One of the basic assumptions in spatial statistic is second-order stationarity, which implies homogeneity and isotropy. However, when using a spatial random field framework to model socio-economical or epidemiological data – just to mention two examples – it is often unreasonable to believe that the relationship between variables could be modelled as a realization of a unique stationary process. In order to provide a more realistic representation, we introduce a latent process which drives the value of the coefficients in a Cliff-Ord-type spatial autoregressive linear model identifying groups of observations with a similar behaviour. The latent process evolves as a Hidden Markov Random Field. This structure allows the topology of the problem to be taken into account when identifying groups. A simulation exercise is performed to investigate the influence of parameter values – estimated via a Markov chain Monte Carlo procedure – on the accuracy of the results. Criteria to perform model comparison in order to establish the optimal number of clusters are also provided. A case study referred to hedonic house prices in Boston illustrates the advantages of the proposed modelling strategy.

空间统计的基本假设之一是二阶平稳性，这意味着均匀性和各向同性。然而，当使用空间随机场框架对社会经济或流行病学数据建模时——仅举两个例子——认为变量之间的关系可以建模为独特的平稳过程的实现通常是不合理的。为了提供更真实的表示，我们引入了一个潜在过程，该过程驱动 Cliff-Ord 型空间自回归线性模型中的系数值，以识别具有相似行为的观察组。潜在过程演变为隐马尔可夫随机场。这种结构允许在识别组时考虑问题的拓扑结构。进行模拟练习以研究参数值（通过马尔可夫链蒙特卡罗程序估计）对结果准确性的影响。还提供了执行模型比较以建立最佳聚类数的标准。一个关于波士顿享乐房价的案例研究说明了所提议的建模策略的优势。