Fast expectation-maximization algorithms for spatial generalized linear mixed models
Fast expectation-maximization algorithms for spatial generalized linear mixed models
复制标题
空间广义线性混合模型的快速期望最大化算法
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
M. Haran
中科院分区：
文献类型：
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作者：
Yawen Guan;M. Haran
空间广义线性混合模型（SGLMixed Model）是一种适用于非高斯空间数据的通用模型。它们对于空间插值以及拟合考虑空间依赖性的回归模型非常有用，并且通常用于许多学科，如流行病学，大气科学和社会学。SGLestimate的推断通常在贝叶斯框架下进行，至少部分是因为计算问题使得最大似然估计具有挑战性，特别是当涉及高维空间数据时。在这里，我们提供了一个计算效率高的投影为基础的最大似然方法和两个计算效率高的算法，经常拟合SGLtd.。提出的两种算法都是期望最大化（EM）算法的变种，使用马尔可夫链蒙特卡罗或拉普拉斯近似的条件期望。我们的方法是通用的，适用于离散域（高斯马尔可夫随机场）以及连续域（高斯过程）的空间模型。我们的方法还能够调整空间混淆问题，这些问题通常会导致解释回归系数的问题。我们表明，通过模拟和真实的数据应用，我们的方法在参数估计和预测方面都表现良好。至关重要的是，我们的方法是计算效率和规模以及与数据的大小，适用于最大似然估计以前是不可行的问题。
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are commonly used in many disciplines such as epidemiology, atmospheric science, and sociology. Inference for SGLMMs is typically carried out under the Bayesian framework at least in part because computational issues make maximum likelihood estimation challenging, especially when high-dimensional spatial data are involved. Here we provide a computationally efficient projection-based maximum likelihood approach and two computationally efficient algorithms for routinely fitting SGLMMs. The two algorithms proposed are both variants of expectation maximization (EM) algorithm, using either Markov chain Monte Carlo or a Laplace approximation for the conditional expectation. Our methodology is general and applies to both discrete-domain (Gaussian Markov random field) as well as continuous-domain (Gaussian process) spatial models. Our methods are also able to adjust for spatial confounding issues that often lead to problems with interpreting regression coefficients. We show, via simulation and real data applications, that our methods perform well both in terms of parameter estimation as well as prediction. Crucially, our methodology is computationally efficient and scales well with the size of the data and is applicable to problems where maximum likelihood estimation was previously infeasible.