Comparison of Poisson Regression Model Estimation for Longitudinal Data Using the Maximum Likelihood (MLE) Method and the Generalized Equations (GEE) Method

Abstract

This study aims to estimate the Poisson regression model for longitudinal data and to compare the efficiency of two estimation methods: Maximum Likelihood Estimation (MLE) and Generalized Estimating Equations (GEE).

Longitudinal data represent a special type of statistical data collected from the same subjects over multiple time periods, leading to within-subject correlation that complicates analysis compared to cross-sectional data.
The study utilized Poisson-distributed longitudinal data, where model parameters were estimated using both methods, and their performance was compared based on accuracy measures such as the Mean Squared Error (Mean Squared Error - MSE)and the Mean Absolute Error (Mean Absolute Error - MAE).
Results indicated that the GEE method provides more stable estimates in the presence of temporal correlation, whereas the MLE method yielded higher precision when within-subject correlation was weak.
This comparison highlights the suitability of each estimation approach depending on the data structure and analytical goals, thereby enhancing the reliability of statistical modeling for longitudinal data.