Traditional analysis of marked spatial point processes often relies on global summary statistics, which tend to obscure local spatial heterogeneity by averaging dependencies across the entire observation window. To overcome this limitation, this paper introduces a framework for Local Indicators of Mark Association (LIMA) specifically designed for composition-valued marks. Such marks, characterized by their non-negative components and sum-to-constant constraint, require a specialized treatment within the Aitchison geometry. By employing log-ratio transformations, we project these constrained marks into a Euclidean space, enabling the point-specific decomposition of global mark characteristics. The efficacy of the proposed clr-based LIMA functions is validated through extensive simulation studies. The results demonstrate a superior capacity to detect localized mark clusters, achieving detection accuracies consistently higher than their global counterparts. The practical utility of this framework is demonstrated using an empirical dataset of economic sector compositions in Castile-La Mancha, Spain. The analysis uncovers latent economic clustering patterns and localized \textit{drainage} effects that are invisible to global metrics, providing granular insights into regional spatial dynamics. Our findings suggest that the extended LIMA framework serves as a vital diagnostic tool for high-dimensional, non-stationary marked point patterns.

翻译：传统标记空间点过程的分析通常依赖于全局汇总统计量，这些统计量通过在整个观测窗口内平均依赖关系，往往会掩盖局部空间异质性。为克服这一局限，本文引入了一个专为成分值标记设计的局部标记关联指标（LIMA）框架。此类标记具有非负分量和总和为常数的约束，需要在艾奇逊几何中进行专门处理。通过采用对数比变换，我们将这些受约束的标记投影到欧几里得空间，从而实现对全局标记特征的点特定分解。所提出的基于clr的LIMA函数的有效性通过广泛的模拟研究得到验证。结果表明，该方法在检测局部标记聚类方面具有优越能力，其检测准确率始终高于全局对应方法。通过使用西班牙卡斯蒂利亚-拉曼恰经济部门构成的实证数据集，展示了该框架的实际效用。分析揭示了全局指标无法发现的潜在经济聚类模式和局部“排水”效应，为区域空间动态提供了精细的洞察。我们的研究结果表明，扩展的LIMA框架可作为高维、非平稳标记点模式的重要诊断工具。