Sains Malaysiana 51(7)(2022): 2237-2247

http://doi.org/10.17576/jsm-2022-5107-24

Extending the GLM Framework of the Lee-Carter Model with Random Forest Recursive Feature Elimination Based Determinants of Mortality

 (Perluasan Model Kerangka GLM Lee-Carter dengan Faktor Penyebab Kematian Berdasarkan Eliminasi Ciri Rekursif Hutan Rawak)

NURUL AITYQAH YAACOB^1,2 DHARINI PATHMANATHAN¹* & IBRAHIM MOHAMED¹

¹Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

²Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Negeri Sembilan, Kampus Kuala Pilah, 72000 Kuala Pilah, Negeri Sembilan Darul Khusus, Malaysia

Diserahkan: 23 Jun 2021/Diterima: 1 Januari 2022

Abstract

The Lee-Carter (LC) model led to the development of many prominent mortality models. This study aims to modify the generalised linear model (GLM) (Poisson, negative binomial, and binomial) framework of the LC model by incorporating factors that affect mortality into the model. The top three factors which affect the mortality for each of the 14 countries studied were selected using the random forest recursive feature elimination (RF-RFE) method which eliminates the least important factors based on the correlation of the predictors with the log-mortality rate. These selected factors were integrated in the form of additional bilinear variates to the GLM models and compared to their original counterparts. The RF-RFE method is effective in selecting the best determinants of mortality by avoiding multicollinearity among predictor variables. The inclusion of the time-factor modulation based on the factors selected improved the model adequacy significantly. Vast improvement was evident in the Poisson and binomial settings. Furthermore, the modified GLM version fits short-base-period data well. This study shows that the inclusion of exogenous determinants of mortality improves the performance of the model significantly.

Keywords: GLM; Lee-Carter model; mortality; random forest; recursive feature elimination

Abstrak

Model Lee-Carter (LC) telah membawa kepada perkembangan banyak model mortaliti yang menyerlah. Kajian ini bertujuan mengubah suai kerangka model linear teritlak (GLM) (Poisson, binomial negatif dan binomial) model LC dengan menggabungkan faktor yang mempengaruhi kematian ke dalam model. Tiga faktor teratas yang mempengaruhi kematian bagi setiap 14 negara yang dikaji, dipilih dengan menggunakan kaedah penghapusan ciri rekursif hutan rawak (RF-RFE) yang berfungsi menyingkirkan faktor yang kurang penting berdasarkan korelasi peramal dengan kadar log kematian. Faktor yang dipilih telah diintegrasikan dalam bentuk bilinear tambahan yang bervariasi dengan model GLM dan kajian perbandingan dengan versi model GLM yang asli telah dijalankan. Kaedah RF-RFE berkesan dalam memilih penentu kematian terbaik dan mengelakkan multikolineariti di antara pemboleh ubah peramal. Modulasi faktor masa yang dimasukkan berdasarkan faktor yang dipilih telah meningkatkan kecukupan model dengan lebih bererti. Peningkatan yang besar dapat dibuktikan pada model Poisson dan binomial. Tambahan pula, versi model GLM yang diubah suai turut sesuai digunakan untuk data jangka masa yang pendek. Kajian ini juga mendedahkan bahawa penggunaan penentu kematian luaran telah meningkatkan prestasi model dengan lebih bererti.

Kata kunci: GLM; hutan rawak; kematian; Model Lee-Carter; penghapusan ciri rekursif

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^*Pengarang untuk surat-menyurat; email: dharini@um.edu.my