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Revisiting the analysis pipeline for overdispersed Poisson and binomial data

期刊

JOURNAL OF APPLIED STATISTICS
卷 50, 期 7, 页码 1455-1476

出版社

TAYLOR & FRANCIS LTD
DOI: 10.1080/02664763.2022.2026897

关键词

Overdispersion; score test; restricted likelihood; parametric bootstrap; graphical tools

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This study aims to clarify the relationships among various statistical methods for detecting and handling overdispersion in categorical data analysis, compare their performances, and propose a method for correcting finite sample bias. It also aims to reconsider the current practice for handling overdispersed categorical data and provide graphical tools for model selection. Furthermore, it investigates the assumptions behind the score statistics and their applicability to analyzing overdispersed data.
Overdispersion is a common feature in categorical data analysis and several methods have been developed for detecting and handling it in generalized linear models. The first aim of this study is to clarify the relationships among various score statistics for testing overdispersion and to compare their performances. In addition, we investigate a principled way to correct finite sample bias in the score statistic caused by estimating regression parameters with restricted likelihood. The second aim is to reconsider the current practice for handling overdispersed categorical data. Although the conventional models are based on substantially different mechanisms for generating overdispersion, model selection in practice has not been well studied. We perform an intensive numerical study for determining which method is more robust to various overdispersion mechanisms. In addition, we provide some graphical tools for identifying the better model. The last aim is to reconsider the key assumption for deriving the score statistics. We study the meaning of testing overdispersion when this assumption is violated, and we analytically show the conditions for which it is not appropriate to employ the current statistical practices for analyzing overdispersed data.

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