Analisis Regresi Robust Estimasi Least Trimmed Square dan Estimasi Maximum Likelihood pada Pemodelan IPM di Pulau Sulawesi

Abstract

Sulawesi Island is one of the islands in Indonesia with the second lowest HDI after Papua in 2011-2018, so it is necessary to study more deeply the factors that affect the HDI on Sulawesi Island. One of the methods in modeling is the robust regression method that can be used even though there are outliers in the data. This study aimed to determine the factors that affect HDI in Sulawesi Island using a robust regression model of Least Trimmed Square (LTS) estimation and Maximum Likelihood (M) estimation and to find out the best method for modeling HDI in Sulawesi Island. The robust regression of the LTS estimate has a reasonably high breakdown point value compared to other estimates, while the M-estimate has a high efficiency. The results showed that the factors that affect HDI on the island of Sulawesi are Life Expectancy (UHH), Expected Years of Schooling (HLS), Average Years of Schooling (RLS), and Real Expenditures per capita (PPP). The best model in HDI modeling in Sulawesi Island is a robust regression model with LTS estimation where the standard error is 0.1513, and the R-Square is 99.78%. A very high R-Square value indicates that the ability of the UHH, HLS, RLS, and PPP variables to explain HDI is very good.

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“…Giving this weight makes the estimate quite resistant to outliers so that it does not have a significant impact on the resulting estimator. There are several estimation methods in robust regression, namely the Scale (S) estimator, Maximum Likelihood (M) estimator, Method of Moment (MM) estimator, Least Median of Square (LMS) Estimator, and Least Trimmed of Square (LTS) Estimator (Akolo & Nadjamuddin, 2022) Therefore, based on the above two explanations, it can be concluded that the coefficient of determination (R 2 ) test indicates the ability of all independent variables to jointly explain the diversity of the dependent variable. If the value of R 2 is equal to 0, we know that the independent variable cannot explain the variation in the dependent variable.…”