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Testing Trend for Count Data with Extra‐Poisson Variability
Author(s) -
Astuti Erni Tri,
Yanagawa Takashi
Publication year - 2002
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2002.00398.x
Subject(s) - poisson distribution , statistics , mathematics , count data , monotone polygon , poisson regression , test (biology) , likelihood ratio test , score test , medicine , paleontology , population , geometry , environmental health , biology
Summary. Trend tests for monotone trend or umbrella trend (monotone upward changing to monotone downward or vise versa) in count data are proposed when the data exhibit extra‐Poisson variability. The proposed tests, which are called the GS1 test and the GS2 test, are constructed by applying an orthonormal score vector to a generalized score test under an r th‐order log‐linear model. These tests are compared by simulation with the Cochran‐Armitage test and the quasi‐likelihood test of Piegorsch and Bailer (1997, Statastics for Enuiron, mental Biology and Toxicology). It is shown that the Cochran‐Armitage test should not be used under the existence of extra‐Poisson variability; that, for detecting monotone trend, the GS1 test is superior to the others; and that the GS2 test has high power to detect an umbrella response.