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Vol 16 No 4 (2022): BAREKENG: Journal of Mathematics and Its Applications
Articles

THE USE OF PENALIZED WEIGHTED LEAST SQUARE TO OVERCOME CORRELATIONS BETWEEN TWO RESPONSES

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  • Anna Islamiyati,
  • Anisa Anisa,
  • Muhammad Zakir,
  • Nasrah Sirajang,
  • Ummi Sari,
  • Fajar Affan,
  • Muhammad Jayzul Usrah
Anna Islamiyati
Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University
Anisa Anisa
Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University
Muhammad Zakir
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University,
Nasrah Sirajang
Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University
Ummi Sari
Hasanuddin University Teaching Hospital
Fajar Affan
Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University
Muhammad Jayzul Usrah
Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University
DOI: https://doi.org/10.30598/barekengvol16iss4pp1497-1504
Published December 15, 2022
Keywords
  • age,
  • height,
  • knots,
  • two responses,
  • weighted penalized,
  • weight
    • ...More
    Less
How to Cite
[1]
A. Islamiyati, “THE USE OF PENALIZED WEIGHTED LEAST SQUARE TO OVERCOME CORRELATIONS BETWEEN TWO RESPONSES”, BAREKENG: J. Math. & App., vol. 16, no. 4, pp. 1497-1504, Dec. 2022.

Copyright (c) 2022 Anna Islamiyati, Anisa Anisa, Muhammad Zakir, Nasrah Sirajang, Ummi Sari, Fajar Affan, Muhammad Jayzul Usrah

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

The non-parametric regression model can consider two correlated responses. However, for these conditions, we cannot use the usual estimation process because there are violations of assumptions. To solve this problem, we use a penalized weighted least square involving knots, smoothing parameters, and weighting in the estimation criteria simultaneously. The estimation process involves a weighted criteria matrix  in the estimation criteria. Estimation results show that the estimated two-response non-parametric regression function with penalized spline is a linear estimation class in y response observation and depends on the knot point and smoothing parameter. Furthermore, the use of the model on toddler growth data shows some changes in the pattern of weight and height gain. The pattern segmentation that experienced a gradual increase was age 7-43 months for weight and age 6-54 months for height

