Sains Malaysiana 51(2)(2022): 599-607

http://doi.org/10.17576/jsm-2022-5102-23

Outlier Detection in Balanced Replicated Linear Functional Relationship Model

(Pengesanan Data Terpencil dalam Model Hubungan Fungsian Linear Bereplika Seimbang)

AZURAINI MOHD ARIF^1,2, YONG ZULINA ZUBAIRI³* & ABDUL GHAPOR HUSSIN⁴

¹Institute of Advanced Studies, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

²Centre for Foundation Studies, National Defence University of Malaysia, 57000 Kuala Lumpur, Federal Territory, Malaysia

³Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

⁴Faculty of Defence Science and Technology, National Defence University of Malaysia, 57000 Kuala Lumpur, Federal Territory, Malaysia

Received: 2 February 2021/Accepted: 19 June 2021

ABSTRACT

Identification of outlier in a dataset plays an important role because their existence will affect the parameter estimation. Based on the idea of COVRATIO statistic, we modified the procedure to accommodate for replicated linear functional relationship model (LFRM) in detecting the outlier. In this replicated model, we assumed the observations are equal and balanced in each group. The derivation of covariance matrices using Fisher Information Matrices is also given for balanced replicated LFRM. Subsequently, the cut-off points and the power of performance are obtained via a simulation study. Results from the simulation studies suggested that the proposed procedure works well in detecting outliers for balanced replicated LFRM and we illustrate this with a practical application to a real data set. The implication of the study suggests that with some modification to the procedures in COVRATIO, one could apply such a method to identify outliers when modelling balanced replicated LFRM which has not been explored before.

Keywords: Covariance matrix; covratio; influential observation; linear functional relationship model; outliers

ABSTRAK

Pengesanan data terpencil di dalam set data adalah penting kerana kewujudannya akan mengganggu penganggaran nilai parameter. Berdasarkan idea statistik COVRATIO, kami mengubah suai prosedur tersebut supaya bersesuaian bagi model hubungan fungsian linear bereplika dan seimbang dalam pengesanan data terpencil. Setiap unsur dalam kumpulan adalah sama dan seimbang dalam model replikasi ini. Pembentukan matriks kovarians melalui matrik maklumat Fisher juga diberikan bagi model ini. Seterusnya, titik potongan dan kuasa prestasi bagi kaedah yang dicadangkan diperoleh melalui kajian simulasi. Hasil keputusan daripada kajian simulasi menunjukkan prosedur yang dicadangkan berfungsi dengan baik dalam pengesanan data terpencil untuk model hubungan fungsian linear bereplika dan seimbang dan kami memberikan contoh ke atas set data sebenar. Implikasi daripada kajian ini menunjukkan bahawa kita boleh mengesan data terpencil dengan sedikit pengubahsuaian terhadap prosedur COVRATIO bagi model hubungan fungsian linear bereplika dan seimbang kerana pengesanan data terpencil menggunakan model ini masih belum lagi diteroka.

Kata kunci: Covratio; data berpengaruh; matriks kovarians; model hubungan fungsian linear; terpencil

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*Corresponding author; email: yzulina@um.edu.my