Introduction of a journal article: Multilevel Regression Analysis with Maximum Likelihood Method
Multilevel regression is a model utilized in hierarchical (nested) data structures (Yulian and Pawitan, 2017). The multilevel model is a statistical method developed from simple regression. Its development is based on the observation that research often reveals differences among the sources of respondents studied in different cases, and that data is hierarchical (having a nested structure) and clustered. Goldstein (1995) introduced the development of regular regression to address issues arising from hierarchical data, namely multilevel modeling analysis.
In the contemporary era, hierarchical data is frequently encountered in survey research where observational units originate from groups. For instance, in a dataset, observed objects are grouped, and variables are defined at different levels. Levels in multilevel models denote the hierarchical data structure. The lowest level is referred to as level 1, and the highest level is termed level 2 (Tantular, Aunuddin, and Wijayanto, 2009). Multilevel methods are commonly applied in educational, social, and health-related cases, especially with hierarchically structured population data.
In this study, the research focus lies on social cases related to population density. Population density is the ratio of population per square kilometer. In developing countries like Indonesia, issues arise with uneven population density across regions, including in Sumatera Selatan Province. In 2020, the population density in Sumatera Selatan Province reached 92.45 people/km², with Palembang city having the highest population density at 4,519.93 people/km² and Musi Rawas Utara district with the lowest density at 31.43 people/km² (Badan Pusat Statistika, 2021).
Uneven population density can lead to economic disparities within communities. Each region has its own issues affecting population density, while government efforts to address this often involve global policies. To tackle this issue, multilevel regression is employed because the independent variables used have a hierarchical structure at the district and sub-district levels, with parameter estimation using Maximum Likelihood Methods.
A multilevel regression analysis with maximum likelihood method has been conducted by Tantular, Aunuddin, and Wijayanto in 2009, selecting the best multilevel regression model with the dependent variable in this study being the final semester exam scores in Statistics Analysis course for postgraduate students at Institut Pertanian Bogor, and the independent variables at level 1 being the students’ first exam scores, at level 2 being the first exam scores at the program level, and at level 3 being the first exam scores at the class level.
Therefore, this study employs multilevel regression analysis using maximum likelihood method to elucidate factors influencing population density in Sumatera Selatan Province in 2020.
References:
Badan Pusat Statistik. 2021. Provinsi Sumatera Selatan Dalam Angka 2021. Badan Pusat Statistik Provinsi Sumatera Selatan, Palembang.
Tantular, B., Aunuddin, and Wijayanto, H. 2009. Pemilihan Model Regresi Linier Multilevel Terbaik. Forum Statistika dan Komputasi. 14(2): 1–7.
Yulian, E. and Pawitan, G. 2017. Pemodelan Status Usaha (Pengusaha dan Pekerja/Karyawan) Menggunakan Regresi Logistik Multilevel. Jurnal Matematika MANTIK. 3(1): 32–40.