The application of spatial Cliff–Ord models requires information about spatial coordinates of statistical units to be reliable, which is usually the case in the context of areal data. With micro-geographic point-level data, however, such information is inevitably affected by locational errors, that can be generated intentionally by the data producer for privacy protection or can be due to inaccuracy of the geocoding procedures. This unfortunate circumstance can potentially limit the use of the spatial autoregressive modelling framework for the analysis of micro data, as the presence of locational errors may have a non-negligible impact on the estimates of model parameters. This contribution aims at developing a strategy to reduce the bias and produce more reliable inference for spatial models with location errors. The proposed estimation strategy models both the spatial stochastic process and the coarsening mechanism by means of a marked point process. The model is fitted through the maximisation of a doubly-marginalised likelihood function of the marked point process, which cleans out the effects of coarsening. The validity of the proposed approach is assessed by means of a Monte Carlo simulation study under different real-case scenarios, whereas it is applied to real data on house prices.

空间Cliff-Ord模型的应用要求有关统计单位的空间坐标的信息要可靠，这在面数据的情况下通常是这种情况。但是，对于微地理点级数据，此类信息不可避免地会受到位置错误的影响，这些位置错误可能是由数据生产者有意生成的，用于保护隐私，或者可能是由于地理编码过程不准确所致。这种不幸的情况可能会限制使用空间自回归建模框架来分析微数据，因为位置错误的存在可能会对模型参数的估计产生不可忽略的影响。该贡献旨在开发一种策略，以减少偏差并为具有位置误差的空间模型提供更可靠的推断。所提出的估计策略通过标记点过程对空间随机过程和粗化机制进行建模。通过最大化标记点过程的双边缘似然函数来拟合模型，从而消除了粗化的影响。通过在不同实际情况下进行的蒙特卡洛模拟研究评估了所提出方法的有效性，而该方法则应用于房价的真实数据。