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Biometrika 1990 77(2):255-264; doi:10.1093/biomet/77.2.255
© 1990 by Biometrika Trust
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A Markov chain model of extrabinomial variation

STEPHAN M. RUDOLFER

Statistical Laboratory, Department of Mathematics, The University Manchester, M13 9PL, U.K.

This paper studies the properties of a {0, 1}-state Markov chain model of extrabinomial variation. If n is even, the Markov chain binomial model is always overdispersed relative to the binomial model with parameters n and p, while if n is odd, it may be over- or underdispersed relative to the binomial model. Expressions for the likelihood and variance functions are obtained, and for n=3, the Markov chain binomial model is compared with the additive and multiplicative binomial models of Altham (1978), as well as to the beta-binomial model.

Key Words: Beta-binomial model • Binary data • Correlated binary variables • Extrabinomial variation • Generalized binomial • Markov chain • Overdispersion


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