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Sains Malaysiana 53(4)(2024): 935-951
http://doi.org/10.17576/jsm-2024-5304-16
Detection of Outliers in Circular Regression
Model via
DFBETAcIS Statistic
(Pengesanan Outlier dalam Model Regresi Bulat melalui Statistik DFBETAcIS
)
INTAN
MASTURA RAMLEE1,2, SAFWATI IBRAHIM1,2,*, LEOW WAI ZHE3 & MOHD IRWAN YUSOFF3
1Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia
2Centre of Excellence for Social Innovation
and Sustainability (COESIS), Universiti Malaysia Perlis, 02600 Arau,
Perlis, Malaysia
3Faculty of Electrical & Technology
Engineering, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02000 Arau, Perlis, Malaysia
Received: 4 July 2023/Accepted: 1 March 2024
Abstract
The outlier issues in circular regression models
have recently received much attention. The presence of outliers may cause the
sign and magnitude of regression coefficients to vary, resulting in inaccurate
model development and incorrect prediction. Many methods for detecting outliers
in a circular regression model have been proposed in previous studies such as COVRATIO, D, M, A, and Chord statistics, but it is suspected
that they are not very successful in the presence of multiple outliers in a
data set since the masking and swamping is not considered in their studies.
This study aimed to develop an outlier detection procedure using DFBETAc
statistic for circular
cases, where this new statistic will investigate and identify multiple outliers
in the Jammalamadaka and Sarma circular regression model (JSCRM) by considering masking and swamping effect.
Monte Carlo simulations are used to determine the corresponding cut-off point
and the power of performance is investigated. The performance of the proposed
statistic is evaluated by the proportion of detected outliers and the rate of
masking and swamping. The simulation procedure is applied at 10% and 20%
contamination levels for varying sample sizes. The results show that the
proposed DFBETAcIS
statistic for JSCRM
successfully detect the outliers. For illustration purposes, this process is
applied to wind direction data.
Keywords: Circular regression model; DFBETAc; outlier
Abstrak
Isu data terpencil dalam model regresi bulat baru-baru ini banyak mendapat perhatian. Kehadiran data terpencil boleh menyebabkan tanda dan magnitud pekali regresi berubah, mengakibatkan pembangunan model
yang tidak tepat dan ramalan yang salah. Banyak kaedah untuk mengesan data terpencil dalam model regresi bulat telah dicadangkan dalam kajian sebelum ini seperti statistik COVRATIO, D, M, A dan Chord tetapi dipercayai bahawa kaedah tersebut tidak begitu berjaya dengan kehadiran berbilang data terpencil dalam set data kerana litupan dan limpahan tidak diambil kira dalam kajian mereka. Kajian ini bertujuan untuk membangunkan prosedur pengesanan data terpencil menggunakan statistik DFBETAc
untuk kes bulatan dengan statistik baharu ini akan mengkaji dan mengenal pasti berbilang data terpencil dalam model regresi bulat Jammalamadaka dan Sarma (JSCRM) dengan mengambil kira kesan litupan dan limpahan. Simulasi Monte Carlo digunakan untuk menentukan titik potong yang sepadan dan kuasa prestasi dikaji. Prestasi statistik yang dicadangkan dinilai oleh perkadaran data terpencil yang dikesan dan kadar litupan dan limpahan. Prosedur simulasi digunakan pada tahap pencemaran 10% dan 20% untuk sampel saiz yang berbeza. Keputusan menunjukkan statistik
DFBETAcIS yang dicadangkan untuk JSCRM berjaya mengesan data terpencil. Untuk tujuan ilustrasi, proses ini digunakan pada data arah angin.
Kata kunci: Data terpencil; DFBETAc;
model regresi bulat
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*Corresponding
author; email: safwati@unimap.edu.my
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