Integrating Spatial Lag and Error Components in a SARMA Model for Tuberculosis Analysis across Indonesian Provinces - Zakiyah Mar'ah; Rahmat H.S. (Jurusan Matematika FMIPA UNM, 2026)
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.