Developing Two Penalized Spline Estimators for Semiparametric Poisson and Zero-inflated Poisson Models: Simulation and Application

Abstract

This article proposes two estimators for two semiparametric count regression models, namely semiparametric partially Poisson (SPPO) and semiparametric partially zero-inflated Poisson (SPZIP), via the penalized smoothing (Ps) spline and P-spline (Pb) estimations to address the common issue of nonparametric relationships between the response variable and covariates. Additionally, the SPZIP model incorporates a zero-inflation component to handle excess zeros in count data. Through extensive Monte Carlo simulations, we rigorously evaluate the performance of the proposed penalized spline estimators by comparing them against traditional parametric estimators using multiple statistical criteria, including the Akaike information criterion, Bayesian information criterion, deviance statistic, mean squared error and root mean squared error (RMSE). The results indicate that our estimators are more efficient than other estimators. Also, the SPZIP and SPPO models consistently outperform parametric (Poisson and zero-inflated Poisson) regression models, particularly in scenarios with high levels of zero inflation, demonstrating their superior ability to model complex data structures. Our findings highlight the practical utility of these models for analyzing complex count data with excess zeros and nonparametric covariate effects. A real-life data application further demonstrates the capabilities of the SPPO and SPZIP models, demonstrating their ability to provide more accurate and adaptable statistical analysis in challenging data settings.

AMS Subject Classification: 62G08, 62J20, 62J05