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On fitting generalized linear and non-linear models of mortality

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  • Iain D. Currie

Abstract

Many common models of mortality can be expressed compactly in the language of either generalized linear models or generalized non-linear models. The R language provides a description of these models which parallels the usual algebraic definitions but has the advantage of a transparent and flexible model specification. We compare eight model structures for mortality. For each structure, we consider (a) the Poisson models for the force of mortality with both log and logit link functions and (b) the binomial models for the rate of mortality with logit and complementary log–log link functions. Part of this work shows how to extend the usual smooth two-dimensional P-spline model for the force of mortality with Poisson error and log link to the other smooth two-dimensional P-spline models with Poisson and binomial errors defined in (a) and (b). Our comments are based on the results of fitting these models to data from six countries: Australia, France, Japan, Sweden, UK and USA. We also discuss the possibility of forecasting with these models; in particular, the introduction of cohort terms generally leads to an improvement in overall fit, but can also make forecasting with these models problematic.

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  • Iain D. Currie, 2016. "On fitting generalized linear and non-linear models of mortality," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(4), pages 356-383, April.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:356-383
    DOI: 10.1080/03461238.2014.928230
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    Cited by:

    1. Jose Garrido & Xavier Milhaud & Anani Olympio & Max Popp, 2024. "Climate Risk and its Impact on Insurance [Risque climatique et impact en assurance]," Post-Print hal-04684634, HAL.
    2. Salvatore Scognamiglio & Mario Marino, 2023. "Backtesting stochastic mortality models by prediction interval-based metrics," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3825-3847, August.
    3. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2023. "Intergenerational actuarial fairness when longevity increases: Amending the retirement age," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 161-184.
    4. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    5. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2022. "Thirty years on: A review of the Lee-Carter method for forecasting mortality," SocArXiv 8u34d, Center for Open Science.
    6. Barigou, Karim & Goffard, Pierre-Olivier & Loisel, Stéphane & Salhi, Yahia, 2023. "Bayesian model averaging for mortality forecasting using leave-future-out validation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 674-690.
    7. Yang Qiao & Chou-Wen Wang & Wenjun Zhu, 2024. "Machine learning in long-term mortality forecasting," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 340-362, April.

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