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All Journal Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Journal of Mathematics, Computation and Statistics (JMATHCOS) SAINSMAT: Jurnal Ilmiah Ilmu Pengetahuan Alam
Zakiyah Mar'ah
Universitas Negeri Makassar
Computer Science & IT Mathematics

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SAR-FEM Spatial Panel Regression for Spatio-Temporal Modeling of Stunting Cases in Indonesia Zakiyah Mar'ah; Isma Muthahharah; Sitti Masyitah Meliyana R
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 14 Issue 2 August 2026
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v14i2.38016

Abstract

Stunting remains a crucial issue in Indonesia, with a prevalence of 21.5\% in 2023. This study aims to model the number of stunting cases in toddlers in 34 provinces in Indonesia (2020--2022) using Spatial Panel Regression to address the weaknesses of traditional regression that ignore the effects of spatial and temporal dependencies.  Predictor variables analyzed include the percentage of malnutrition, underweight, poor population, access to basic health facilities, and access to drinking water services. The selection of the best model specification was carried out using the Chow test, Hausman, and the Bayesian log-marginal posterior probabilities approach. The results of the diagnostic test confirmed the existence of spatial and temporal autocorrelation in stunting cases. Based on the Bayesian analysis, the Spatial Autoregressive (SAR) Fixed Effect (FEM) model was selected as the most optimal model with a log-marginal value of -21.360, a posterior probability of 0.630, and a coefficient of determination ($R^2$) of 0.880. Impact analysis shows that the percentage of underweight children and access to health facilities have a significant direct effect on stunting in a region. However, no significant indirect spillover effect from neighboring provinces was found. Therefore, policymakers are advised to formulate stunting management strategies that focus on precisely addressing local determinants in each region.
A Systematic Simulation Study of Semiparametric Spline Estimators for Nonlinear Data Structures in R Rahmat Hidayat; Aswi Aswi; Zakiyah Mar'ah
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/Jmathcos11728

Abstract

In many real-world applications, the assumption of linearity in classical regression models is often violated, leading to model misspecification and inaccurate estimation when data exhibit complex nonlinear patterns. Although nonparametric approaches provide flexibility, they frequently suffer from poor interpretability and instability in high-dimensional settings. To address these limitations, this study examines the implementation of semiparametric spline regression as a flexible yet interpretable alternative. The model integrates a linear component for certain predictors and a spline-based nonparametric component to capture local data fluctuations. Through a simulation study using the R programming language, the performance of the spline estimator was evaluated based on the Generalized Cross Validation (GCV) criterion for optimal knot selection. The results demonstrate that the semiparametric spline model achieves superior accuracy, with a coefficient of determination (R²) reaching 97.35%, compared to 81.18% for the classical linear model. In addition, the Mean Square Error (MSE) is significantly reduced from 2.158 to 0.303. Residual diagnostic analysis confirms that the model satisfies normality and homoscedasticity assumptions. These findings highlight the effectiveness of spline-based semiparametric regression in modeling complex nonlinear data structures.
Integrating Spatial Lag and Error Components in a SARMA Model for Tuberculosis Analysis across Indonesian Provinces Zakiyah Mar'ah; Rahmat H.S.
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/Jmathcos12186

Abstract

Tuberculosis (TB) remains a critical public health challenge, necessitating an in-depth understanding of its regional determinants to formulate effective, targeted interventions. This study investigates the underlying factors driving TB cases and identifies the optimal spatial regression model for analyzing its regional distribution. Utilizing cross-sectional data from 34 observation areas during the year 2023, the prevalence of TB was evaluated against five independent variables: life expectancy (X1), access to basic sanitation (X2), availability of primary healthcare facilities (X3), smoking prevalence (X4), and treatment success rates (X5). Initial exploratory analysis revealed a significant spatial autocorrelation of TB cases across the regions (Moran’s I = 0.566, p-value = 0.0003). Consequently, spatial regression modeling was applied using Spatial Autoregressive (SAR), Spatial Error Model (SEM), and Spatial Autoregressive Moving Average (SARMA) approaches. By comparing the Akaike Information Criterion (AIC), Log-Likelihood, and R² metrics, the SARMA model emerged as the most robust fit for the dataset (R² = 0.674, AIC =283.82). The empirical results demonstrate that, at a 10% significance level, access to basic sanitation negatively impacts TB cases. Furthermore, the significance of the spatial parameters confirms that neighboring regional dynamics and geographical proximity play a crucial role in the spread of Tuberculosis.
EPIDEMIOLOGICALMAPPING OF TUBERCULOSIS IN SOUTH SULAWESI USING LOCAL INDICATORS OF SPATIAL ASSOCIATION (LISA) AND K-MEANSCLUSTERING Zakiyah Mar'ah; Hardianti Hafid; Sitti Masyita Meliyana R
Sainsmat : Jurnal Ilmiah Ilmu Pengetahuan Alam Vol. 14 No. 01 (2025): Volume 14 Nomor 1 (Maret 2025)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/acj74269

Abstract

Spatial statistics is a statistical approach that links data to the location of events. The most basic way to test whether data can be analyzed using spatial statistics is to find spatial dependence. Local spatial dependence is tested using Local Indicators of Spatial Association (LISA). This research aims to use a form of LISA, LocalMoran, to cluster and map epidemiological data, the number of tuberculosis (TB) cases in South Sulawesi. The data were provided by the Health Service of South Sulawesi Province and Statistics Indonesia of South Sulawesi Province. This research mapsTB infectious disease in South Sulawesi using Local Moran, as well as clustering area using K-Means. The distribution pattern of TB cases in South Sulawesi tended to be clustered and the areas that had significant spatial dependency were Makassar, Maros and Takalar. The positive Moran value in Makassar shows that the characteristics of TB cases in Makassar tended to be similar to its neighbor. Meanwhile, the negative Moran values in Maros and Takalar indicates that the characteristics of TB cases in both areas were not similar to their neighbors. The result of K-Means shows that the areas with the highest number of TB cases in South Sulawesi were Bone, Gowa and Makassar.
Co-Authors Aswi, Aswi Hardianti Hafid Isma Muthahharah Rahmat H.S. Rahmat Hidayat Sitti Masyita Meliyana R Sitti Masyitah Meliyana R.