Developing a Semi-parametric Zero-Inflated Beta Regression Model Using P-splines: Simulation and Application

Abstract

Analyzing proportional data with excessive zeros and complex relationships presents a significant challenge in various fields. To address this, we propose a developing semiparametric zero-inflated Beta Regression (SPZIBE) regression model using both penalized smoothing (Ps) spline and P-spline (Pb) estimators, referred to as SPZIBE-Ps and SPZIBE-Pb, respectively. This model offers a unique combination of flexibility and interpretability, allowing for the modeling of nonparametric relationships and the identification of factors contributing to zero-inflation. Extensive simulations demonstrate the SPZIBE-Pb model's superior model fit and predictive accuracy compared to existing parametric regression models and semiparametric advanced regression models such as SPZIBE-Ps. The SPZIBE-Pb regression model achieves competitive results on metrics such as the akaike information criterion (AIC), bayesian information criterion (BIC), deviance statistic (DVS) and root mean squared error (RMSE), as confirmed by Monte Carlo simulation studies and real-world applications. The SPZIBE-Pb regression model has broad applications in various fields, including political science, economics, and social sciences. To demonstrate its utility, we applied it to the varieties of democracy (V-Dem) dataset. In conclusion, the SPZIBE-Pb regression model offers a robust and versatile tool for analyzing proportional data with excessive zeros and complex relationships. Its ability to capture both parametric and nonparametric effects, coupled with its interpretability, makes it a valuable asset for researchers across various domains.