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References

  1. A. Islamiyati, Raupong, and Anisa, “Use of penalized spline linear to identify change in pattern of blood sugar based on the weight of diabetes patients,” Int. J. Acad. Appl. Res., vol. 3, no. 12, pp. 75–78, 2019.
  2. A. Islamiyati, Fatmawati, and N. Chamidah, “Changes in blood glucose 2 hours after meals in type 2 diabetes patients based on length of treatment at Hasanuddin University Hospital, Indonesia,” Rawal Med. J., vol. 45, no. 1, pp. 31–34, 2020.
  3. N. Chamidah, K. H. Gusti, E. Tjahjono, and B. Lestari, “Improving of classification accuracy of cyst and tumor using local polynomial estimator,” Telkomnika (Telecommunication Comput. Electron. Control., vol. 17, no. 3, pp. 1492–1500, 2019, doi: 10.12928/TELKOMNIKA.V17I3.12240.
  4. I. N. Budiantara, V. Ratnasari, M. Ratna, W. Wibowo, N. Afifah, and D. P. Rahmawati, “Modeling percentage of poor people in Indonesia using kernel and fourier series mixed in nonparametric regression,” Investig. Operacional, vol. 40, no. 4, pp. 538–551, 2019.
  5. N. P. A. M. Mariati, I. N. Budiantara, and V. Ratnasari, “Modeling poverty percentages in the papua islands using fourier series in nonparametric regression multivariable,” J. Phys. Conf. Ser., vol. 1397, no. 1, pp. 1–7, 2019, doi: 10.1088/1742-6596/1397/1/012071.
  6. X. C. Zhou and J. G. Lin, “Wavelet estimator in nonparametric regression model with dependent error’s structure,” Commununication Stat. – Theory Methods, vol. 43, no. 22, pp. 4707–4722, 2014.
  7. A. Islamiyati, A. Kalondeng, N. Sunusi, M. Zakir, and A. K. Amir, “Biresponse nonparametric regression model in principal component analysis with truncated spline estimator,” J. King Saud Univ. - Sci., vol. 34, no. 3, pp. 1–9, 2022, doi: 10.1016/j.jksus.2022.101892.
  8. B. Lestari, Fatmawati, I. N. Budiantara, and N. Chamidah, “Smoothing parameter selection method for multiresponse nonparametric regression model using smoothing spline and Kernel estimators approaches,” J. Phys. Conf. Ser., vol. 1397, no. 1, 2019, doi: 10.1088/1742-6596/1397/1/012064.
  9. A. Islamiyati, N. Sunusi, A. Kalondeng, F. Fatmawati, and N. Chamidah, “Use of two smoothing parameters in penalized spline estimator for bi-variate predictor non-parametric regression model,” J. Sci. Islam. Repub. Iran, vol. 31, no. 2, pp. 175–183, 2020, doi: 10.22059/JSCIENCES.2020.286949.1007435.
  10. Musafirah, A. Islamiyati, and N. Sunusi, “Estimation of penalized spline linear regression models through robust M estimator,” Int. J. Acad. Appl. Res., vol. 5, no. 11, pp. 166–168, 2021.
  11. Q. Zou and Z. Zhu, “M-estimators for single-index model using b-spline,” Metrika, vol. 77, pp. 225–246, 2014.
  12. W. N. A. Puteri, A. Islamiyati, and A. Anisa, “Penggunaan regresi kuantil multivariat pada perubahan trombosit pasien demam berdarah dengue,” ESTIMASI J. Stat. Its Appl., vol. 1, no. 1, pp. 1–9, 2020, doi: 10.20956/ejsa.v1i1.9224.
  13. A. Islamiyati, “Spline longitudinal multi-response model for the detection of lifestyle-based changes in blood glucose of diabetic patients,” Curr. Diabetes Rev., vol. 18, no. 7, pp. 98–104, 2021, doi: 10.2174/1573399818666211117113856.
  14. A. Islamiyati, Fatmawati, and N. Chamidah, “Penalized spline estimator with multi smoothing parameters in bi-response multi-predictor nonparametric regression model for longitudinal data,” Songklanakarin J. Sci. Technol., vol. 42, no. 4, pp. 897–909, 2020.
  15. W. Ramadan, N. Chamidah, B. Zaman, L. Muniroh, and B. Lestari, “Standard growth chart of weight for height to determine wasting nutritional status in East Java based on semiparametric least square spline estimator,” IOP Conf. Ser. Mater. Sci. Eng., vol. 546, no. 5, pp. 1–8, 2019, doi: 10.1088/1757-899X/546/5/052063.
  16. R. Hidayat, I. N. Budiantara, B. W. Otok, and V. Ratnasari, “The regression curve estimation by using mixed smoothing spline and kernel (MsS-K) modeltle,” Commun. Stat. - Theory Methods, vol. 50, no. 17, pp. 3942–3953, 2021.
  17. A. Islamiyati, Fatmawati, and N. Chamidah, “Ability of covariance matrix in bi-response multi-prredictor penalized spline model through longitudinal data simulation,” Int. J. Acad. Appl. Res., vol. 3, no. 3, pp. 8–11, 2019.
  18. A. Islamiyati, Fatmawati, and N. Chamidah, “Estimation of covariance matrix on bi-response longitudinal data analysis with penalized spline regression,” J. Phys. Conf. Ser., vol. 979, no. 1, pp. 1–7, 2018, doi: 10.1088/1742-6596/979/1/012093.
  19. A. Islamiyati, A. Kalondeng, and U. Sari, “Estimating the confidence interval of the regression coefficient of the blood sugar model through a multivariable linear spline with known variance,” Stat. Transit., vol. 23, no. 1, pp. 201–212, 2022, doi: 10.21307/stattrans-2022-012.
  20. V. Makarenkov, A. Boc, J. Xie, P. Peres-Neto, F. J. Lapointe, and P. Legendre, “Weighted bootstrapping: A correction method for assessing the robustness of phylogenetic trees,” BMC Evol. Biol., vol. 10, no. 1, pp. 3–16, 2010, doi: 10.1186/1471-2148-10-250.
  21. A. Islamiyati, “Model regresi spline untuk data longitudinal dengan penalized likelihood pada pasien diabeted mellitus tipe II di Rumah Sakit Wahidin Sudirohusodo Makassar,” 2009.
  22. N. Chamidah, E. Tjahjono, A. R. Fadilah, and B. Lestari, “Standard growth charts for weight of children in East Java using local linear estimator,” J. Phys. Conf. Ser., vol. 1097, no. 1, pp. 1–6, 2018, doi: 10.1088/1742-6596/1097/1/012092.
  23. N. Chamidah and T. Saifudin, “Estimation of children growth curve based on kernel smoothing in multi-response nonparametric regression,” Appl. Math. Sci., vol. 7, no. 37–40, pp. 1839–1847, 2013, doi: 10.12988/ams.2013.13168.