Compositional data analysis for modelling and forecasting mortality using the α-transformation

Age coherence describes the property that forecast mortality rates across ages will not diverge in the long run. Although intuitively and biologically reasonable, this property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. In this paper, we propose two effective extensions of the LC model, allowing for the geometric (LC-G) and hyperbolic (LC-H) decayed relative speed of mortality decline at each age, over the out-of-sample forecasting steps. Those approaches are based on the original in-sample estimates of LC, which are easy to obtain. An inversed Epanechnikov kernel is employed to model the geometric and hyperbolic parameters across ages, and unknown parameters are selected via a data-driven method. With little added computational cost to LC, our approaches incorporate the dynamic and rotating relative speeds of mortality decline over ages, recognize the growing difficulty of such declines at older ages, provide age-coherent forecasts of mortality rates in the long run, and is easily extensible to multi-population cases. Using a large sample of 15 countries, we demonstrate that LC-G and LC-H, as well as their multi-population counterparties, consistently improve the forecasting accuracy of the competing LC model and its single- and multi-population extensions.Feng, L., Shi, Y., & Chang, L. (2021). Forecasting mortality with a hyperbolic spatial temporal VAR model. International Journal of Forecasting, 37(1), 255–273.

A person's life expectancy is one of the statistical measures used to determine how long they will live. However, in Sri Lanka, there is a lack of long-term, data-driven mortality forecasting, which limits the ability to make informed decisions in public health, insurance, and policy planning. This study addresses this gap by applying the Lee-Carter (LC) mortality estimation method to improve life expectancy analysis and mortality forecasting. In general, a life table that details the effects of mortality is used to calculate life expectancy. As a result, mortality predictions and life table analysis are important in the insurance, actuarial science, government, and pension planning sectors. The Registrar General's Office and the Department of Census and Statistics in Sri Lanka provided the mid-year population data and deaths as historical data for this study from 1992 to 2014. The Lee-Carter (LC) mortality estimation method is used to forecast mortality using actual death rates and mid-year populations from 1992 to 2014. ax (the average age-specific log mortality rate over time), bx (the sensitivity of mortality at each age to changes in the mortality index), and kt (the overall mortality index over time) parameters are estimated using the Singular Value Decomposition (SVD) method in the Lee-Carter methodology between 1992 and 2014. kt is forecasted for the years 2015–2035 using the traditional time series approach, and no specific time series model such as ARIMA or Exponential Smoothing was used. In 2035, the probability of dying as a 55-year-old woman and man are 0.023 and 0.051, respectively, according to the research. The following is a statement of the study's results: South Asia's average life expectancy is 69.41 years, while Sri Lanka's is 74.5 years. A country's future can be improved by thoroughly investigating demographics and life expectancy, as these factors directly affect financial stability.

Compositional Data Analysis (CoDA) as a tool to study the (paleo)ecology of coccolithophores from coastal-neritic settings off central Portugal

A new method for correlation analysis of compositional (environmental) data – a worked example

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.

BackgroundIt is unclear whether walking can decrease cardiovascular disease (CVD) risk or if high intensity physical activity (HIPA) is needed, and whether the association is modified by age. We investigated how sedentary behaviour, walking, and HIPA, were associated with systolic blood pressure (SBP), waist circumference (WC), and low-density lipoprotein cholesterol (LDL-C) among adults and older adults in a general population sample using compositional data analysis. Specifically, the measure of association was quantified by reallocating time between sedentary behaviour and 1) walking, and 2) HIPA.MethodsCross-sectional data from the fifth examination of the Copenhagen City Heart Study was used. Using the software Acti4, we estimated daily time spent in physical behaviours from accelerometer data worn 24 h/day for 7 days (i.e., right frontal thigh and iliac crest; median wear time: 6 days, 23.8 h/day). SBP, WC, and LDL-C were measured during a physical examination. Inclusion criteria were ≥ 5 days with ≥16 h of accelerometer recordings per day, and no use of antihypertensives, diuretics or cholesterol lowering medicine. The 24-h physical behaviour composition consisted of sedentary behaviour, standing, moving, walking, HIPA (i.e., sum of climbing stairs, running, cycling, and rowing), and time in bed. We used fitted values from linear regression models to predict the difference in outcome given the investigated time reallocations relative to the group-specific mean composition.ResultsAmong 1053 eligible participants, we found an interaction between the physical behaviour composition and age. Age-stratified analyses (i.e., </≥65 years; 773 adults, 280 older adults) indicated that less sedentary behaviour and more walking was associated with lower SBP among older adults only. For less sedentary behaviour and more HIPA, the results i) indicated an association with a lower SBP irrespective of age, ii) showed an association with a smaller WC among adults, and iii) showed an association with a lower LDL-C in both age groups.ConclusionsLess sedentary behaviour and more walking seems to be associated with lower CVD risk among older adults, while HIPA types are associated with lower risk among adults. Therefore, to reduce CVD risk, the modifying effect of age should be considered in future physical activity-promoting initiatives.

