Simulation Study on Local Influence Diagnosis for Poisson Mixed-Effect Linear Model

TL;DR

This paper extends GLMMs to Poisson Mixed-Effect Linear Models for hierarchical count data, evaluates outlier detection methods through simulations, and enhances data visualization of influential components.

Contribution

It introduces visualization techniques for local influence analysis in Poisson mixed models, improving interpretability over previous methods.

Findings

The outlier detection method is effective in some cases but not always.

Visualization of influential components is clearer and more informative.

Simulation results highlight limitations and potential improvements in the approach.

Abstract

Given that hierarchical count data in many fields are not Normally-distributed and include random effects, this paper extends the Generalized Linear Mixed Models (GLMMs) into Poisson Mixed-Effect Linear Model (PMELM) and do numerical simulation experiments to verify the approach proposed by Rakhmawati et al. (2016) in detecting outliers. This paper produces random data based on epilepsy longitudinal data in Thall and Vail (1990), use six ways to contaminate it and try to use code mentioned in supplementary materials in previous research to detect the man-made outlier. Output shows that this method is effective sometimes but does not always work, this is probably because of the limitation of coding or some other reasons. Even though the data set and local influence method has been researched and analyzed extensively in previous papers, this paper makes contributions in data visualization. Figures in this paper show the effect of each influencial component, which are clearer than the original output in R and SAS.