Sains Malaysiana 48(7)(2019): 1557–1563

http://dx.doi.org/10.17576/jsm-2019-4807-25

Outlier Detection in Multiple Circular Regression Model using DFFITC Statistic

(Pengesanan Nilai Tersisih dalam Model Regresi Berkeliling Berganda menggunakan Statistik DFFITc)

NAJLA AHMED ALKASADI¹, SAFWATI IBRAHIM¹*, ALI H. M. ABUZAID², MOHD IRWAN YUSOFF³, HASHIBAH HAMID⁴, LEOW WAI ZHE⁵ & AMELIA BT ABD RAZAK⁵

¹Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis Indera Kayangan, Malaysia

²Department of Mathematics, Faculty of Science, Al-Azhar University-Gaza, Palestine

³Center for Diploma Studies, S2-L1-26, Kampus Uniciti Sungai Chuchuh, Universiti Malaysia Perlis, 02100 Padang Besar (U), Perlis Indera Kayangan, Malaysia

⁴School of Quantitative Sciences, College of Arts & Sciences, Universiti Utara Malaysia (UUM), 06010 UUM Sintok, Kedah Darul Aman, Malaysia

⁵School of Electrical System Engineering, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis Indera Kayangan, Malaysia

Diserahkan: 16 Oktober 2018/Diterima: 3 Mei 2019

ABSTRACT

This paper presents the identification of outliers in multiple circular regression model (MCRM), where the model studies the relationship between two or more circular variables. To date, most of the published papers concentrating on detecting outliers in circular samples and simple circular regression model with one independent circular variable. However, no related studies have been found for more than one independent circular variable. The existence of outliers could alert the sign and change the magnitude of regression coefficients and may lead to inaccurate model development and wrong prediction. Hence, the intention is to develop an outlier detection procedure using DFFITS statistic for circular case. This method has been successfully used in multiple linear regression model. Therefore, the DFFITc statistic for circular variable has been derived. The corresponding critical values and the performance of the procedure are studied via simulations. The results of simulation studies show that the proposed statistic perform well in detecting outliers in MCRM using DFFITc statistic. The proposed statistic was applied to a real data for illustration purposes.

Keywords: Circular data; circular regression model; DFFITS; outlier

ABSTRAK

Kertas ini membentangkan pengesanan nilai tersisih dalam model regresi berkeliling berganda (MCRM) dengan model tersebut mengkaji hubungan antara dua atau lebih pemboleh ubah berkeliling. Sehingga kini, kebanyakan kertas yang diterbitkan menumpukan ke atas pengesanan nilai tersisih dalam sampel berkeliling dan model regresi berkeliling ringkas untuk satu pemboleh ubah tak bersandar. Walau bagaimanapun, tiada kajian yang berkaitan telah dijumpai untuk lebih daripada satu pemboleh ubah berkeliling tak bersandar. Kewujudan nilai tersisih dapat memberi isyarat tanda dan mengubah perubahan magnitud pekali regresi dan mungkin menyebabkan pembangunan model yang tidak tepat dan ramalan yang salah. Oleh itu, objektif kajian adalah untuk membangunkan kaedah pengesanan nilai tersisih menggunakan statistik DFFITS untuk kes berkeliling. Kaedah ini telah berjaya digunakan dalam model regresi linear berganda. Oleh itu, statistik DFFITc untuk pemboleh ubah berkeliling telah diterbitkan. Nilai genting sepadan dan prestasi prosedur dikaji melalui simulasi. Hasil kajian simulasi menunjukkan bahawa statistik yang dicadangkan menunjukkan prestasi yang baik dalam mengesan nilai tersisih di dalam MCRM menggunakan statistik DFFITc. Statistik yang dicadangkan diaplikasikan kepada data sebenar untuk tujuan ilustrasi.

Kata kunci: Data berkeliling; DFFITS; model regresi berkeliling; nilai tersisih

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*Pengarang untuk surat-menyurat; email: isafwati@gmail.com