Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model

Abstract

This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), each of them relying on a single shrinkage parameter. The PMTPLE uses two shrinkage parameters, which enhances its adaptability and robustness in the presence of multicollinearity between explanatory variables. To assess the performance of the PMTPLE compared to the four existing estimators (the PMLE, PRRE, PLE, and PALE), a simulation study is conducted that encompasses various scenarios and two empirical applications. The evaluation of the performance is based on the mean square error (MSE) criterion. The theoretical comparison, simulation results, and findings of the two applications consistently demonstrate the superiority of the PMTPLE over the other estimators, establishing it as a robust solution for count data analysis under multicollinearity conditions.

Validación de la Escala de Competencias Parentales Emocionales y Sociales para Padres y Madres con Adolescentes (ECOPES-A)

“…Se exploró inicialmente la base de datos para identificar casos atípicos o valores perdidos que pudieran limitar los análisis posteriores, para ser reemplazados al azar con la prueba Missing Completely at Random Test (MCAR) (Little, 1988). Se analizó la normalidad de los ítems, así como su posible multicolinealidad, eliminando aquellos con correlación ≥ 0,90 (Abdelwahab et al, 2024). Para comprobar la estructura de la escala o validez de constructo se siguió la Teoría Clásica del Test (TCT) (López-Pina y Veas, 2024) y se realizó análisis factorial exploratorio (AFE) y confirmatorio (AFC).…”