For spatial linear regression, the traditional approach to capture spatial dependence is to use a parametric linear mixed-effects model. Spline surfaces can be used as an alternative to capture spatial variability, giving rise to a semiparametric method that does not require the specification of a parametric covariance structure. The spline component in such a semiparametric method, however, impacts the estimation of the regression coefficients. In this paper, we investigate such an impact in spatial linear regression with spline-based spatial effects. Statistical properties of the regression coefficient estimators are established under the model assumptions of the traditional spatial linear regression. Further, we examine the empirical properties of the regression coefficient estimators under spatial confounding via a simulation study. A data example in precision agriculture research regarding soybean yield in relation to field conditions is presented for illustration.

中文翻译：

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基于样条的地统计数据空间线性回归方法

对于空间线性回归，捕获空间依赖性的传统方法是使用参数线性混合效应模型。样条曲面可以用作捕获空间变异性的替代方法，从而产生了一种不需要指定参数协方差结构的半参数方法。但是，这种半参数方法中的样条曲线分量会影响回归系数的估计。在本文中，我们研究了基于样条曲线的空间效应对空间线性回归的影响。回归系数估计量的统计属性是在传统空间线性回归的模型假设下建立的。此外，我们通过模拟研究检查了空间混杂条件下回归系数估计量的经验性质。