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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

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

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

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

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.

Spatial Dependence and Co-Kriging Prediction of Stunting Prevalence Using the Linear Model of Coregionalization Zakiyah Mar'ah; Isma Muthahharah; Mahendri Deayu Putri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44312

Stunting remains a major public health challenge in Indonesia, marked by substantial regional disparities. This study analyzed the spatial dependence structure of stunting prevalence and its determinants using the Linear Model of Coregionalization (LMC) and co-kriging, which exploit spatial cross-correlation among variables rather than autocorrelation alone. Secondary data for 38 provinces in 2024 from the Indonesian Health Profile comprised stunting prevalence and nine explanatory variables, modeled jointly through empirical semivariograms and cross-semivariograms. The selected model combined a nugget effect with a spherical structure of 600 km effective range (LMC = Nug + Sph(600 km)); the nugget was non-zero for every variable and reported explicitly. Stunting prevalence showed moderate spatial dependence (SDP = 68.78%). Low birth weight showed positive cross-spatial dependence with stunting, whereas exclusive breastfeeding and pediatric health service coverage showed negative dependence. The poverty pattern was weak and mixed in the full sample but turned clearly positive once the two provinces reporting 0% prevalence were excluded. These are co-spatial patterns among provincial aggregates, not causal effects. Co-kriging revealed distinct clustering, with East Nusa Tenggara, parts of Papua, and Sulawesi showing relatively high predicted prevalence. Leave-one-out cross-validation gave a mean error of 0.264 and an RMSE of 6.423 percentage points, close to the between-province standard deviation (7.68), with prediction standard errors of 5.67.7, indicating moderate accuracy. Excluding the 0% values left the dependence class, effective range, and cross-covariance signs unchanged. Multivariate geostatistics thus offers spatial evidence for geographically targeted, ecological-level stunting interventions.

Spatial Dynamics of Digital Society Index in Indonesia: A Spatial Autoregressive Approach Zakiyah Mar'ah; Rahmat H. S.; Rahmat Hidayat
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.9217

The equitable distribution of digital transformation in Indonesia is a strategic issue, given the importance of technology in supporting national development. Indeks Masyarakat Digital Indonesia (IDSI) or Indonesian Digital Society Index (IDSI) was developed to measure the level of digital literacy, inclusion, and digital infrastructure readiness at the provincial level. However, the distribution of IDSI values shows striking spatial disparities. This research aims to identify spatial dependency patterns and significant factors influencing IDSI using a Spatial Autoregressive (SAR) model. The data used is the 2024 IDSI from 34 provinces in Indonesia, with five independent variables: access and adoption of digital technology, learning ecosystem, ICT introduction, empowerment, and employment. A spatial autocorrelation test using Moran's I revealed a significant positive spatial dependency, indicating a clustered pattern in IDSI distribution. The Lagrange Multiplier test showed spatial dependency in the lag or response variable, making the SAR model suitable. Estimation results demonstrate that all five independent variables significantly impact IDSI, with a coefficient of determination (R²) of 0.98. These findings indicate that geographically proximate regions tend to have similar IDSI values. Therefore, spatial approaches like SAR are crucial for formulating national digital equity policies.

A Semiparametric Geographically Weighted Regression Approach to Modeling Human Development Index Disparity in South Sulawesi Zakiyah Mar'ah; Ruliana Ruliana; Sudarmin Sudarmin
Journal of Mathematics, Computations and Statistics Vol. 9 No. 3 (2026): Volume 09 Issue 03 (September 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/4xdvbz17

Human Development Index (HDI) values in the 24 regencies and cities of South Sulawesi ranged from 69.45 to 85.23 in 2024. This study asks which indicators account for that gap and whether their associations with HDI vary by location, using Semiparametric Geographically Weighted Regression (SGWR), which keeps some coefficients fixed province-wide and lets others vary locally. Nine predictors from BPS-Statistics of South Sulawesi Province were used, including three HDI dimension indicators (life expectancy, expected years of schooling and per-capita expenditure), whose coefficients are read as the weight of each dimension in the observed disparity. Distances were great-circle distances between regency capitals. Each coefficient was classified as local or global with a Monte Carlo test of spatial variability, bandwidths were chosen by AICc, and local t-tests used the da Silva–Fotheringham adjusted level. Only the intercept and the construction cost index varied significantly (p = 0.013 and 0.003), with the same result for polygon centroids. The resulting SGWR fitted slightly better than OLS (AICc 18.34 against 20.03, a difference below 2), a fully local GWR overfitted (AICc 40.13), and no local coefficient was significant. Expenditure per capita, expected years of schooling and life expectancy were the significant province-wide associations. HDI disparity across South Sulawesi's regencies is therefore driven mainly by the expenditure and education dimensions, in much the same way across the province.

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