Bivariate Inverse Gaussian Regression on Stunting and Malnutrition in Children
Abstract View: 21,
DOI:
https://doi.org/10.32665/statkom.v5i1.6407Keywords:
BIGR, BFGS, Stunting, Malnutrition in ChildrenAbstract
Background: Research on Bivariate Inverse Gaussian Regression (BIGR) as a multivariate model is currently limited to theoretical applications. Furthermore, no studies have addressed BIGR parameter estimation using optimization methods like Broyden-Fletcher-Goldfarb-Shanno (BFGS). Meanwhile, a robust analysis is needed to identify the driving factors of child stunting and malnutrition in Central Java, given their fluctuating rates. Since stunting and malnutrition are inherently correlated, BIGR provides an appropriate joint modeling for this context.
Objective: The purpose of this study is to identify the contributing variables to stunting and malnutrition in children with BIGR.
Methods: The analysis transitions from a univariate Inverse Gaussian Regression (IGR) to a BIGR framework to effectively capture the inherent dependency between the two nutritional deficiencies. Parameter estimation was performed via Maximum Likelihood Estimation (MLE), where the non-linear log-likelihood functions were numerically optimized using the BFGS.
Results: Based on the BIGR model, the correlation coefficient between stunting and malnutrition in children was 0.48, reflecting a relatively strong correlation between the two conditions. Additionally, BIGR outperformed the independent IGR model due to its smaller AIC. The model further revealed that the number of infants with early initiation of breastfeeding is the primary driving factor for both stunting and malnutrition.
Conclusion: BIGR modeling results show that the factors causing stunting and child malnutrition in Central Java are the number of infants with early initiation of breastfeeding.
References
Ahadi, G. D., & Zain, N. N. L. E. (2023). Pemeriksaan Uji Kenormalan dengan Kolmogorov-Smirnov, Anderson-Darling dan Shapiro-Wilk. EIGEN MATHEMATICS JOURNAL, 11–19. https://doi.org/10.29303/emj.v6i1.131
Al-Hameed, K. A. A. (2022). Spearman’s correlation coefficient in statistical analysis. J. Nonlinear Anal. Appl., 13(1), 3249–3255. https://ijnaa.semnan.ac.ir/article_6079_b33de0a741ab703e8afa7a63fc2ebfb4.pdf
Auliarahmi, A., Purhadi, P., & Andari, S. (2025). Parameter estimation and hypothesis testing of bivariate poisson generalized inverse gaussian regression model. AIP Conference Proceedings, 3317, 050005. https://doi.org/10.1063/5.0263244
Awasthi, P., Das, A., Sen, R., & Suresh, A. T. (2021). On the benefits of maximum likelihood estimation for Regression andn Forecasting. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2106.10370
Bahar, M. A., Galistiani, G. F., Eliyanti, U., & Mohi, A. R. (2024). Gambaran Nilai Utilitas Kesehatan Anak dengan Malnutrisi : Studi pada Kasus Stunting, Wasting, dan Underweight di Indonesia. Jurnal Mandala Pharmacon Indonesia, 10(2), 610–617. https://doi.org/10.35311/jmpi.v10i2.656
Bouncken, R. B., Czakon, W., & Schmitt, F. (2025). Purposeful sampling and saturation in qualitative research methodologies: recommendations and review. Review of Managerial Science, 20(2), 579–615. https://doi.org/10.1007/s11846-025-00881-2
Chen, R., Zhang, C., Wang, S., & Hong, L. (2022). Bivariate-Dependent Reliability estimation model based on inverse gaussian processes and copulas fusing multisource information. Aerospace, 9(7), 392. https://doi.org/10.3390/aerospace9070392
Chhikara, R., & Folks, J. L. (2024). The Inverse Gaussian Distribution. CRC Press. https://doi.org/10.1201/9781003573746
Cui, E. H., Li, Y., & Liu, Z. (2025). Crossing the Kolmogorov-Smirnov boundary: exact tails, sharp bounds, and broken pivots. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2503.11673
Dalal, D. K. (2023). (Multi)Collinearity in behavioral Sciences research. Oxford Research Encyclopedia of Business and Management. https://doi.org/10.1093/acrefore/9780190224851.013.410
Difinubun, S., Nara, O. D. ., & Abdin, M. . (2023). Analisis Pengaruh Sumber Daya Manusia Terhadap Aspek Kinerja Pekerja Pada Proyek Pembangunan Gedung Laboratorium Terpadu Pendukung Blok Masela Universitas Pattimura. Journal Agregate, 2(1), 76–86. https://doi.org/10.31959/ja.v2i1.1252
