Indexing
All Issues
Submission
Author Guidelines
Reviewers
Editorial Members
Publication Fee
Vol.1 , No. 4, Publication Date: Sep. 29, 2014, Page: 59-62
. The modelling approach of the GLMs centered on the assumptions of no correlation between the explanatory variables which may be age, cohort, year as the case may be for most of the mortality models. Many mortality models often had inherent trivial correlation between any of the earlier listed variables thus multicollinearity set in. In this paper, a new fitting methodology using Ridge Regression (RR) under the class of shrinkage methods is proposed to tackle the trivial correlation problem, which might be inherent in mortality models via model specification. By way of example, the Age-Period-Cohort model, which exhibits the trivial correlation problem, was used to demonstrate the fitting procedure using Monte-carlo simulation and France mortality real life data set. The results from the monte-carlo simulation and real life data set established the supremacy of the fitting methodology over the existing fitting procedure via mean square error of prediction, log-likelihood and Bayesian Information Criterion (BIC).&picture=http://www.aascit.org/aascit/decorators/img/journal/921.jpg)
| [1] | Oyebayo Olaniran, Department of Statistics, University of Ilorin, PMB 1515, Ilorin, Nigeria. |
| [2] | Moyosola Bamidele, Department of Statistics, University of Ilorin, PMB 1515, Ilorin, Nigeria. |
Some mortality models can be expressed in the form of generalized linear model framework (GLMs). The modelling approach of the GLMs centered on the assumptions of no correlation between the explanatory variables which may be age, cohort, year as the case may be for most of the mortality models. Many mortality models often had inherent trivial correlation between any of the earlier listed variables thus multicollinearity set in. In this paper, a new fitting methodology using Ridge Regression (RR) under the class of shrinkage methods is proposed to tackle the trivial correlation problem, which might be inherent in mortality models via model specification. By way of example, the Age-Period-Cohort model, which exhibits the trivial correlation problem, was used to demonstrate the fitting procedure using Monte-carlo simulation and France mortality real life data set. The results from the monte-carlo simulation and real life data set established the supremacy of the fitting methodology over the existing fitting procedure via mean square error of prediction, log-likelihood and Bayesian Information Criterion (BIC).
Keywords
Ridge Regression, Generalized Linear Models, Age-Period-Cohort Models
Reference
| [01] | Currie, I.D., Durban, M. and Eilers, P.H.C. (2004) Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279-298. |
| [02] | Currie, I.D., Durban, M. and Eilers, P.H.C. (2006) Generalized linear array models with applications to multidimensional smoothing. Journal of the Royal Statistical Society, Series B, 68, 259-280. |
| [03] | Cairns, A.J.G., Blake, D., and Dowd, K. (2006a) “Pricing death: Frameworks for the valuation and securitization of mortality risk”, ASTIN Bulletin, 36: 79-120. |
| [04] | Currie, I. D. (2013). Fitting models of mortality with generalized linear and non-linear models. Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK. |
| [05] | Hoerl, A. E. and Kennard R. W. (1970): Ridge regression biased estimation for non-orthogonal problems: Technometrics 12 (1): 55-67. |
| [06] | Lee, R.D., and Carter, L.R. (1992) “Modeling and forecasting U.S. mortality”, Journal of the American Statistical Association, 87: 659-675. |
| [07] | Mansson K. and Shukur B.M.G. (2011). A Poisson Ridge Regression Estimator. Communication in Statistics Theory and Methods. |
| [08] | McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. London: Chapman and Hall. |
| [09] | R Core Team (2014) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. (http://www.R-project.org). |
| [10] | Renshaw, A.E., and Haberman, S. (2006) “A cohort-based extension to the Lee-Carter model for mortality reduction factors”, Insurance: Mathematics and Economics, 38: 556-570. |
| [11] | Searle, S.R. (1982). Matrix Algebra Useful for Statistics. New York: Wiley. |
