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Resolving the ambiguity of random-effects models with singular precision matrix

机译：用奇异精密矩阵解决随机效果模型的模糊性

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摘要

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.
机译：随机散步，内在自动增加，状态空间模型，平滑样条，等待各种统计领域。 但是，希望使用现有的随机效果模型拟合这些模型的从业者通常面临其协方差矩阵没有唯一确定的困难。 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。 即使我们做出了关于规范的决定，它也没有立即显而易见的是如何从这些模型中推断出来。 有关于如何克服这种困难的各种建议。 但是，它们有所不同，暗示还没有商定的补救措施。 在本文中，我们在这些替代方案中提供了统一的观点，并通过包含合适的一组协变量来说明如何在协方差方面进行不变。 几个例子用于说明方法。

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