Penalized Spline Semiparametric Regression for Bivariate Response in Modeling Macro Poverty Indicators

Cinta Rizki Oktarina, Idhia Sriliana, Sigit Nugroho

Abstract

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

References

I. N. Budiantara, Regresi Nonparametrik Spline Truncated. Surabaya: ITS Press, 2019.

P. P. Gabrela, J. D. T. Purnomo, and I. N. Budiantara, “The estimation of mixed truncated spline and fourier series estimator in bi-response nonparametric regression,” AIP Conf. Proc., vol. 2903, no. 1, 2023, doi: 10.1063/5.0177224.

N. Y. Adrianingsih, I. N. Budiantara, and J. D. T. Purnomo, “Mixture model nonparametric regression and its application,” J. Phys. Conf. Ser., vol. 1842, no. 1, 2021, doi: 10.1088/1742-6596/1842/1/012044.

W. Griggs, Penalized Spline Regression and Its Application. Whitman College, 2013.

A. R. Fadilah, A. Fitrianto, and I. M. Sumertajaya, “Outlier identification on penalized spline regression modeling for poverty gap index in Java,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 4, pp. 1231–1240, 2022, doi: 10.30598/barekengvol16iss4pp1231-1240.

W. P. Aji, “Pemodelan faktor-faktor yang mempengaruhi indeks keparahan kemiskinan pada tahun 2015 menggunakan regresi spline truncated,” Institut Teknologi Seputuh Nopember, 2018. [Online]. Available: https://repository.its.ac.id/51114/1/1313100034-undergraduate_theses.pdf

D. C. Montgomery, E. A. Peck, and G. . Vinning, Linear Regression Analysis. John Wiley & Sons, Inc, 2021. doi: 10.2307/1268395.

D. N. Gujarati, Econometrics by Example, 2nd ed. Palgrave, 2015.

R. Jhonson and D. Winchern, Applied Multivariate Statistical Analysis. Pearson Education Limited, 2014.

A. C. Rencher and W. F. Cristensen, Methods of multivariate analysis. A JOHN WILEY & SONS, INC., PUBLICATION, 2012. doi: 10.5860/choice.33-1586.

H. Nurcahayani, I. N. Budiantara, and I. Zain, “The curve estimation of combined truncated spline and fourier series estimators for multiresponse nonparametric regression,” Mathematics, vol. 9, no. 10, 2021, doi: 10.3390/math9101141.

Z. Azizah, “Interval Konfidensi untuk Parameter Model Regresi Semiparametrik Birespon dengan Pendekatan Spline Truncated (Aplikasi pada Data Kemiskinan dan Pengeluaran Per Kapita Makanan Provinsi Jawa Timur),” Institut Teknologi Seputuh Nopember, 2018.

P. . Green and B. . Silverman, Nonparametric Regression and Generalized Linear Models. Springer Science Business Media, 1994.

L. Yang and Y. Hong, “Adaptive penalized splines for data smoothing,” Comput. Stat. Data Anal., vol. 108, pp. 70–83, 2017, doi: 10.1016/j.csda.2016.10.022.

X. Li et al., “A practical and effective regularized polynomial smoothing (RPS) method for high-gradient strain field measurement in digital image correlation,” Opt. Lasers Eng., vol. 121, no. April, pp. 215–226, 2019, doi: 10.1016/j.optlaseng.2019.04.017.

G. Wahba, Spline Models for Observational Data. Pennsylvania: Society For Industrial And Applied Mathematics., 1990.

D. Ruppert, M. P. Wand, and R. . Carroll, Semiparametric Regression. Cambridge University Press, 2003. doi: 10.1201/9781420091984-c17.

DOI: https://doi.org/10.13057/ijas.v8i1.94370

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