There is an increasing attention on the joint modelling of multiple populations. Populations are related in several ways, such as neighbouring countries, females and males, and socioeconomic subgroups within a population. They are associated due to certain common driving forces, and mortality projection models should be constructed to allow for such underlying relationships. One such example is the Poisson common factor model. In this paper, we consider some extensions of the original Poisson common factor model. The first is to use a different number of additional factors for each sex. With this, the potential trend differences between the two sexes can be captured. The second is to incorporate a common age sensitivity effect into the additional factors. It may help improve parameter parsimony. A hybrid version between these two extensions is also considered. Overall, the modified versions deliver better fitting and projection results than the original model, using mortality data from eight developed countries. Qualitatively speaking, the new models provide much more flexibility in modelling populations with different mortality patterns. Empirically, they are shown to be able to produce improved performance in fitting and projection. The models are selected as the optimal choices based on information criteria statistics, and they tend to produce more accurate forecasts of the male-to-female ratios of death rates.

中文翻译：

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修改后的共同因素模型，用于共同模拟两性死亡率

越来越多的关注对多个人口的联合建模。人口以几种方式相关，例如邻国，男女，以及人口中的社会经济子群体。由于某些共同的驱动力，它们是相关的，因此应该构建死亡率预测模型以考虑到这种潜在的关系。泊松公共因子模型就是这样一个例子。在本文中，我们考虑了原始泊松公共因子模型的一些扩展。首先是对每种性别使用不同数量的其他因素。这样，可以捕获两个性别之间潜在的趋势差异。第二是将常见的年龄敏感性效应纳入其他因素。它可能有助于改善参数简约性。还考虑了这两个扩展之间的混合版本。总体而言，使用来自八个发达国家的死亡率数据，修改后的版本比原始模型提供更好的拟合和预测结果。从质量上讲，新模型为建模具有不同死亡率模式的人群提供了更大的灵活性。根据经验，它们显示出能够在装配和投影方面产生改进的性能。这些模型是根据信息标准统计数据选择的最佳选择，它们倾向于对死亡率的男女比例产生更准确的预测。新模型为建模具有不同死亡率模式的人群提供了更大的灵活性。根据经验，它们显示出能够在装配和投影方面产生改进的性能。这些模型是根据信息标准统计数据选择的最佳选择，它们倾向于对死亡率的男女比例产生更准确的预测。新模型为建模具有不同死亡率模式的人群提供了更大的灵活性。根据经验，它们显示出能够在装配和投影方面产生改进的性能。这些模型是根据信息标准统计数据选择的最佳选择，它们倾向于对死亡率的男女比例产生更准确的预测。