Nonparametric Spline Truncated Regression with Knot Point Selection Method Generalized Cross Validation and Unbiased Risk

Authors

  • Tutik Handayani Statistics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda
  • Sifriyani Sifriyani Statistics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda
  • Andrea Tri Rian Dani Statistics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda

DOI:

https://doi.org/10.31764/jtam.v7i3.14034

Keywords:

GCV, Nonparametric Regression, Linear Truncated Spline Stunting, UBR.

Abstract

Nonparametric regression approaches are used when the shape of the regression curve between the response variable and the predictor variable is assumed to be unknown. Nonparametric excess regression has high flexibility. A frequently used nonparametric regression approach is a truncated spline that has excellent ability to handle data whose behavior is variable at certain sub-intervals. The aim of this study was to obtain the best model of multivariable nonparametric regression with linear and quadratic truncated spline approaches using Generalized Cross Validation (GCV) and Unbiased Risk (UBR) methods and to find out the factors influencing stunting prevalence in Indonesia in 2021. The data used are the prevalence of stunting as a response variable and the predictor variable used by the percentage of infants receiving Exclusive breastfeeding for 6 months, the percentage of households with proper sanitation, the percentage of toddlers receiving Early Childhood Cultivation (IMD), the percentage of the poor population, and the percentage of pregnant womenIt's a risk. Results show that the best linear and quadratic nonparametric spline truncated regression model in modeling the stunting prevalence is linear truncated spline using the GCV method with three knot points. This model has the minimum GCV value of 7.29 with MSE value of 1.82. Factors influencing the incidence of stunting in Indonesia in 2021 include the percentage variable of infants receiving Exclusive breastfeeding for 6 months, the percentage of households with proper sanitation, the percentage of poor people, and the percentage of pregnant women at risk of KEK.

 

References

Almoosawi, S., Jones, A. R., Parkinson, K. N., Pearce, M. S., Collins, H., & Adamson, A. J. (2016). Parental Perception of Weight Status: Influence on Children’s Diet in the Gateshead Millennium Study. PLOS ONE, 11(2), e0144931. https://doi.org/10.1371/journal.pone.0144931

Cheng, T. S., Loy, S. L., Cheung, Y. B., Chan, J. K. Y., Tint, M. T., Godfrey, K. M., Gluckman, P. D., Kwek, K., Saw, S. M., Chong, Y.-S., Lee, Y. S., Yap, F., & Lek, N. (2016). Singaporean Mothers’ Perception of Their Three-year-old Child’s Weight Status: A Cross-Sectional Study. PLOS ONE, 11(1), e0147563. https://doi.org/10.1371/journal.pone.0147563

da Silva, I. C. M., França, G. V, Barros, A. J., Amouzou, A., Krasevec, J., & Victora, C. G. (2018). Socioeconomic Inequalities Persist Despite Declining Stunting Prevalence in Low- and Middle-Income Countries. The Journal of Nutrition, 148(2), 254–258. https://doi.org/10.1093/jn/nxx050

Danaei, G., Andrews, K. G., Sudfeld, C. R., Fink, G., McCoy, D. C., Peet, E., Sania, A., Smith Fawzi, M. C., Ezzati, M., & Fawzi, W. W. (2016). Risk Factors for Childhood Stunting in 137 Developing Countries: A Comparative Risk Assessment Analysis at Global, Regional, and Country Levels. PLOS Medicine, 13(11), e1002164. https://doi.org/10.1371/journal.pmed.1002164

Desyanti, C., & Nindya, T. S. (2017). Hubungan Riwayat Penyakit Diare dan Praktik Higiene dengan Kejadian Stunting pada Balita Usia 24-59 Bulan di Wilayah Kerja Puskesmas Simolawang, Surabaya. Amerta Nutrition, 1(3), 243. https://doi.org/10.20473/amnt.v1i3.2017.243-251

