Tehran University of Medical Sciences Journal of Biostatistics and Epidemiology 2383-4196 11 4 2026 10 07 394 414 Eghbal Zandkarimi Department of Epidemiology and Biostatistics, School of Medicine, Kurdistan University of Medical Sciences, Sanandaj, Iran Abbas Moghimbeigi Department of Biostatistics and Epidemiology, School of Health, Alborz University of Medical Sciences, Karaj, Iran 2025 06 24 2025 10 20 This study introduces the multilevel zero-inflated generalized Poisson (MZIGP) model for modeling zero-inflated count data with over- and under-dispersion. While maximum likelihood estimation (MLE) is typically used, it is sensitive to outliers and data contamination. Therefore, we propose robust estimation methods using Mallow’s class. In the logistic component, the design matrix is weighted to reduce leverage effects; in the generalized Poisson (GP) component, a general class of M-estimators is applied where the effects of both covariates and responses are bounded. Simulation results demonstrate that the robust expectation-solution (RES) method outperforms the EM algorithm in the presence of outliers and varying levels of zero-inflation. A real-data application using the 2015 IrMIDH fertility data set is also provided. https://jbe.tums.ac.ir/index.php/jbe/article/view/1695