Robust Modeling Framework for Principal Fitted Component Poisson Regression: Addressing Ill-Conditioned Features and Anomalies

Principal Component Regression (PCR) is widely used to address multicollinearity and high-dimensional data challenges in regression modeling. However, its predictive capability is limited because it constructs Principal Components (PCs) without considering the response variable. PC Poisson Regression (PCPR) extends PCR to count outcome variables. Yet, it remains sensitive to outliers and influential observations, which can distort inference about the regression coefficients. In this paper, we propose two hybrid approaches that integrate robust estimation techniques with PCR within the Poisson regression framework. These methods incorporate information from the response variable during the computation of PCs. Our approaches effectively address multicollinearity, outliers, and high-dimensional data in models involving count responses. Through extensive simulation studies, we demonstrate that the proposed techniques outperform conventional methods. Real-life data applications further highlight their effectiveness.