基于重参数化重要性抽样的带参数连接的空间广义线性混合模型的估计与预测
Estimation and prediction for spatial generalized linear mixed models with parametric links via reparameterized importance sampling
摘要：
空间广义线性混合模型是分析非高斯空间数据的常用模型。这些模型假设一个规定的链接功能，涉及潜在的空间场的平均响应。在某些情况下，例如当数据包含离群观测值时，使用规定的链接函数可能会导致拟合不佳，这可以通过使用参数链接函数来改善。一些流行的链接函数，如Box-Cox，是不合适的，因为它们与空间场的高斯假设不一致。我们提出了合理的选择参数连接函数，具有理想的性能。重要的是要估计链接函数的参数，而不是假设一个已知的值。为此，我们提出了一个广义重要性抽样（GIS）估计的基础上，多个马尔可夫链的经验贝叶斯分析的SGL。GIS估计器，虽然比简单的重要性抽样更有效，但在用于估计某些链接函数的参数时可能是高度可变的。使用适当的蒙特卡罗样本重新参数化，我们提出了不受高变异性影响的修改后的GIS估计量。我们使用拉普拉斯近似来选择GIS估计器中的多个重要性密度。最后，我们开发了一种方法来选择模型与适当的链接函数的家庭，它扩展到选择空间相关函数以及。我们提出了一个集合预测的平均响应适当加权不同的模型的估计。使用模拟和真实数据的例子说明了所提出的方法。
英文摘要：
Spatial generalized linear mixed models (SGLMMs) are popular for analyzing non-Gaussian spatial data. These models assume a prescribed link function that relates the underlying spatial field with the mean response. There are circumstances, such as when the data contain outlying observations, where the use of a prescribed link function can result in poor fit, which can be improved by using a parametric link function. Some popular link functions, such as the Box-Cox, are unsuitable because they are inconsistent with the Gaussian assumption of the spatial field. We present sensible choices of parametric link functions which possess desirable properties. It is important to estimate the parameters of the link function, rather than assume a known value. To that end, we present a generalized importance sampling (GIS) estimator based on multiple Markov chains for empirical Bayes analysis of SGLMMs. The GIS estimator, although more efficient than the simple importance sampling, can be highly variable when used to estimate the parameters of certain link functions. Using suitable reparameterizations of the Monte Carlo samples, we propose modified GIS estimators that do not suffer from high variability. We use Laplace approximation for choosing the multiple importance densities in the GIS estimator. Finally, we develop a methodology for selecting models with appropriate link function family, which extends to choosing a spatial correlation function as well. We present an ensemble prediction of the mean response by appropriately weighting the estimates from different models. The proposed methodology is illustrated using simulated and real data examples.
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