Sains Malaysiana 46(2)(2017): 317–326

http://dx.doi.org/10.17576/jsm-2017-4602-17

 

Missing Value Estimation Methods for Data in Linear Functional Relationship Model

(Kaedah Menganggar Data Lenyap menggunakan Model Linear Hubungan Fungsian)

 

ADILAH ABDUL GHAPOR1, YONG ZULINA ZUBAIRI2* & A.H.M. RAHMATULLAH IMON3

 

1Institute of Graduate Studies, University of Malaya, 50603 Kuala Lumpur, Federal Territory

Malaysia

 

2Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur,

Federal Territory, Malaysia

 

3Department of Mathematical Sciences, Ball State University, 47306 Indiana, United States

of America

 

Received: 1 December 2015/Accepted: 9 June 2016

 

ABSTRACT

Missing value problem is common when analysing quantitative data. With the rapid growth of computing capabilities, advanced methods in particular those based on maximum likelihood estimation has been suggested to best handle the missing values problem. In this paper, two modern imputing approaches namely expectation-maximization (EM) and expectation-maximization with bootstrapping (EMB) are proposed in this paper for two kinds of linear functional relationship (LFRM) models, namely LFRM1 for full model and LFRM2 for linear functional relationship model when slope parameter is estimated using a nonparametric approach. The performance of EM and EMB are measured using mean absolute error, root-mean-square error and estimated bias. The results of the simulation study suggested that both EM and EMB methods are applicable to the LFRM with EMB algorithm outperforms the standard EM algorithm. Illustration using a practical example and a real data set is provided.

 

Keywords: Bootstrap; expectation-maximization; linear functional relationship model; missing value

 

ABSTRAK

Data lenyap sering terjadi dalam analisis data kuantitatif. Dengan berkembangnya keupayaan pengiraan, kaedah terkini iaitu kaedah kebolehjadian maksimum merupakan antara cara yang terbaik untuk menguruskan masalah data lenyap. Di dalam kertas ini, dua kaedah gantian moden diperkenalkan iaitu jangkaan pemaksimuman (EM) dan jangkaan pemaksimum bootstrap (EMB) untuk digunakan di dalam model linear hubungan fungsian (LFRM) iaitu LFRM1 bagi model penuh dan LFRM2 bagi model linear hubungan fungsian apabila parameter kecerunan dianggarkan menggunakan kaedah bukan berparameter. Prestasi EM dan EMB diukur berdasarkan purata ralat mutlak, punca purata kuasa dua ralat, dan anggaran terpincang. Melalui simulasi, kami dapati EM dan EMB kedua-duanya boleh digunakan oleh LFRM dan keputusan menunjukkan bahawa algoritma EMB adalah lebih baik daripada algoritma EM. Kajian ini disertakan dengan contoh data set yang sebenar.

 

Kata kunci: Bootsrap; data lenyap; jangkaan pemaksimum; model linear hubungan fungsian

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*Corresponding author; email: yzulina@um.edu.my

 

 

 

 

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