是，模型的不同规格导致不同的协方差结构，给出不同的分析。即使我们对规范做出决定，如何从这些模型中进行推断也不是很明显。关于如何克服这些困难，人们提出了各种建议。然而，它们不同，这意味着目前还没有商定的补救措施。在本文中，我们对这些备选方案提供了统一的观点，并展示了如何通过包含一组合适的协变量来使分析相对于协方差的选择保持不变。使用了几个示例来说明该方法。