SummaryCause-specific mortality forecasting is often based on predicting cause-specific death rates independently. Only a few methods have been suggested that incorporate dependence between causes. An attractive alternative is to model and forecast cause-specific death distributions, rather than mortality rates, as dependence between the causes can be incorporated directly. We follow this idea and propose two new models which extend the current research on mortality forecasting using death distributions. We find that adding age, time and cause-specific weights and decomposing both joint and individual variation between different causes of death increased the forecast accuracy of cancer deaths by using data for French and Dutch populations.

Accurate forecasts of mortality rates are essential to various types of demographic research such as population projection, and the pricing of insurance products such as pensions and annuities. Recent studies have considered a spatial temporal autoregressive (STAR) model for the mortality surface, where mortality rates for each age depend (temporally) on their historical values as well as (spatiality) on those of neighboring age cohorts. This model has sound statistical properties including cointegrated dependent variables and the existence of closed‐form solutions. Despite its improved forecasting performance over the famous Lee–Carter (LC) model, the constraint that only the effects of the same and neighboring cohorts are significant can be too restrictive. In this study, we adopt a data‐driven adaptive weighted structure and propose the adaptive STAR (ASTAR) model. Retaining all the desirable features of the STAR, our model uniformly outperforms the LC and STAR counterparts in terms of forecasting accuracy, when mortality data for ages 0–100 from the UK, France, Italy, Spain, and Japan over the period 1950–2016 are considered. Two sensitivity tests and additional simulation results also lead to robust conclusions. The proposed ASTAR model could therefore be a widely useful tool for modeling and forecasting mortality rates in other contexts, and may be extended to multipopulation modeling.

Park, N.-W. and Jang, D.-H., 2020. Geostatistical classification of intertidal surface sediments using log-ratio transformation and high-resolution remote sensing imagery. In: Jung, H.-S.; Lee, S.; Ryu, J.-H., and Cui, T. (eds.), Advances in Geospatial Research of Coastal Environments. Journal of Coastal Research, Special Issue No. 102, pp. 157-165. Coconut Creek (Florida), ISSN 0749-0208.This paper presents a multivariate geostatistical approach to classify intertidal surface sediments by combining compositional data analysis and high-resolution remote sensing imagery. An isometric log-ratio (ilr) transformation is first applied to the sediment composition data prior to employing geostatistical analysis to consider the compositional properties of the sediment compositions. To complement the information deficiency of sparse field measurements, high-resolution remote sensing imagery is considered as exhaustive soft information and integrated with the ilr transformed balances via simple kriging with varying local means (SKLM). An inverse ilr transformation is then applied to the SKLM results to obtain sediment compositions over the study area. Finally, Shepard's classification scheme is applied to the sediment compositions to classify the intertidal surface sediments. A case study was conducted on the Baramarae tidal flats in Korea with high-resolution KOMPSAT-2 imagery to demonstrate the effectiveness of the proposed geostatistical approach. The classification results produced by the integration of high-resolution remote sensing imagery via ilr transformation and SKLM outperformed those based on cokriging of sediment compositions, with an improvement of approximately 11.7 %p in overall accuracy. This improvement was attributed to the superior prediction capability of SKLM for sediment compositions. Further, detailed variations in the sediment distributions in the study area, which could not be observed when using only a limited number of sediment samples, could be revealed by integrating the high-resolution remote sensing imagery. Therefore, the geostatistical integration approach that properly accounts for both the property of sediment compositions and the exhaustive soft information from remote sensing imagery could be effectively applied for the classification of intertidal surface sediments.

