Application of Robust Regression with MM-Estimation to Aggregated Data on Iron Tablet Receipt and Consumption among Pregnant Women in North Sumatra Province - Putri, Octa Yulanda; Cipta, Hendra (Universitas Islam Negeri Raden Intan Lampung, 2026)
Aggregated administrative data are widely used to monitor large-scale public health programs, yet their statistical analysis is often challenged by population heterogeneity and the presence of influential observations that can undermine conventional regression inference. This study applies robust regression with MM-estimation to aggregated data on iron tablet receipt and consumption among pregnant women in North Sumatra Province. As a baseline, ordinary least squares regression is first employed to examine associations between program-related indicators and the reported number of compliant pregnant women. Diagnostic evaluations reveal substantial leverage and influential units, indicating that ordinary least squares estimates are sensitive to extreme observations and scale-driven distortions inherent in regional administrative data. To address this issue, robust regression using MM-estimation is applied due to its high breakdown point and efficiency under conditions of influential observations. The comparative analysis demonstrates notable differences in coefficient stability and inferential conclusions between the conventional and robust models, highlighting how population scale effects can mechanically dominate regression outcomes when robustness is not considered. Rather than advancing causal claims regarding program effectiveness, this study emphasizes the methodological implications of applying robustness-oriented estimation techniques to aggregated administrative data. The findings underscore the importance of robust regression as a corrective analytical strategy for improving inferential stability and reliability in applied statistical analyses of regional health data characterized by heterogeneity and influential observations.