Sains Malaysiana 52(12)(2023): 3879-3892

http://doi.org/10.17576/jsm-2023-5212-19

An Efficient Method of Identification of Influential Observations in Multiple Linear Regression and Its Application to Real Data

 (Kaedah yang Cekap bagi Pengecaman Cerapan Berpengaruh dalam Model Regresi Linear Berganda dan Kegunaannya dalam Set Data Sebenar)

HABSHAH MIDI^1,* , HASAN TALIB HENDI¹ , HASSAN URAIBI², JAYANTHI ARASAN ³ &  SHELAN SAIED ISMAEEL⁴

¹Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

²Department of Statistics, University of Al-Qadisiyah, IRAQ

 ³Department of Mathematics & Statistics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

⁴Department of Mathematics, Faculty of Science, University of Zakho, Iraq

Diserahkan: 20 Jun 2023/Diterima: 14 November 2023

Abstract

Influential observations (IOs) are those observations which either alone or together with several other observations have detrimental effect on the computed values of various estimates. As such, it is very important to detect their presence. Several methods have been proposed to identify IOs that include the fast improvised influential distance (FIID). The FIID method has been shown to be more efficient than some existing methods. Nonetheless, the shortcoming of the FIID method is that, it is computationally not stable, still suffers from masking and swamping effects, time consuming issues and not using proper cut-off point. As a solution to this problem, a new robust version of influential distance method (RFIID) which is based on Reweighted Fast Consistent and High Breakdown (RFCH) estimator is proposed.  The results of real data and Monte Carlo simulation study indicate that the RFIID able to correctly separate the IOs from the rest of data with the least computational running times, least swamping effect and no masking effect compared to the other methods in this study.

Keywords: Good leverage point; influential distance; influential observations; Reweighted Fast Consistent and High Breakdown (RFCH) estimator

Abstrak

Cerapan berpengaruh (IO) ditakrifkan sebagai cerapan sama ada bersendirian atau bersama dengan beberapa cerapan lain yang mempunyai kesan memudaratkan ke atas nilai kiraan pelbagai anggaran. Oleh itu, sangat penting untuk mengecam kehadiran cerapan berpengaruh. Beberapa kaedah telah dicadangkan untuk mengecam IO termasuk kaedah penambahbaikan jarak berpengaruh pantas (FIID). Kaedah FIID telah ditunjukkan lebih cekap dibandingkan dengan kaedah sedia ada. Walau bagaimanapun, kaedah FIID mempunyai kelemahan iaitu pengiraannya tidak stabil, masih mempunyai kesan penyorokan dan limpahan, isu masa pengiraan yang panjang dan tidak menggunakan titik genting yang betul. Kaedah teguh versi baharu bagi jarak berpengaruh yang berasaskan penganggar berpemberat konsisten pantas dan titik musnah tinggi (RFIID) dicadangkan untuk mengatasi masalah ini. Keputusan data sebenar dan kajian simulasi Monte Carlo menunjukkan RFIID berupaya untuk mengasingkan IO daripada keseluruhan data dengan masa pengiraan paling singkat, kesan limpahan paling kecil tanpa kesan penyorokan dibandingkan dengan kaedah lain dalam kajian ini.

Kata kunci: Cerapan berpengaruh; jarak berpengaruh; penganggar pantas tekal berpemberat dan titik musnah tinggi; titik tuasan baik

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*Pengarang untuk surat-menyurat; email: habshah@upm.edu.my