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Revisiting the analysis pipeline for overdispersed Poisson and binomial data
Woojoo Lee1, Jeonghwan Kim2, Donghwan Lee2
1Department of Public Health Science, Graduate School of Public Health, Seoul National University, Seoul, Korea of Republic.
Journal of Applied Statistics
|May 17, 2023
Summary
This study clarifies score statistics for overdispersion in generalized linear models and evaluates methods for handling overdispersed categorical data. It also examines the impact of violated assumptions on statistical practices.
Area of Science:
- Statistics
- Data Analysis
Background:
- Overdispersion is prevalent in categorical data analysis.
- Existing methods for generalized linear models have limitations.
Purpose of the Study:
- To clarify relationships and compare performances of score statistics for overdispersion.
- To investigate bias correction in score statistics.
- To evaluate and provide tools for handling overdispersed categorical data.
- To analyze the impact of violated assumptions on overdispersion testing.
Main Methods:
- Comparative analysis of score statistics.
- Numerical simulations for robustness assessment.
- Development of graphical tools for model identification.
- Analytical investigation of score statistic assumptions.
Main Results:
- Clarified relationships among score statistics and their performance.
- Identified robust methods for handling overdispersion.
- Provided graphical tools for practical application.
- Determined conditions where current practices are inappropriate.
Conclusions:
- The study offers a comprehensive evaluation of overdispersion detection and handling methods.
- It provides guidance on model selection and highlights limitations of current statistical practices under violated assumptions.
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