Dewi, A. R., Dewi, Y. L. R., & Murti, B. (2019). Life Course Factors Associated with Stunting in Children Aged 2-5 Years: A Path Analysis. Journal of Maternal and Child Health, 4(5), 348–357. https://doi.org/10.26911/thejmch.2019.04.05.09

Drennen, C. R., Coleman, S. M., Ettinger de Cuba, S., Frank, D. A., Chilton, M., Cook, J. T., Cutts, D. B., Heeren, T., Casey, P. H., & Black, M. M. (2019). Food Insecurity, Health, and Development in Children Under Age Four Years. Pediatrics, 144(4). https://doi.org/10.1542/peds.2019-0824

Geberselassie, S. B., Abebe, S. M., Melsew, Y. A., Mutuku, S. M., & Wassie, M. M. (2018). Prevalence of stunting and its associated factors among children 6-59 months of age in Libo-Kemekem district, Northwest Ethiopia; A community based cross sectional study. PLOS ONE, 13(5), e0195361. https://doi.org/10.1371/journal.pone.0195361

Hendraswari, C. A., Purnamaningrum, Y. E., Maryani, T., Widyastuti, Y., & Harith, S. (2021). The Determinants of Stunting in 24-59 Month-Old Children in Kulon Progo District 2019. Kesmas: National Public Health Journal, 16(2). https://doi.org/10.21109/kesmas.v16i2.3305

Indanah, I., Wanda, D., & Nurhaeni, N. (2022). Empowerment of Parents with Stunting Children. Jurnal Aisyah : Jurnal Ilmu Kesehatan, 7(4). https://doi.org/10.30604/jika.v7i4.1183

Koshy, B., Srinivasan, M., Gopalakrishnan, S., Mohan, V. R., Scharf, R., Murray-Kolb, L., John, S., Beulah, R., Muliyil, J., & Kang, G. (2022). Are early childhood stunting and catch-up growth associated with school age cognition?—Evidence from an Indian birth cohort. PLOS ONE, 17(3), e0264010. https://doi.org/10.1371/journal.pone.0264010

Latuihamallo, A., Margawati, A., Mexitalia, M., Ediati, A., & Syauqy, A. (2022). Differences in Development and Diet of Stunting and Non-Stunting Children in the Rowosari Health Center Work Area, Semarang, Indonesia. Jurnal Gizi Indonesia (The Indonesian Journal of Nutrition), 10(2), 161–167. https://doi.org/10.14710/jgi.10.2.161-167

Liem, S., Marta, Dr. R. F., & Panggabean, Prof. Dr. phil. H. (2019). Sanitation Behavior and Risk of Stunting: Understanding the Discourse of a Public Service Announcement. Jurnal The Messenger, 11(2), 168. https://doi.org/10.26623/themessenger.v11i2.1317

Mediani, H. S. (2020). Predictors of Stunting Among Children Under Five Year of Age in Indonesia: A Scoping Review. Global Journal of Health Science, 12(8), 83. https://doi.org/10.5539/gjhs.v12n8p83

Mehedi Hasan Abid, Dm., Haque, A., & Kamrul Hossain, Md. (2021). Factors Causing Stunting Among Under-Five Children in Bangladesh (pp. 45–53). https://doi.org/10.1007/978-981-15-5856-6_5

Nahar, B., Hossain, M., Mahfuz, M., Islam, M. M., Hossain, M. I., Murrayâ€Kolb, L. E., Seidman, J. C., & Ahmed, T. (2020). Early childhood development and stunting: Findings from the MALâ€ED birth cohort study in Bangladesh. Maternal & Child Nutrition, 16(1). https://doi.org/10.1111/mcn.12864

Padatuan, A. B., Sifriyani, S., & Prangga, S. (2021). Pemodelan Angka Harapan Hidup Dan Angka Kematian Bayi Di Kalimantan Dengan Regresi Nonparametrik Spline Birespon. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 15(2), 283–296. https://doi.org/10.30598/barekengvol15iss2pp283-296