Mortality forecasting has always been a target of study by academics and practitioners. Since the introduction and rising significance of securitization of risk in mortality and longevity, more in-depth studies regarding mortality have been carried out to enable the fair pricing of such derivatives. In this article, a comparative analysis is performed on the mortality forecasting accuracy of four mortality models. The methodology employs the Age-Period-Cohort model, the Cairns-Blake-Dowd model, the classical Lee-Carter model and the Kou-Modified Lee-Carter model. The Kou-Modified Lee-Carter model combines the classical Lee-Carter with the Double Exponential Jump Diffusion model. This paper is the first study to employ the Kou model to forecast French mortality data. The dataset comprises death data of French males from age 0 to age 90, available for the years 1900–2015. The paper differentiates between two periods: the 1900–1960 period where extreme mortality events occurred for French males and the 1961–2015 period where no significant jump is observed. The Kou-modified Lee-Carter model turns out to give the best mortality forecasts based on the RMSE, MAE, MPE and MAPE metrics for the period 1900–1960 during which the two World Wars occurred. This confirms that the consideration of jumps and leptokurtic features conveys important information for mortality forecasting.

Forecasting mortality has been a vital issue in demography and actuarial science.It also has profound implications for pension plan and long-term economic forecasts of the nation.In the present paper we examine various forecasting methods for mortality in the framework of cointegrated time series analysis.The Lee-Carter (LC) method has been regarded as the benchmark for forecasting mortality.However, its forecasting accuracy has been known to be particularly poor for short-term forecasts, while it is well for long-term forecasts.Recently, a new methods called the multivariate time series variance component (MTV) method has been proposed which explicitly satisfies cointegration restrictions of the series.It overcomes weak points of the LC method.In the present paper we propose two new methods.The first one is the modified MTV (mMTV) method which modifies the MTV method in order to get more accurate forecast of the trend component of the method.The second is the all-component Lee-Carter (LCA) method which generalizes the Lee-Carter method, by using all principal components, in order to improve short-term forecasts of the LC method.However, it may be noted that the LCA method does not satisfy cointegration restrictions.We analytically compare forecasting accuracy of the proposed methods with the Lee-Carter method and the MTV method in the framework of cointegrated time series.We further compare them in a Monte Carlo experiment and in an empirical application of forecasting mortality for Japanese male.It is shown that the mMTV method is generally the most accurate in the Monte Carlo experiment and in Japanese data.The MTV method works almost as well.However, since the drift estimator is inefficient, it is slightly less accurate than the mMTV method in some occasions.The forecast accuracy of the LCA method is reasonably high and can be equivalent to the mMTV method in some occasions, but is generally inferior to the MTV method and the mMTV method.As expected, the LC method is the worst among methods examined in the present study.The mMTV method is recommended for practical use.

Loadings and scores of principal component analysis are popularly displayed together in a planar graph, called biplot, with an intuitive interpretation. In case of compositional data, multivariate observations that carry only relative information (represented usually in proportions or percentages), principal component analysis cannot be used for the original compositions. They first need to be transformed using the centered logratio (clr) transformation. If outlying observations occur in compositional data, even the clr (compositional) biplot can lead to useless conclusions. A robust alternative biplot can be computed by using the isometric logratio (ilr) transformation, and by robustly estimating location and covariance. The robust compositional biplot has a big potential in many applications, like in geology, analytical chemistry, or social sciences.

Modelling the paleopedological development of loess/palaeosol sections using discriminant function analysis of compositional geoscience data, case study in Eastern Croatia

Uses and misuses of compositional data in sedimentology

Understanding and forecasting mortality by cause is an essential branch of actuarial science, with wide-ranging implications for decision-makers in public policy and industry. To accurately capture trends in cause-specific mortality, it is critical to consider dependencies between causes of death and produce forecasts by age and cause coherent with aggregate mortality forecasts. One way to achieve these aims is to model cause-specific deaths using compositional data analysis (CODA), treating the density of deaths by age and cause as a set of dependent, nonnegative values that sum to one. A major drawback of standard CODA methods is the challenge of zero values, which frequently occur in cause-of-death mortality modeling. Thus, we propose using a compositional power transformation, the $\alpha$ -transformation, to model cause-specific life-table death counts. The $\alpha$ -transformation offers a statistically rigorous approach to handling zero value subgroups in CODA compared to ad hoc techniques: adding an arbitrarily small amount. We illustrate the $\alpha$ -transformation in England and Wales and US death counts by cause from the Human Cause-of-Death database, for cardiovascular-related causes of death. The results demonstrate the $\alpha$ -transformation improves forecast accuracy of cause-specific life-table death counts compared with log-ratio-based CODA transformations. The forecasts suggest declines in the proportions of deaths from major cardiovascular causes (myocardial infarction and other ischemic heart diseases).