Binary regression models are commonly used in disciplines such as epidemiology and ecology to determine how spatial covariates influence individuals. In many studies, binary data are shared in a spatially aggregated form to protect privacy. For example, rather than reporting the location and result for each individual that was tested for a disease, researchers may report that a disease was detected or not detected within geopolitical units. Often, the spatial aggregation process obscures the values of response variables, spatial covariates, and locations of each individual, which makes recovering individual-level inference difficult. We show that applying a series of transformations, including a change of support, to a bivariate point process model allows researchers to recover individual-level inference for spatial covariates from spatially aggregated binary data. The series of transformations preserves the convenient interpretation of desirable binary regression models that are commonly applied to individual-level data. Using a simulation experiment, we compare the performance of our proposed method under varying types of spatial aggregation against the performance of standard approaches using the original individual-level data. We illustrate our method by modeling individual-level probability of infection using a data set that has been aggregated to protect an at-risk and endangered species of bats. Our simulation experiment and data illustration demonstrate the utility of the proposed method when access to original non-aggregated data is impractical or prohibited.

二元回归模型常用于流行病学和生态学等学科，以确定空间协变量如何影响个体。在许多研究中，二进制数据以空间聚合形式共享以保护隐私。例如，研究人员可能报告在地缘政治单位内检测到或未检测到疾病，而不是报告每个接受疾病检测的个体的位置和结果。通常，空间聚合过程会掩盖每个个体的响应变量、空间协变量和位置的值，这使得恢复个体级别的推理变得困难。我们展示了应用一系列转换，包括支持的改变，到双变量点过程模型允许研究人员从空间聚合的二进制数据中恢复空间协变量的个体级推理。这一系列转换保留了对通常应用于个人级别数据的理想二元回归模型的方便解释。使用模拟实验，我们将我们提出的方法在不同类型的空间聚合下的性能与使用原始个人级数据的标准方法的性能进行了比较。我们通过使用已汇总的数据集对个体级别的感染概率进行建模来说明我们的方法，该数据集已汇总以保护处于危险中和濒临灭绝的蝙蝠物种。