Assessing associations between a response of interest and a set of covariates in spatial areal models is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects can mask or even bias estimates of such associations due to confounding effects if they are not carefully handled. Though potentially harmful, confounding issues have often been ignored in practice leading to wrong conclusions about the underlying associations between the response and the covariates. In spatio-temporal areal models, the temporal dimension may emerge as a new source of confounding, and the problem may be even worse. In this work, we propose two approaches to deal with confounding of fixed effects by spatial and temporal random effects, while obtaining good model predictions. In particular, restricted regression and an apparently—though in fact not—equivalent procedure using constraints are proposed within both fully Bayes and empirical Bayes approaches. The methods are compared in terms of fixed-effect estimates and model selection criteria. The techniques are used to assess the association between dowry deaths and certain socio-demographic covariates in the districts of Uttar Pradesh, India.

评估感兴趣的响应与空间区域模型中的一组协变量之间的关联是生态回归的主旨。然而，如果不小心处理，空间相关随机效应的存在可能会掩盖甚至偏差对这种关联的估计，这是由于混杂效应造成的。尽管可能有害，但在实践中经常忽略混杂的问题，从而导致关于响应与协变量之间潜在关联的错误结论。在时空区域模型中，时间维度可能会成为新的混淆源，问题可能会更严重。在这项工作中，我们提出了两种方法来处理空间和时间随机效应对固定效应的混淆，同时获得良好的模型预测。特别是，在完全贝叶斯方法和经验贝叶斯方法中都提出了受限回归和使用约束的明显（尽管实际上不是）等效的过程。这些方法在固定效应估计和模型选择标准方面进行了比较。这些技术用于评估印度北方邦地区的嫁妆死亡与某些社会人口统计学协变量之间的关联。