In modern spatial statistics, the structure of data has become more heterogeneous. Depending on the types of spatial data, different modeling strategies are used. For example, kriging approaches for geostatistical data; Gaussian Markov random field models for lattice data; or log Gaussian Cox process models for point-pattern data. Despite these different modeling choices, the nature of underlying data-generating (latent) processes is often the same, which can be represented by some continuous spatial surfaces. A unifying framework is introduced for process-based multivariate spatial fusion models. The framework can jointly analyze all three aforementioned types of spatial data or any combinations thereof. Moreover, the framework accommodates different likelihoods for geostatistical and lattice data. It is shown that some established approaches, such as linear models of coregionalization, can be viewed as special cases of the proposed framework. A flexible and scalable implementation using R-INLA is provided. Simulation studies confirm that the prediction of latent processes improves as one moves from univariate spatial models to multivariate spatial fusion models. The framework is illustrated via a case study using datasets from a cross-sectional study linked with a national cohort in Switzerland. The differences in underlying spatial risks between respiratory disease and lung cancer are examined in the case study.

在现代空间统计中，数据的结构变得更加异构。根据空间数据的类型，使用不同的建模策略。例如，地统计数据的克里金法；高斯马尔可夫随机场模型的晶格数据；或记录高斯Cox处理模型以获取点模式数据。尽管有这些不同的建模选择，但是底层数据生成（潜在）过程的性质通常是相同的，这可以由一些连续的空间表面来表示。为基于过程的多元空间融合模型引入了统一框架。框架可以共同分析所有三种上述类型的空间数据或其任何组合。此外，该框架为地统计和格网数据提供了不同的可能性。结果表明，一些已建立的方法，例如共区域化的线性模型，可以看作是所提出框架的特殊情况。提供了使用R-INLA的灵活且可扩展的实现。仿真研究证实，随着人们从单变量空间模型转向多元空间融合模型，对潜在过程的预测会有所改善。通过案例研究说明了该框架，该案例研究使用了与瑞士国家队列相关的横断面研究的数据集。本案例研究了呼吸系统疾病和肺癌之间潜在的空间风险差异。仿真研究证实，随着人们从单变量空间模型转向多元空间融合模型，对潜在过程的预测会有所改善。通过案例研究说明了该框架，该案例研究使用了与瑞士国家队列相关的横断面研究的数据集。本案例研究了呼吸系统疾病和肺癌之间潜在的空间风险差异。仿真研究证实，随着人们从单变量空间模型转向多元空间融合模型，对潜在过程的预测会有所改善。通过案例研究说明了该框架，该案例研究使用了与瑞士国家队列相关的横断面研究的数据集。本案例研究了呼吸系统疾病和肺癌之间潜在的空间风险差异。