Quantile regression modeling with group least absolute shrinkage and selection operator classification on tuberculosis data

Abstract

Tuberculosis (TB) is one of the top 10 causes of death in the world and is a deadly infectious disease in Indonesia. One of Indonesia's provinces that contributed the most TB cases in 2018 was South Sulawesi, with 84 cases per 100,000 population. This study aims to identify variables that can explain the proportion of TB cases in South Sulawesi, potentially leading to more effective prevention and treatment strategies. The data used has many predictor variables, and there are outliers. Quantile regression can be used to overcome outlier data, but it cannot overcome multicollinearity problems. Multicollinearity causes the variance of the estimated parameters to be too large and reduces the accuracy of the estimates, thus requiring a different approach to data analysis. There are various methods for handling regression analysis on data that experiences multicollinearity problems. One of the most commonly known penalized regression methods is Group LASSO. Group LASSO can be used to select variables and overcome multicollinearity. In this study, six naturally formed sector group variables are thought to influence the proportion of TB cases. Quantile regression modeling with LASSO group penalties was carried out using 3 quantile levels, namely (0.25, 0.5, and 0.75). The results of the quantile regression analysis with the LASSO penalty group obtained a different model for each quantile. The best model that is able to explain the proportion of TB cases obtained at the 0.5 quantile level with an R² value of 0.99 is closer to 1 than the other quantile model levels.