Bilinear modulation models for seasonal tables of counts

We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Two-dimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases

Model confidence sets and forecast combination: an application to age-specific mortality

Background: Model averaging combines forecasts obtained from a range of models, and it often produces more accurate forecasts than a forecast from a single model. Objective: The crucial part of forecast accuracy improvement in using the model averaging lies in the determination of optimal weights from a finite sample. If the weights are selected sub-optimally, this can affect the accuracy of the model-averaged forecasts. Instead of choosing the optimal weights, we consider trimming a set of models before equally averaging forecasts from the selected superior models. Motivated by Hansen et al. (2011), we apply and evaluate the model confidence set procedure when combining mortality forecasts. Data & Methods: The proposed model averaging procedure is motivated by Samuels and Sekkel (2017) based on the concept of model confidence sets as proposed by Hansen et al. (2011) that incorporates the statistical significance of the forecasting performance. As the model confidence level increases, the set of superior models generally decreases. The proposed model averaging procedure is demonstrated via national and sub-national Japanese mortality for retirement ages between 60 and 100+. Results: Illustrated by national and sub-national Japanese mortality for ages between 60 and 100+, the proposed model-average procedure gives the smallest interval forecast errors, especially for males. Conclusion: We find that robust out-of-sample point and interval forecasts may be obtained from the trimming method. By robust, we mean robustness against model misspecification

Mortality forecasting in Colombia from abridged life tables by sex

[EN] BACKGROUND: An adequate forecasting model of mortality that allows an analysis of different population changes is a topic of interest for countries in demographic transition. Phenomena such as the reduction of mortality, ageing, and the increase in life expectancy are extremely useful in the planning of public policies that seek to promote the economic and social development of countries. To our knowledge, this paper is one of the first to evaluate the performance of mortality forecasting models applied to abridged life tables. OBJECTIVE: Select a mortality model that best describes and forecasts the characteristics of mortality in Colombia when only abridged life tables are available. DATA AND METHOD: We used Colombian abridged life tables for the period 1973-2005 with data from the Latin American Human Mortality Database. Different mortality models to deal with modeling and forecasting probability of death are presented in this study. For the comparison of mortality models, two criteria were analyzed: graphical residuals analysis and the hold-out method to evaluate the predictive performance of the models, applying different goodness of fit measures. RESULTS: Only three models did not have convergence problems: Lee-Carter (LC), Lee-Carter with two terms (LC2), and Age-Period-Cohort (APC) models. All models fit better for women, the improvement of LC2 on LC is mostly for central ages for men, and the APC model's fit is worse than the other two. The analysis of the standardized deviance residuals allows us to deduce that the models that reasonably fit the Colombian mortality data are LC and LC2. The major residuals correspond to children's ages and later ages for both sexes. CONCLUSION: The LC and LC2 models present better goodness of fit, identifying the principal characteristics of mortality for Colombia.Mortality forecasting from abridged life tables by sex has clear added value for studying differences between developing countries and convergence/divergence of demographic changes.Support for the research presented in this paper was provided by a grant from the Ministerio de Economía y Competitividad of Spain, project no. MTM2013-45381-P.Diaz-Rojo, G.; Debón Aucejo, AM.; Giner-Bosch, V. (2018). Mortality forecasting in Colombia from abridged life tables by sex. Genus. Journal of Population Sciences (Online). 74(15):1-23. https://doi.org/10.1186/s41118-018-0038-6S1237415Aburto, J.M., & García-Guerrero, V.M. (2015). El modelo aditivo doble multiplicativo. Una aplicacion a la mortalidad mexicaná. Papeles de Población, 21(84), 9–44.Acosta, K., & Romero, J. (2014). Cambios recientes en las principales causas de mortalidad en Colombia. 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(2014). Demography: forecasting mortality, fertility, migration and population data. R package version 1.18. https://CRAN.R-project.org/package=demography .Hyndman, R.J., & Ullah, M.S (2007). Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 51(10), 4942–4956.Kennes, T. (2017). The convergence and robustness of cohort extensions of mortality models. MaRBLe, 1, 36–53.Lee, R., & Carter, L. (1992). Modelling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.Lee, R., & Rofman, R. (1994). Modelación y proyección de la mortalidad en Chile. Notas de Poblacion, 6(59), 183–213.Lee, W. (1997). Characterizing exposure-disease association in human populations using the Lorenz curve and Gini index. Statistics in Medicine, 16(7), 729–739.Levitt, S., & Rubio, M. (2000). Understanding crime in Colombia and what can be done about it. 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La mortalidad y la longevidad en la cuantificación del riesgo actuarial para la población de México. PhD thesis: Universitat de Barcelona.Remund, A., Camarda, C.G., Riffe, T., et al. (2017). A cause-of-death decomposition of the young adult mortality hump. Technical report. Rostock, Germany: Max Planck Institute for Demographic Research.Renshaw, A.E., & Haberman, S. (2003). Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33(2), 255–272.Renshaw, A.E., & Haberman, S. (2006). A cohort-based extensionto the Lee-Carter model for mortality reduction factors. Insurance: Mathematic and Economics, 38(3), 556–570.Reyes, A.R. (2010). Una aproximación al costo fiscal en pensiones como consecuencia del envejecimiento de la población en Colombia y el efecto de la sobre-mortalidad masculina. Master’s thesis: Universidad Nacional de Colombia.Richards, S. (2008). Detecting year-of-birth mortality patterns with limited data. 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Structural breaks in mortality models and their consequences

In recent years, the issue of life expectancy has become of upmost importance to pension providers, insurance companies and the government bodies in the developed world. Significant and consistent improvements in mortality rates and, hence, life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and, hence, quantify the costs of providing for future aging populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age and cohort, and forecast these trends into the future using standard statistical methods. The modeling approaches used failed to capture the effects of any structural change in the trend and, thus, potentially produced incorrect forecasts of future mortality rates. In this paper, we look at a range of leading stochastic models of mortality and test for structural breaks in the trend time series

Implementation of the Technological Plan for Education in Portugal, a School Perspective

International audienceThe Portuguese Ministry of Education has intervened in the Technologies and Information Systems (TIS) of the educational system with a Technological Plan for Education (TPE). The TPE is the Portuguese initiative for ICT in education, and is an intervention in three axis - Technology axis, Contents and Training which cover in an integrated and transverse way all areas related to the modernization of the educational system in Portugal. The full impact generated by this action is of particular importance due to the high performance enabled by the integration of ICT in the management and quality of the educational system thus allowing for an increase in confidence, performance and competitiveness. In this paper we follow a model in the implementation of the TPE in secondary schools. It shows a solution we came up. A strategic plan and is iterative assessment, from the need to address this problem