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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