Although there is substantial literature on identifying structural changes for continuous spatio-temporal processes, the same is not true for categorical spatio-temporal data. This work bridges that gap and proposes a novel spatio-temporal model to identify changepoints in ordered categorical data. The model leverages an additive mean structure with separable Gaussian space-time processes for the latent variable. Our proposed methodology can detect significant changes in the mean structure as well as in the spatio-temporal covariance structures. We implement the model through a Bayesian framework that gives a computational edge over conventional approaches. From an application perspective, our approach's capability to handle ordinal categorical data provides an added advantage in real applications. This is illustrated using county-wise COVID-19 data (converted to categories according to CDC guidelines) from the state of New York in the USA. Our model identifies three changepoints in the transmission levels of COVID-19, which are indeed aligned with the ``waves'' due to specific variants encountered during the pandemic. The findings also provide interesting insights into the effects of vaccination and the extent of spatial and temporal dependence in different phases of the pandemic.

翻译：尽管针对连续时空过程的结构变化识别已有大量文献，但针对分类时空数据的同类研究尚不充分。本研究填补了这一空白，提出了一种新颖的时空模型，用于识别有序分类数据中的变化点。该模型利用潜变量的可加均值结构及可分离高斯时空过程进行建模。所提出的方法能够同时检测均值结构以及时空协方差结构的显著变化。我们通过贝叶斯框架实现该模型，相较传统方法具有计算优势。从应用角度来看，本方法处理有序分类数据的能力在实际应用中提供了额外优势。我们利用美国纽约州按县划分的COVID-19数据（根据美国疾病控制与预防中心指南转化为分类数据）对此进行说明。模型识别出COVID-19传播水平的三个变化点，这些变化点与疫情期间特定变异毒株引发的"波次"高度吻合。研究结果还揭示了疫苗接种效果以及疫情不同阶段时空依赖程度的深刻见解。