Park, S. H. (2017). Asian Parents’ Perception of Child Weight Status: A Systematic Review. Journal of Child and Family Studies, 26(9), 2363–2373. https://doi.org/10.1007/s10826-017-0765-x

Pasarella, M. D., Sifriyani, S., & Amijaya, F. D. T. (2022). Nonparametrik Regression Model Estimation With The Fourier Series The Fourier Series Approach And ITS Application To The Accumulative Covid-19 Data In Indonesia. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(4), 1167–1174. https://doi.org/10.30598/barekengvol16iss4pp1167-1174

Purnaraga, T., Sifriyani, S., & Prangga, S. (2020). Regresi Nonparamaetrik Spline Pada Data Laju Pertumbuhan Ekonomi Di Kalimantan. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 14(3), 343–356. https://doi.org/10.30598/barekengvol14iss3pp343-356

Remmers, T., van Grieken, A., Renders, C. M., Hirasing, R. A., Broeren, S. M. L., & Raat, H. (2014). Correlates of Parental Misperception of Their Child’s Weight Status: The ‘Be Active, Eat Right’ Study. PLoS ONE, 9(2), e88931. https://doi.org/10.1371/journal.pone.0088931

Schmidt, C. W. (2014). Beyond Malnutrition: The Role of Sanitation in Stunted Growth. Environmental Health Perspectives, 122(11). https://doi.org/10.1289/ehp.122-A298

Sifriyani, Ilmi, H., & Mar’ah, Z. (2021). Application of Nonparametric Geographically Weighted Spline Regression Model for Spatial Mapping of Open Unemployment Rate in Kalimantan. Journal of Physics: Conference Series, 2123(1), 012038. https://doi.org/10.1088/1742-6596/2123/1/012038

Sifriyani, S., Rasjid, M., Rosadi, D., Anwar, S., Wahyuni, R. D., & Jalaluddin, S. (2022). Spatial-Temporal Epidemiology of COVID-19 Using a Geographically and Temporally Weighted Regression Model. Symmetry, 14(4), 742. https://doi.org/10.3390/sym14040742

Singh, A., Upadhyay, A. K., & Kumar, K. (2017). Birth Size, Stunting and Recovery from Stunting in Andhra Pradesh, India: Evidence from the Young Lives Study. Maternal and Child Health Journal, 21(3), 492–508. https://doi.org/10.1007/s10995-016-2132-8

Sudfeld, C. R., Charles McCoy, D., Danaei, G., Fink, G., Ezzati, M., Andrews, K. G., & Fawzi, W. W. (2015). Linear Growth and Child Development in Low- and Middle-Income Countries: A Meta-Analysis. Pediatrics, 135(5), e1266–e1275. https://doi.org/10.1542/peds.2014-3111

Torlesse, H., Cronin, A. A., Sebayang, S. K., & Nandy, R. (2016). Determinants of stunting in Indonesian children: evidence from a cross-sectional survey indicate a prominent role for the water, sanitation and hygiene sector in stunting reduction. BMC Public Health, 16(1), 669. https://doi.org/10.1186/s12889-016-3339-8

Yulianti, I., Nurasmi, N., & Padlilah, R. (2022). Stunting Risk Factors In Children Under 5 Years Old In Indonesian Border Regions (North Kalimantan-Malaysia). International Journal of Health and Pharmaceutical (IJHP), 2(2), 275–283. https://doi.org/10.51601/ijhp.v2i1.42

Zarkasi, R. N., Sifriyani, S., & Prangga, S. (2021). Identifikasi Faktor-Faktor Yang Mempengaruhi Indeks Pembangunan Manusia Di Kalimantan Menggunakan Regresi Panel. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 15(2), 277–282. https://doi.org/10.30598/barekengvol15iss2pp277-282

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Published

2023-07-17

Issue

Vol. 7 No. 3 (2023): July

Section

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