Robust Inference to Parameter Estimates in the Zero-Inflated Generalized Poisson: The Risk Factors Affecting the Fertility Rate

Abstract

Introduction: Fertility data frequently exhibit excess zeros, overdispersion, and within-cluster correlation, rendering conventional count models inadequate.

Methods: We propose a multilevel zero-inflated generalized Poisson (ZIGP) model based on the Robust Expectation– Solution (RES) algorithm. The model comprises two components: (i) a logistic component to model the probability of structural zeros and (ii) a generalized Poisson component for count responses. Random intercepts at the city and cluster levels account for the hierarchical data structure. All algorithms were implemented by the authors through original programming in R (version 4.3.1), without reliance on pre-existing packages, ensuring flexibility and transparency. Robust estimation employs Huber’s ψ-function and Mallows-type weights to mitigate sensitivity to contamination and outliers.

Results: Simulation studies across various contamination scenarios demonstrated that the robust multilevel ZIGP model yields more stable parameter estimates, with approximately 45% lower bias and 38% lower mean squared error compared to conventional estimators. Model fit criteria (AIC and BIC, unitless) confirmed the superior performance of the proposed model.

Conclusion: The robust multilevel ZIGP model provides a practical and reliable framework for analyzing clustered count data with excess zeros, particularly under contamination. The original R implementation ensures reproducibility and adaptability for biostatistical and epidemiological applications. Application to real fertility data from Sistan and Baluchestan Province, Iran, showed significant zero-inflation and overdispersion, and identified age at marriage, education, and income as factors associated with fertility.