Spherical regression models with general covariates and anisotropic errors
Spherical regression models with general covariates and anisotropic errors
复制标题
具有一般协变量和各向异性误差的球面回归模型
DOI：
10.1007/s11222-019-09872-2
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发表时间：
2019
影响因子：
2.2
通讯作者：
A. Wood
中科院分区：
文献类型：
--
作者：
P. J. Paine;S. Preston;M. Tsagris;A. Wood
现有的参数回归模型在文献中的响应数据的单位球假设协变量具有特别简单的结构，例如，他们要么是标量或本身的单位球，和/或误差分布是各向同性的。在许多实际情况下，这种模式过于僵化。在这里，我们开发了更丰富的参数球面回归模型，其中协变量可以具有相当一般的结构（例如，它们可以在单位球面上，在欧几里得空间中，分类或这些的某种组合），并且其中误差是各向异性的。我们考虑两个各向异性的误差分布的肯特分布和椭圆对称角高斯分布和两个parametrisations，使不同的方式来模拟响应如何依赖于协变量。各种感兴趣的假设，如特定协变量的显著性或误差的各向异性，很容易测试，例如通过经典的似然比测试。我们还引入了新的基于模型的残差来评估拟合模型。在我们考虑的例子中，假设检验表明强有力的证据，有利于新的模型比简单的现有的。
Existing parametric regression models in the literature for response data on the unit sphere assume that the covariates have particularly simple structure, for example that they are either scalar or are themselves on the unit sphere, and/or that the error distribution is isotropic. In many practical situations, such models are too inflexible. Here, we develop richer parametric spherical regression models in which the covariates can have quite general structure (for example, they may be on the unit sphere, in Euclidean space, categorical or some combination of these) and in which the errors are anisotropic. We consider two anisotropic error distributions—the Kent distribution and the elliptically symmetric angular Gaussian distribution—and two parametrisations of each which enable distinct ways to model how the response depends on the covariates. Various hypotheses of interest, such as the significance of particular covariates, or anisotropy of the errors, are easy to test, for example by classical likelihood ratio tests. We also introduce new model-based residuals for evaluating the fitted models. In the examples we consider, the hypothesis tests indicate strong evidence to favour the novel models over simpler existing ones.