EXPLICIT MEAN PARAMETERIZATION AND BHHH-BASED ESTIMATION IN THE PGIG REGRESSION MODEL

  • Yusrianti Hanike Department of Statistics, Faculty of Education and Teacher Training, Universitas Islam Negeri A.M. Sangaji Ambon, Indonesia https://orcid.org/0000-0002-1503-3396
  • Purhadi Purhadi Department of Statistics, Faculty of Mathematics, Computing, and Data Science, Institut Teknologi Sepuluh Nopember, Indonesia https://orcid.org/0000-0002-1186-2664
  • Achmad Choiruddin Department of Statistics, Faculty of Mathematics, Computing, and Data Science, Institut Teknologi Sepuluh Nopember, Indonesia https://orcid.org/0000-0003-2568-2274
DOI: https://doi.org/10.30598/barekengvol20iss4pp2813-2824
Keywords: BHHH, Exposure, Maternal mortality, MLRT, PGIGR

Abstract

Modeling dispersed count data remains a substantial challenge in applied research, especially when traditional models struggle to capture complex dispersion structures or yield interpretable results. In this study, we introduce and evaluate the Poisson Generalized Inverse Gaussian Regression (PGIGR) model, which offers a flexible four-parameter framework with explicit mean parameterization. The model is applied to 2023 maternal mortality data from 38 cities and municipalities in East Java, Indonesia. The response variable was the number of maternal deaths, while the six predictors were the percentage of pregnant women receiving nutritional tablets, the percentage of malnourished pregnant women, contraceptive use, antenatal care coverage, healthcare professional availability, and access to proper sanitation. The results indicate that higher nutritional tablet coverage among pregnant women and greater antenatal care coverage are significantly associated with lower maternal mortality. In contrast, higher percentages of malnourished pregnant women, contraceptive users, healthcare professionals, and households with access to proper sanitation are significantly associated with higher maternal mortality. The unexpected positive associations observed for contraceptive use, healthcare professional availability, and proper sanitation may reflect differences in regional health needs, service allocation, reporting practices, or other unobserved factors and therefore require further investigation. Goodness-of-fit testing confirms the suitability of the PGIGR model for the data, and the maximum likelihood estimation procedure—supported by the BHHH optimization algorithm—yields statistically significant parameter estimates. This research underlines the applicability of the PGIGR model for modeling count data characterized by dispersion, while maintaining interpretability of the regression parameters. Such a framework can support informed decision-making in public health management and the strategic allocation of healthcare resources. The data on maternal mortality were obtained from the 2023 Health Profile of East Java Province, published by the East Java Provincial Health Office.

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Published
2026-08-24
How to Cite
[1]
Y. Hanike, P. Purhadi, and A. Choiruddin, “EXPLICIT MEAN PARAMETERIZATION AND BHHH-BASED ESTIMATION IN THE PGIG REGRESSION MODEL”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 2813-2824, Aug. 2026.
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Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
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Copyright (c) 2026 Yusrianti Hanike, Purhadi Purhadi, Achmad Choiruddin

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