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All Journal Jurnal Ilmu Pertanian Indonesia FORUM STATISTIKA DAN KOMPUTASI Media Statistika Disease Prevention and Public Health Journal JURNAL PETERNAKAN Sosioinforma JUITA : Jurnal Informatika International Journal of Advances in Intelligent Informatics BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) JURNAL ILMIAH PETERNAKAN TERPADU J Statistika: Jurnal Ilmiah Teori dan Aplikasi Statistika Jambura Journal of Mathematics ComTech: Computer, Mathematics and Engineering Applications J-ADIMAS (Jurnal Pengabdian kepada Masyarakat) JURNAL AKUNTANSI KEUANGAN DAN MANAJEMEN Jurnal Pendidikan dan Kebudayaan Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Jurnal Indonesia Sosial Sains Jurnal Natural Xplore: Journal of Statistics Jurnal Pengabdian Masyarakat dan Lingkungan PRAGMATIS Jurnal Manajemen dan Bisnis Jurnal Medika Veterinaria Scientific Journal of Informatics Indonesian Journal of Statistics and Its Applications Jurnal Info Kesehatan
Indahwati
Department Of Statistics, Faculty Of Mathematics And Natural Science, IPB University, Bogor, Indonesia
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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
Performance of LAD-LASSO and WLAD-LASSO on High Dimensional Regression in Handling Data Containing Outliers Cahya, Septa Dwi; Sartono, Bagus; Indahwati, Indahwati; Purnaningrum, Evita
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 4 (2022): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i4.8968

Abstract

In several research areas, it is common to have a dataset with more explanatory variables than the number of observations, called high-dimensional data. This condition can lead to multicollinearity problem. The least absolute shrinkage and selection operator (LASSO) solves the problem by shrinking the estimated coefficient to zero so that it can simultaneously carry on the variable selection and the parameter estimation.  But LASSO performs poorly when the data contains some outliers in the response or explanatory variables. Robust methods have addressed this problem based on the least-absolute-deviation approach, such as LAD-LASSO and WLAD-LASSO. This current research aims to evaluate the performance of the LAD-LASSO and WLAD-LASSO methods on high-dimensional and low-dimensional data containing outliers. To evaluate the performance of these methods, the simulation study was conducted. The simulation study used three scenarios (without outliers, outliers on the response variable (5%, 10%, 15%), outliers both on the response and explanatory variables (5%, 10%, 15%)). We also used the Minimum Regularized Covariance Determinant (MRCD) estimator in calculating the weights on the WLAD-LASSO. The best method from this simulation then will be applied to sembung leaf extract data to identify antioxidant marker compounds in sembung leaf extract. The simulation results show that LAD-LASSO tends to be very tight in selecting, while LASSO tends to be too loose.  Meanwhile, WLAD-LASSO is in the middle of those two techniques and performs the best in identifying the important variables correctly. Even the existence of weights cause WLAD-LASSO more robust against the presence of outliers in the response and explanatory variables compared to LAD-LASSO. Furthermore, performance of these methods on high-dimensional data decrease compared to low-dimensional data. The performance of these methods also tends to decrease when the rate of outlier increases. The WLAD-LASSO was then implemented in actual data to find the compound of antioxidant markers in the sembung leaf extract. The compounds/formulas obtained are Umbelliferone, 12-Hydroxyjasmonic Acid, C22H14N8O2, and Acetyleugenol (with a prediction error is 0.133050). These compounds/formulas can be developed as natural antioxidants and have the potential to be developed as medicinal ingredients.
Co-Authors A. A., Muftih Aditya Ramadhan Agus Mohamad Soleh Agustini , Ni Ketut Yulia Agustini, Ni Ketut Yulia Aji Hamim Wigena Akbar Rizki Alahmad, Ali Omar Aliu, Mufthi Alwi ALIU, MUFTIH ALWI Amelia, Reni Amin, Yudi Fathul Anang Kurnia Anik Djuraidah Antonius Benny Setyawan Ari Handayani Arie Anggreyani Aristawidya, Rafika Assyifa Lala Pratiwi Hamid Aunuddin . Bagus Sartono Budi Susetyo Cahya, Septa Dwi Cahyani Oktarina Chrisinta, Debora Daswati, Oktaviyani Dea Fisyahri Akhilah Putri Dian Kusumaningrum Erfiani Erfiani Erfiani Etis Sunandi Eva Wany, Eva Farit Mochamad Afendi Farit Mohamad Afendi Fatimah Fatimah Fira Nurahmah Al Aminy Fitrianto, Anwar Fulazzaky, Tahira Ghina Fauziah Hanifa Izzati Hari Wijayanto Harismahyanti A., Andi Hasanah, Lailatul I Gusti Putu Purnaba I Made Sumertajaya Iin Maena Indah, Yunna Mentari Irawan Irawan Jaya, Eddy Santosa Julianti, Elisa D Kamil, Farid Ikram Karunia, Nia Kefi Amtiran, Chandraone Putra Khairil Anwar Notodiputro Khikmah, Khusnia Nurul Kholidiah, Kholidiah Khusnia Nurul Khikmah Kristorio, Kevin Kusman Sadik Latifah, Leli Lestari, Nila Lili Puspita Rahayu Miranti, Ita Miranti, Ita Mohammad Masjkur Mualifah, Laily Nissa Mualifah, Laily Nissa Atul Muhammad Nur Aidi Naima Rakhsyanda Narindria, Yasmin Nadhiva Nurul Fadhilah Panjaitan, Intan Juliana Puput Cahya Ambarwati Purnaningrum, Evita Putra, Stefanus Morgan Setyadi Perdana Putri, Christiana Anggraeni Ramdani, Indri Rasyid, Baharun Ray Sastri Regan, Regan Reni Amelia Reni Amelia Reza, Charolina Therezia Rifki Hamdani Rindy Anggun Pertiwi Salvina Salvina Silmi Annisa Rizki Manaf Siti Hafsah Siwi Haryu Pramesti Tina Aris Perhati Titin Agustina Titin Suhartini Titin Suhartini, Titin Utami Dyah Syafitri Vera Maya Santi Vitona, Desi Wahyudi Setyo Yenni Angraini Yuniarty, Titin Zulkarnain, Rizky _ Aunuddin