Sains Malaysiana 51(12)(2022):
4153-4160
http://doi.org/10.17576/jsm-2022-5112-22
Performance
Analysis and Discrimination Procedure of Two-Group Location Model with Some
Continuous and High-Dimensional of Binary Variables
(Analisis Prestasi dan Prosedur Pembezaan Model Lokasi Dua Kumpulan dengan Sebilangan Pemboleh Ubah Selanjar dan Dimensi Tinggi Pemboleh Ubah Binari)
HASHIBAH
HAMID1,*, FRIDAY ZINZENDOFF OKWONU2,
NOR AISHAH AHAD1 & HASLIZA ABDUL RAHIM3
1School of Quantitative Sciences, UUM
College of Arts and Sciences, Universiti Utara
Malaysia, 06010 UUM Sintok, Kedah, Malaysia
2Department of Mathematics, Delta State
University, Abraka, Delta, P.M.B.1, Nigeria
3School of
Computer and Communication Engineering, Universiti Malaysia
Perlis, 02600 UniMAP Arau, Perlis, Malaysia
Diserahkan: 23
April 2022/Diterima: 26 Ogos 2022
Abstract
This
research’s primary goal was to evaluate the performance analysis of the
recently constructed smoothed location models (SLMs) for discrimination
purposes by combining two kinds of multiple correspondence analysis (MCA) to
handle high dimensionality problems arising from the binary variables. A
previous study of SLM, together with MCA as well as principal component
analysis (PCA), displayed that the misclassification rate was still very high
with respect to a large number of binary variables. Thus, two new SLMs are
constructed in this paper to solve this particular problem. The first model
results from the combination of SLM with Burt MCA (denoted as SLM+Burt), and the second one is with the joint
correspondence analysis (denoted as SLM+JCA). The findings showed that both
models performed well for all sample sizes (n) and all binary variables
(b) under investigation, except n=60 and b=25 for the
SLM+JCA model. Overall, the SLM+JCA model yields a greater performance in
contrast to the SLM+Burt model. Moreover, the concept
and procedures of the discrimination for the two-group classification conducted
in this paper can be extended to multi-class classification as practitioners
often deal with many groups and complexities of variables.
Keywords:
Discrimination; large binary variables; misclassification rate; multiple
correspondence analysis; smoothed location model
Abstrak
Matlamat utama penyelidikan ini adalah untuk menilai analisis prestasi model lokasi terlicin (SLMs) yang dibina sebelum ini untuk tujuan pembezaan dengan menggabungkan dua jenis analisis kesepadanan berganda (MCA) bagi menangani masalah dimensi tinggi yang berlaku daripada pemboleh ubah binari.
Kajian terdahulu mengenai SLM bersama-sama dengan MCA serta analisis komponen utama (PCA), menunjukkan bahawa kadar salah pengelasan masih sangat tinggi dengan sejumlah besar bilangan pemboleh ubah binari.
Oleh itu, dalam kajian ini, dua SLMs baharu dibina untuk menyelesaikan masalah khusus ini. Model pertama terhasil daripada gabungan SLM dengan Burt MCA (ditandakan sebagai SLM+Burt), dan yang kedua adalah dengan analisis kesepadanan bersama (ditandakan sebagai SLM+JCA).
Hasil kajian menunjukkan bahawa kedua-dua model menunjukkan prestasi yang baik untuk semua saiz sampel (n) dan semua pemboleh ubah binari (b) di bawah kajian, kecuali untuk kes n=60 dan b=25 bagi model SLM+JCA. Secara keseluruhan, model SLM+JCA menghasilkan prestasi yang lebih baik berbanding model SLM+Burt. Selain itu, konsep dan prosedur pembezaan untuk pengelasan dua kumpulan yang dijalankan dalam kajian ini boleh diperluaskan kepada pengelasan berbilang kumpulan kerana pengamal sering berurusan dengan banyak kumpulan dan kerumitan pemboleh ubah.
Kata kunci: Analisis kesepadanan berganda; diskriminasi; kadar salah pengelasan; model lokasi terlicin; pembezaan; pemboleh ubah binari besar
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*Pengarang untuk surat-menyurat; email:
hashibah@uum.edu.my
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