Feng, Y., Zheng, C., Yu, L., Zhang, D., Zhang, Y., & Zhou, R. (2025). A bivariate inverse Gaussian degradation process induced by a common random effect with RUL prediction for wet clutches. Measurement, 251, 117284. https://doi.org/10.1016/j.measurement.2025.117284
Fentahun, W., Wubshet, M., & Tariku, A. (2016). Undernutrition and associated factors among children aged 6-59 months in East Belesa District, northwest Ethiopia: a community based cross-sectional study. BMC Public Health, 16(1), 506. https://doi.org/10.1186/s12889-016-3180-0
Finch, W. H. (2016). Comparison of Multivariate Means across Groups with Ordinal Dependent Variables: A Monte Carlo Simulation Study. Frontiers in Applied Mathematics and Statistics, 2. https://doi.org/10.3389/fams.2016.00002
Goward, K., Cheng, C., Cooray, K., & Dahal, K. R. (2025). A new generalized inverse Gaussian distribution with Bayesian estimators. Discover Data, 3(1). https://doi.org/10.1007/s44248-025-00066-y
Hanagal, D. D., & Pandey, A. (2018). Correlated inverse Gaussian frailty models for bivariate survival data. Communication in Statistics- Theory and Methods, 49(4), 845–863. https://doi.org/10.1080/03610926.2018.1549256
Hawkins, D. (2019). Tests of relationship: correlation. In Oxford University Press eBooks. https://doi.org/10.1093/hesc/9780198807483.003.0012
Hennink, M., & Kaiser, B. N. (2022). Sample Sizes for Saturation in Qualitative Research: a Systematic Review of Empirical Tests. Social Science & Medicine, 292(1), 1–10. https://doi.org/10.1016/j.socscimed.2021.114523
Hu, W., Fang, K., & Peng, X. (2025). Representative points of the inverse Gaussian distribution and their applications. Entropy, 27(12), 1190. https://doi.org/10.3390/e27121190
Jahan, F., Siddika, B., & Islam, M. A. (2016). AN APPLICATION OF THE GENERALIZED LINEAR MODEL FOR THE GEOMETRIC DISTRIBUTION. Journal of Statistics Advances in Theory and Applications, 16(1), 45–65. https://doi.org/10.18642/jsata_7100121695
Jo, S., Lee, M., & Lee, W. (2021). On the goodness-of-fit tests for gamma generalized linear models. Journal of the Korean Statistical Society, 50(1), 315–332. https://doi.org/10.1007/s42952-020-00095-0
Jusni, Akhfar, K., Isnaeny, & Rahmawati. (2024). Peningkatan Peran Ibu Dalam Pencegahan Stunting Pada Balita. Journal of Community Services, 6(1). https://garuda.kemdiktisaintek.go.id/documents/detail/4015490
Kementerian Kesehatan. (2018, January 26). Mengenal Stunting dan Gizi Buruk. Penyebab, Gejala, Dan Mencegah. Direktorat Promosi Kesehatan Dan Pemberdayaan Kesehatan. https://ayosehat.kemkes.go.id/mengenal-stunting-dan-gizi-buruk-penyebab-gejala-dan-mencegah
Khoiriyah, H., & Ismarwati, I. (2023). Faktor kejadian stunting pada Balita : Systematic Review. Jurnal Ilmu Kesehatan Masyarakat, 12(01), 28–40. https://doi.org/10.33221/jikm.v12i01.1844
Mishra, S. K., Panda, G., Chakraborty, S. K., Samei, M. E., & Ram, B. (2020). On q-BFGS algorithm for unconstrained optimization problems. Advances in Difference Equations, 2020(1). https://doi.org/10.1186/s13662-020-03100-2
Morita, L. H. M., Tomazella, V. L., Balakrishnan, N., Ramos, P. L., Ferreira, P. H., & Louzada, F. (2020). Inverse Gaussian process model with frailty term in reliability analysis. Quality and Reliability Engineering International, 37(2), 763–784. https://doi.org/10.1002/qre.2762
Neves, P. a. R., Vaz, J. S., Maia, F. S., Baker, P., Gatica-Domínguez, G., Piwoz, E., Rollins, N., & Victora, C. G. (2021). Rates and time trends in the consumption of breastmilk, formula, and animal milk by children younger than 2 years from 2000 to 2019: analysis of 113 countries. The Lancet Child & Adolescent Health, 5(9), 619–630. https://doi.org/10.1016/s2352-4642(21)00163-2
Nisa, E. K., & Maslihah, S. (2024). Pemodelan regresi logistik Firth Penalized Maximum Likelihood Estimation pada kepemilikan tempat usaha. AKSIOMA Jurnal Matematika Dan Pendidikan Matematika, 15(3), 326–339. https://doi.org/10.26877/aks.v15i3.21088
Nisa, E. K., & Maulina, R. (2024). The comparison of inverse gaussian and gamma regression: application on stunting data in Jepara. Jurnal Matematika Statistika Dan Komputasi, 21(1), 334–344. https://doi.org/10.20956/j.v21i1.36351
Nisa, E. K., & Miasary, S. D. (2024). Parameter estimation and application of inverse Gaussian regression. AIP Conference Proceedings, 3104, 020008. https://doi.org/10.1063/5.0194666
