APPLICATION OF JACKKNIFE NEGATIVE BINOMIAL RIDGE REGRESSION IN MODELING TODDLER STUNTING IN NORTH SUMATRA

Abstract

This study aims to model stunting cases using cross-sectional count data from 33 districts/cities in North Sumatra Province in 2023. To account for differences in population size across regions, a log(Balita) offset was incorporated into the model, allowing the outcome to be interpreted in terms of stunting incidence rates rather than absolute counts. The presence of overdispersion and multicollinearity among explanatory variables creates challenges for standard count regression models and may lead to unstable parameter estimates. Therefore, the Jackknife Negative Binomial Ridge Regression (JNBR) approach was employed to improve estimation reliability under correlated predictors and overdispersed count data. This study specifically focuses on determining the optimal ridge parameter within the JNBR framework based on the Mean Squared Error (MSE) criterion. The results show that the optimal JNBR estimator with ridge parameter k = 0.0435 produced the smallest MSE value (48.8816) compared with the standard Negative Binomial Maximum Likelihood Estimator (94.1042), indicating improved estimation stability under multicollinearity conditions. The findings suggest that the JNBR approach provides a more stable and efficient estimation framework for modeling stunting incidence rates in the presence of multicollinearity and overdispersion. These results support the suitability of the proposed method for complex count data structures in public health applications.