Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates. However, estimation of interaction and covariate effects may be seriously biased in the presence of unobserved spatial confounders. In this paper we introduce a new class of semi-parametric Markov point processes that adjusts for spatial confounding through a non-parametric factor that accommodates effects of latent spatial variables common to all types of points. We introduce a conditional pseudo likelihood for parameter estimation and show that the resulting estimator has desirable asymptotic properties. Our methodology not least has great potential in studies of industry agglomeration and we apply it to study spatial patterns of locations of two types of banks in France.

翻译：多类型马尔可夫点过程为建模复杂多类型点模式提供了一个灵活框架，该框架适用于捕捉点之间的相互作用以及依赖于观测协变量的大尺度趋势。然而，在存在未观测空间混杂因素的情况下，相互作用和协变量效应的估计可能存在严重偏差。本文提出了一类新的半参数马尔可夫点过程，通过一个非参数因子来调整空间混杂效应，该因子能够适应所有类型点所共有的潜在空间变量的影响。我们引入了用于参数估计的条件伪似然方法，并证明所得估计量具有良好的渐近性质。我们的方法尤其在产业集聚研究中具有巨大潜力，并将其应用于法国两类银行区位空间模式的研究中。