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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Sihombing, Joshua Capri Gunawan
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Mathematics

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Generalized Poisson Spatial Autoregressive Modeling of Pneumonia Cases in Children Under Five in Tuban Sihombing, Joshua Capri Gunawan; Sutikno, Sutikno; Choiruddin, Achmad
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.37288

Abstract

The number of pneumonia cases in children under five in Tuban Regency presents two significant data challenges, namely, overdispersion and spatial dependency. This study aims to develop and apply the Generalized Poisson Spatial Autoregressive (GPSAR) model to address both issues simultaneously. The model was estimated using a MLE-BHHH procedure and validated using 10-fold cross-validation (CV). The results confirm the model's validity and superiority. The GPSAR model outperformed the non-spatial GPR model in terms of goodness-of-fit (AIC: 1301.09 vs. 1312.67) and predictive accuracy (Out-of-Sample CV-RMSE: 8.451 vs. 8.716). Statistically, the structural parameters for spatial lag and overdispersion were highly significant. Two predictor variables, exclusive breastfeeding and complete basic immunization, were also found to be statistically significant factors. This research provides a robust regression framework for spatial count data exhibiting overdispersion and offers new insights into pneumonia case determinants in the region.
Co-Authors Choiruddin, Achmad Sutikno Sutikno