Testing trend for count data with extra-Poisson variability |
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Authors: | Astuti Erni Tri Yanagawa Takashi |
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Affiliation: | Institute of Statistics, Jakarta Timur, Indonesia. |
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Abstract: | 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 rth-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, Statistics for Environmental 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. |
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Keywords: | Cochran–Armitage test Generalized score test Negative binomial distribution Orthonormal score vector Toxicology |
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