Nisa, E. K., & Muanalifah, A. (2021). The comparison results of Logit and Probit regression on factors of woman criminal. JTAM (Jurnal Teori dan Aplikasi Matematika), 5(2), . https://doi.org/10.31764/jtam.v5i2.4150
Nurhikmah, N., & Supandi, E. D. (2025b). Penerapan analisis konjoin dan regresi logistik pada preferensi dan keputusan konsumen mie gacoan di Yogyakarta. Jurnal Statistika Dan Komputasi, 4(2), 106–117. https://doi.org/10.32665/statkom.v4i2.5779
Portet, S. (2020). A primer on model selection using the Akaike Information Criterion. Infectious Disease Modelling, 5, 111–128. https://doi.org/10.1016/j.idm.2019.12.010
Punuh, M. I., Akili, R. H., & Tucunan, A. (2021). The relationship between early initiation of breastfeeding, exclusive breastfeeding with stunting and wasting in toddlers in Bolaang regency of east Mongondow. International Journal of Community Medicine and Public Health, 9(1), 71. https://doi.org/10.18203/2394-6040.ijcmph20214983
Putri, T. A., Salsabilla, D. A., & Saputra, R. K. (2021). The effect of low birth weight on stunting in children under five: a meta analysis. Journal of Maternal and Child Health, 6(4), 496–506. https://doi.org/10.26911/thejmch.2021.06.04.11
Qusrinie, I., Satriyandari, Y., & Wahyuhidaya, P. (2024). Hubungan berat badan lahir dan pemberian ASI eksklusif dengan kejadian stunting pada balita. Journal of Midwifery Care, 5(1), 70–77. https://doi.org/10.34305/jmc.v5i1.1403
Roustaei, N. (2024). Application and interpretation of linear-regression analysis. Medical Hypothesis Discovery & Innovation in Ophthalmology, 13(3), 151–159. https://doi.org/10.51329/mehdiophthal1506
Sari, I. P., Wiganata, S. A., Susilowati, A. D., & Damariswara, R. (2023). FAKTOR PENYEBAB KEKURANGAN GIZI PADA BALITA (KAJIAN META SINTESIS). Jurnal Ilmiah PANNMED (Pharmacist Analyst Nurse Nutrition Midwivery Environment Dentist), 18(2), 260–275. https://doi.org/10.36911/pannmed.v18i2.1611
Shrestha, N. (2020). Detecting multicollinearity in regression analysis. American Journal of Applied Mathematics and Statistics, 8(2), 39–42. https://doi.org/10.12691/ajams-8-2-1
Simanjuntak, B. Y. (2018). Early Initiation of Breastfeeding and Vitamin A supplementation with Nutritional Status of Children under Five years (6-59 Months). Kesmas National Public Health Journal, 12(3). https://doi.org/10.21109/kesmas.v12i3.1747
Surjanovic, N., Lockhart, R. A., & Loughin, T. M. (2023). A generalized Hosmer–Lemeshow goodness-of-fit test for a family of generalized linear models. Test, 33(2), 589–608. https://doi.org/10.1007/s11749-023-00912-8
Susianto, S. C., Suprobo, N. R., & Maharani. (2022). Early Breastfeeding Initiation Effect in stunting: A Systematic review. Asian Journal of Health Research, 1(1), 1–5. https://doi.org/10.55561/ajhr.v1i1.11
Suyantri, E., Handayani, B. S., Lestari, T. A., Setiawan, H., Kurniawan, R., Hidayat, X. A., …
Permatasari, D. D. (2024). Sosialisasi Pencegahan Stunting Dan Gizi Buruk Pada Masyarakat Pesisir Desa Cendi Manik, Sekotong, Lombok Barat. Jurnal Pengabdian Magister Pendidikan IPA, 7(3), 968–974. https://doi.org/10.29303/jpmpi.v7i3.9152
Tim Medis Siloam Hospitals. (2024, August 22). Ini Perbedaan dan Stunting dan Gizi Buruk yang Perlu Dipahami. Siloam Hospitals. https://www.siloamhospitals.com/informasi-siloam/artikel/perbedaan-stunting-dan-gizi-buruk
Wati, L., & Musnadi, J. (2022). Hubungan Asupan Gizi Dengan Kejadian Stunting Pada Anak Di Desa Padang Kecamatan Manggeng Kabupaten Aceh Barat Daya. Jurnal Biology Education, 10(1), 44–52. https://doi.org/10.32672/jbe.v10i1.4116
Yuan, G., Yang, Y., Li, Y., Zhao, X., & Meng, Z. (2025). Integration of adaptive projection BFGS and inertial extrapolation step for nonconvex optimization problems and its application in machine learning. Journal of the Franklin Institute, 362(7), 107652. https://doi.org/10.1016/j.jfranklin.2025.107652
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Eva Khoirun Nisa, Hadi Prasetyo, Wiwit Yuliani
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License - Share Alike that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
USER RIGHTS
All articles published Open Access will be immediately and permanently free for everyone to read and download. We are continuously working with our author communities to select the best choice of license options, currently being defined for this journal as follows:
Abstract View: 21,
PDF Download: 27
SIMILARITY INDEX Download: 0
