Mixed models are commonly used to analyze spatial data which frequently occur in practice such as in health sciences and life studies. It is customary to incorporate spatial random effects into the model to account for spatial variation of the data. In particular, Poisson mixed models are used to analyze spatial count data. It is often assumed that the observations in each area, conditional on the spatial random effects, are independent of each other. However, this may not be a valid assumption in practice. For instance, multiple asthma visits by a child to physicians (within a year) are not clearly independent observations. To address this issue, this paper develops spatial models with repeated events. In particular, compound Poisson mixed models are introduced to account for the repeated events as well as the spatial variation of the data. Performance of the proposed approach is evaluated through simulation studies and by a real dataset of children asthma visits to physicians in the province of Manitoba, Canada.

混合模型通常用于分析在实践中经常出现的空间数据，例如在健康科学和生命研究中。通常将空间随机效应合并到模型中以说明数据的空间变化。特别是，泊松混合模型用于分析空间计数数据。通常认为，在每个区域中，以空间随机效应为条件的观测值是相互独立的。但是，这实际上可能不是有效的假设。例如，一个孩子多次去看医生（一年之内）并不是明确的独立观察。为了解决这个问题，本文开发了具有重复事件的空间模型。特别是，引入了复合Poisson混合模型来说明重复事件以及数据的空间变化。