Multivariate models for spatial count data are currently receiving attention in disease mapping to model two or more diseases jointly. They have been thoroughly studied from a theoretical point of view, but their use in practice is still limited because they are computationally expensive and, in general, they are not implemented in standard software to be used routinely. Here, a new multivariate proposal, based on the recently derived M models for spatial data, is developed for spatio-temporal areal data. The model takes account of the correlation between the spatial and temporal patterns of the phenomena being studied, and it also includes spatio-temporal interactions. Though multivariate models have been traditionally fitted using Markov chain Monte Carlo techniques, here we propose to adopt integrated nested Laplace approximations to speed up computations as results obtained using both fitting techniques were nearly identical. The techniques are used to analyse two forms of crimes against women in India. In particular, we focus on the joint analysis of rapes and dowry deaths in Uttar Pradesh, the most populated Indian state, during the years 2001–2014.

目前，空间计数数据的多元模型在疾病制图中受到关注，以共同对两种或多种疾病进行建模。从理论的角度对它们进行了彻底的研究，但是它们在实践中的使用仍然受到限制，因为它们在计算上很昂贵，并且通常它们没有在常规使用的标准软件中实现。在此，根据时空面数据开发了一种基于最近导出的空间数据M模型的新多元建议。该模型考虑了正在研究的现象的时空格局之间的相关性，并且还包括时空相互作用。尽管传统上已经使用马尔可夫链蒙特卡洛技术拟合了多元模型，在这里，我们建议采用集成的嵌套Laplace逼近来加快计算速度，因为使用两种拟合技术获得的结果几乎相同。该技术用于分析印度针对妇女的两种犯罪形式。特别是，我们着重于在2001-2014年间人口最多的印度北方邦，对强奸和嫁妆造成的死亡进行联合分析。