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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 Diserahkan: 1 Disember 2015/Diterima: 9 Jun 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 RUJUKAN
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