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Testing modified zeros for Poisson regression models.

Authors
  • Tang, Yi1
  • Tang, Wan2
  • 1 Department of Mathematics, Tulane University, New Orleans, LA, USA.
  • 2 Department of Global Biostatistics and Data Science, School of Public Health and Tropical Medicine, Tulane University New, Orleans, LA, USA.
Type
Published Article
Journal
Statistical Methods in Medical Research
Publisher
SAGE Publications
Publication Date
Jan 01, 2019
Volume
28
Issue
10-11
Pages
3123–3141
Identifiers
DOI: 10.1177/0962280218796253
PMID: 30198417
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

Excessive zeros are common in practice and may cause overdispersion and invalidate inferences when fitting Poisson regression models. Zero-inflated Poisson regression models may be applied if there are inflated zeros; however, it is desirable to test if there are inflated zeros before such zero-inflated Poisson models are applied. Assuming a constant probability of being a structural zero in a zero-inflated Poisson regression model, the existence of the inflated zeros may be tested by testing whether the constant probability is zero. In such situations, the Wald, score, and likelihood ratio tests can be applied. Without specifying a zero-inflated Poisson model, He et al. recently developed a test by comparing the amount of observed zeros with that expected under the Poisson model. In this paper, we develop a closed form for the test and compare it with the Wald, score, and likelihood ratio tests through simulation studies. The simulation studies show that the test of He et al. is the best in controlling type I errors, while the score test generally has the least power among the tests. The tests are illustrated with two real data examples.

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