Affiliation:
1. Department of Epidemiology and Biostatistics, West China School of Public Health and West China Fourth Hospital Sichuan University Chengdu China
2. Department of Chronic Disease Surveillance Sichuan Center for Disease Control and Prevention Chengdu China
3. Institute of Systems Epidemiology, West China School of Public Health and West China Fourth Hospital Sichuan University Chengdu China
Abstract
AbstractThe Poisson ridge estimator (PRE) is a commonly used parameter estimation method to address multicollinearity in Poisson regression (PR). However, PRE shrinks the parameters toward zero, contradicting the real association. In such cases, PRE tends to become an insufficient solution for multicollinearity. In this work, we proposed a new estimator called the Poisson average maximum likelihood‐centered penalized estimator (PAMLPE), which shrinks the parameters toward the weighted average of the maximum likelihood estimators. We conducted a simulation study and case study to compare PAMLPE with existing estimators in terms of mean squared error (MSE) and predictive mean squared error (PMSE). These results suggest that PAMLPE can obtain smaller MSE and PMSE (i.e., more accurate estimates) than the Poisson ridge estimator, Poisson Liu estimator, and Poisson K‐L estimator when the true s have the same sign and small variation. Therefore, we recommend using PAMLPE to address multicollinearity in PR when the signs of the true s are known to be identical in advance.
Funder
National Natural Science Foundation of China
Sichuan Province Science and Technology Support Program
Subject
Statistics, Probability and Uncertainty,Statistics and Probability