# COMPARISON OF LASSO AND ADAPTIVE LASSO METHODS IN IDENTIFYING VARIABLES AFFECTING POPULATION EXPENDITURE

## Authors

• Atika Rahayu Department of Mathematics, Universitas Islam Negeri Sumatera Utara, Medan, Indonesia
• Ismail Husein Department of Mathematics, Universitas Islam Negeri Sumatera Utara, Medan, Indonesia

## Keywords:

Regression, LASSO, Adaptive LASSO, Comparison, Variables

## Abstract

Abstract: Since 2019, the difference in the increase in per capita expenditure of the population has continued to decline, and the most significant was only IDR 18,464 in 2021, indicating that the level of consumption of the population has not improved significantly, and the turnover of the community's economy is also not good. Multiple linear regression is more appropriate than other types of linear regression because it considers the influence of more than one independent variable on the dependent variable. However, problems may arise in the use of multiple linear regression, such as multicollinearity. To overcome this problem, other methods such as LASSO and adaptive LASSO should be used. Both methods have the ability to overcome multicollinearity between independent variables, thereby reducing the risk of misestimation. Nevertheless, the LASSO and Adaptive LASSO methods have differences in selecting important variables, so it is necessary to compare which method is better in terms of identifying influential variables. Based on the MSE and R-square comparison values, it is concluded that the Adaptive LASSO method model is the best model with a lower MSE value and a higher R-square value of 93%. The variable selection results of the Adaptive LASSO model are population size, number of households, average number of household members, constant price GDP, confirmed cases of COVID-19, human development index, percentage of the poor population, university student participation rate, and open unemployment rate.

GS Cited Analysis

## References

Ardiansyah, M., Notodiputro, K. A., & Sartono, B. (2020). Peningkatan Presisi Dugaan Berat Gabah Melalui Proses Seleksi Peubah Dalam Pembelajaran Mesin Statistika. Jurnal Seminar Nasional Varians, 171–183.

Azis, H., Purnawansyah, Fattah, F., & Putri, I. P.(2020). Performa Klasifikasi K-NN Dan Cross-Validation Pada Data Pasien Pengidap Penyakit Jantung. ILKOM Jurnal Ilmiah. 12 (2), 81-86.

Berrar, D. (2018). Cross-validation. In Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics (Vols. 1–3). https://doi.org/10.1016/B978-0-12-809633-8.20349-X

BPS Provinsi Sumatera Utara. (2022). https://sumut.bps.go.id/subject/154/konsumsi-dan-pengeluaran.html.

Ghozali, I. (2016). Aplikasi Analisis Multivariete dengan Program IBM SPSS 23 (VIII). Semarang: Badan Penerbit Universitas Diponegoro. Cetakan Ke VIII. Semarang: Badan Penerbit Universitas Diponegoro, 14(July).

Hodson, T. O. (2021). Mean Square Error Deconstructed. James: Journal Of Advances In Modeling Earth Systems.

Kuncoro, D. (2022). Kecerdasan Komputasional. Teknik Informatika: Universitas Pancasakti Bekasi.

Melkumova, L. E., & Shatskikh, S. Y. (2017). Comparing Ridge and LASSO estimators for data analysis. Procedia Engineering, 201. https://doi.org/10.1016/j.proeng.2017.09.615

Paiman. (2019). Teknik Analisis Korelasi dan Regresi Ilmu. UPY Press.

Qian, W., & Yang, Y. (2013). Model Selection Via Standard Error Adjusted Adaptive Lasso. 65(2), 295–318.

Rahmawati, F., & Suratman, R. Y. (2022). PERFORMA REGRESI RIDGE DAN REGRESI LASSO PADA DATA DENGAN MULTIKOLINEARITAS. Leibniz: Jurnal Matematika, 2(2).

Retnawati, H. (2017). Pengantar Analisis Regresi Dan Korelasi. FMIPA Pendidikan Matematika.

Sethi, J. K., & Mittal, M. (2021). An efficient correlation based adaptive LASSO regression method for air quality index prediction. Earth Science Informatics, 14(4), 1777–1786. https://doi.org/10.1007/s12145-021-00618-1

Sihombing, P. R., Notodiputro, K. A., & Sartono, B. (2021). Klasifikasi Status Bekerja Individu di Provinsi Banten Tahun 2020 dengan Menggunakan Metode LASSO dan Adaptive LASSO. STATISTIKA Journal of Theoretical Statistics and Its Applications, 21(1). https://doi.org/10.29313/jstat.v21i1.7810

Wang, W., Wang, W., & Ding, E. (2019). Identification of Critical-to-quality Characteristic in Complex Products Based on the Adaptive-Lasso Method. Proceedings of 2019 IEEE 4th Advanced Information Technology, Electronic and Automation Control Conference, IAEAC 2019. https://doi.org/10.1109/IAEAC47372.2019.8998012