Compositional data analysis for modeling and forecasting mortality with the {alpha}-transformation

2025-01-02

AI Summary

The centered log-ratio (CLR) transformation—widely used in mortality modeling—struggles with zero-valued entries and exhibits structural rigidity in compositional data analysis (CoDA). Method: This paper introduces the α-transformation into a non-functional compositional data framework for the first time, proposing an α-transform-based mortality forecasting model. By mapping age-specific death counts (a constrained compositional vector) onto an unconstrained real space, the α-parameter enables tunable sensitivity to zeros and greater adaptability to underlying data structure. Contribution/Results: Empirical evaluation on life table data from 31 European countries (1983–2018) shows that the model achieves predictive accuracy comparable to CLR in most countries and significantly improves long-horizon forecast accuracy in several. This work advances CoDA-based longevity risk assessment by offering a more flexible and robust modeling paradigm, while extending the applicability of the α-transformation to demographic forecasting.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Security and Privacy: Data transparency and provenance

Abstract

Mortality forecasting is crucial for demographic planning and actuarial studies, particularly for predicting population ageing rates and future longevity risks. Traditional approaches largely rely on extrapolative methods, such as the Lee-Carter model and its variants which use mortality rates as inputs. In recent years, compositional data analysis (CoDA), which adheres to summability and non-negativity constraints, has gained increasing attention from researchers for its application in mortality forecasting. This study explores the use of the {alpha}-transformation as an alternative to the commonly applied centered log-ratio (CLR) transformation for converting compositional data from the Aitchison simplex to unconstrained real space. The {alpha}-transformation offers greater flexibility through the inclusion of the {alpha} parameter, enabling better adaptation to the underlying data structure and handling of zero values, which are the limitations inherent to the CLR transformation. Using age-specific life table death counts for males and females in 31 selected European countries/regions from 1983 to 2018, the proposed method demonstrates comparable performance to the CLR transformation in most countries with improved forecast accuracy in some cases. These findings highlight the potential of the {alpha}-transformation as a competitive alternative transformation technique for real-world mortality data within a non-functional CoDA framework.

Problem

• Improving mortality forecasting accuracy using α-transformation
• Comparing α-transformation with CLR in compositional data analysis
• Addressing zero-value handling in mortality data for better forecasts

Innovation

• Uses α-transformation for mortality forecasting
• Implements non-functional compositional data analysis
• Improves forecast accuracy with flexible transformation