Penalized Spline Semiparametric Regression for Bivariate Response in Modeling Macro Poverty Indicators - Cinta Rizki Oktarina; Idhia Sriliana; Sigit Nugroho (Universitas Sebelas Maret, 2025)
Semiparametric spline regression has become an increasingly popular method for modeling data due to its flexibility and objectivity, especially as a parameter estimation method. Spline functions are highly effective in semiparametric regression because they offer unique statistical interpretations by segmenting each predictor variable in relation to the response variable. Bivariate semiparametric regression can be applied to data where observations tend to have disparities between regions, making it suitable for poverty data, particularly the poverty depth index and the poverty severity index. The objective of this research is to analyze the models of the poverty depth index and poverty severity index, as well as to perform segmentation and interpretation of these models. This study utilized observations from 60 districts/cities in the southern part of Sumatra. Several predictor variables were considered, including the percentage of households with a floor area of ≤19 m², labor force participation rate, and life expectancy as parametric components, while the nonparametric components included the average length of schooling and the percentage of households with tap water sources. The estimation methods used were penalized least squares and penalized weighted least squares, involving a full search algorithm for selecting the number and location of knots. The results of the study indicated that the penalized weighted least squares method was the best estimator, with an MSE value of 0.3122 and two knots for each predictor, yielding GCV values of 4.3604 and 4.0794.Keywords: semiparametric regression; bivariate response; poverty; knot; penalized weighted least square