This study introduces a novel Generalized Additive Mixed Model (GAMM) for mortality modelling, employing mortality covariates $k_t$ and $k_{ct}$ as proposed by Dastranj- Kol\'a\vr (DK-LME). The GAMM effectively predicts age-specific death rates (ASDRs) in both single and multi-population contexts. Empirical evaluations using data from the Human Mortality Database (HMD) demonstrate the model's exceptional performance in accurately capturing observed mortality rates. In the DK-LME model, the relationship between log ASDRs, and $k_t$ did not provide a perfect fit. Our study shows that the GAMM addresses this limitation. Additionally, as discussed in the DK-LME model, ASDRs represent longitudinal data. The GAMM offers a suitable alternative to the DK-LME model for modelling and forecasting mortality rates. We will compare the forecast accuracy of the GAMM with both the DK-LME and Li-Lee models in multi-population scenarios, as well as with LC models in single population scenarios. Comparative analyses highlight the GAMM's superior sample fitting and out-of-sample forecasting performance, positioning it as a promising tool for mortality modelling and forecasting.

翻译：本研究提出了一种新的广义可加混合模型（GAMM），用于死亡率建模，采用Dastranj-Kolář（DK-LME）提出的死亡率协变量$k_t$和$k_{ct}$。该GAMM能够有效预测单群体和多群体背景下的年龄别死亡率（ASDRs）。基于人类死亡率数据库（HMD）数据的实证评估表明，该模型在准确捕捉观测死亡率方面表现出色。在DK-LME模型中，对数ASDRs与$k_t$之间的关系未能实现完美拟合。本研究表明，GAMM可以弥补这一不足。此外，正如DK-LME模型中所讨论的，ASDRs代表纵向数据。GAMM为建模和预测死亡率提供了DK-LME模型之外的合适替代方案。我们将在多群体场景中比较GAMM与DK-LME和Li-Lee模型的预测精度，并在单群体场景中与LC模型进行对比。比较分析凸显了GAMM卓越的样本内拟合和样本外预测性能，使其成为死亡率建模与预测领域极具前景的工具。